Arrangement and method for measuring the direct sound radiated by acoustical sources

Abstract

The invention provides an arrangement and a method for measuring the direct sound w.sub.rad radiated by an acoustical source under test (e.g. loudspeakers) under the influence of acoustic ambient noise sources Q.sub.1 and reflections at acoustical boundaries (e.g. room walls). An acquisition device measures a state variable p.sub.t(r.sub.m) of the sound field at a plurality of measurement points r.sub.m in a scanning range G.sub.m by a sensor and generates a scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1. Based on this data set an analyzer determines the coefficients C.sub.rad.sup.Q.sup.0 associated with expansion functions which are solutions of the wave equation. An identifier uses the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 for generating parameter information P for the analyzer which are the basis for separating the direct sound w.sub.rad from room reflections w.sub.ref and other waves w.sub.sec scattered at the surface of the source under test. An extrapolator predicts the state variable p.sub.rad.sup.Q.sup.0 of the direct sound w.sub.rad at any point outside the scanning range G.sub.m by using the coefficients C.sub.rad.sup.Q.sup.0 of the wave expansion.

Claims

1. An arrangement for determining direct sound radiated by a sound source under test comprising: an acquisition device, generating a scanned data set by measuring a state variable of a sound field surrounding the sound source under test at a plurality of measurement points wherein the measurement points are arranged in a scanning range and the scanned data set describes the superposition of the direct sound with at least one of the following other sound components: an incoming sound generated by the direct sound reflected on an external boundary, a secondary sound generated by interaction of said incoming sound with the surface of the sound source under test; an identifier, based on the scanned data set generating parameter information, which comprise filtered wave coefficients associated with the expansion of the scanned data set in the scanning range by considering the time delay of the sound components in the scanned data set, wherein the early arriving direct sound is preserved and the later arriving sound components are attenuated; an analyzer, based on the scanned data set generating direct wave coefficients associated with the expansion of the direct sound, said analyzer contains the following elements: a field separation module, based on the scanned data set generating separated direct wave coefficients, which represents the direct sound for frequencies below a defined cut-off frequency; an evaluator, based on assessment information provided by the field separation module or the identifier generating a crossover frequency corresponding to said cut-off frequency; a crossover, which assigns the separated direct wave coefficients to the direct wave coefficients for signal frequencies below said crossover frequency and assigns the filtered wave coefficients to the direct wave coefficients for signal frequencies which are higher or equal to said crossover frequency; and an extrapolator, based on direct wave coefficients generating a predicted state variable describing the radiated direct sound at a defined observation point outside the inner boundary of the scanning range.

2. The arrangement according to claim 1, wherein: said parameter information describes a transfer function between the incoming sound and the secondary sound; said identifier contains: a filter, based on said scanned data set generating a filtered scanned data set, wherein a reverberant sound part in the scanned data set is preserved and a direct sound part in the scanned data set is attenuated; an IO-field separation module, based on the filtered scanned data set generating late incoming wave coefficients associated with the expansion of the reverberant part of the incoming sound and generating late outgoing wave coefficients associated with the expansion of the late parts of the secondary sound when the direct sound is decayed; and said analyzer contains: an IO-field separation module, based on scanned data set generating total incoming wave coefficients associated with the expansion of the total incoming sound, and generating total outgoing wave coefficients associated with the expansion of total outgoing sound comprising the secondary sound and direct sound; and a PS-field separation module, based on the total incoming wave coefficients and the total outgoing wave coefficients and the late incoming wave coefficients and the late outgoing wave coefficients generating primary wave coefficients associated with the expansion of the direct sound radiated from the sound source under test.

3. The arrangement according to claim 2, wherein said PS-field separation module comprises: a comparator, based on both the late incoming wave coefficients and the late outgoing wave coefficients generating a transparency parameter, which describes the acoustical transparency of the space enclosed by the scanning range; a synthesizer, based on the total incoming wave coefficients and the transparency parameter generating secondary wave coefficients associated with the expansion of the secondary sound radiated from the sound source under test; and a combiner, based on total outgoing wave coefficients and the secondary wave coefficients generating said direct wave coefficients.

4. The arrangement according to claim 2, wherein said PS-field separation module comprises: a correlator, based on both the total incoming wave coefficients and the late incoming wave coefficients generating a transmission parameter, which describes the concurrence of the directivity of the total incoming sound and the directivity of the reverberant part of the incoming sound; a synthesizer, based on both the total incoming wave coefficients and the transmission parameter generating secondary wave coefficients associated with the expansion of the secondary sound radiated from the sound source under test; and a combiner, based on total outgoing wave coefficients and the secondary wave coefficients generating said direct wave coefficients.

5. The arrangement according to claim 1, wherein said identifier contains: a filter, based on the scanned data set generating a filtered scanned data set, wherein said filter attenuates signal components having a time delay larger than a predefined value; and a free-field expander, based on the filtered scanned data set generating said filtered wave coefficients and generating said assessment information; wherein said assessment information describes the amplitude of the incoming sound.

6. The arrangement according to claim 1, wherein: said analyzer receives field information describing the properties of the sound field generated by the source under test; said identifier, based on the direct wave coefficients or scanned data set generating said field information comprising at least one of: an expansion point associated with the position of the acoustical center of the source under test, orientation information associated with the main radiation direction of the source under test, rotational symmetry information of the sound field generated by the source under test, and reflection symmetry information of the sound field generated by the source under test.

7. The arrangement according to claim 6, wherein said acquisition device contains one of: at least one a scanning sensor, each measuring the state variable of the sound field at the current position of the scanning sensor; a scanning generator, based on the field information generating a scanning vector, wherein the scanning vector comprising the position of at least one additional measurement point which gives unique information about the direct sound generated by the source under test; and a positioning device, which moves the scanning sensor to the additional measurement point defined by the scanning vector.

8. The arrangement according to 6, wherein said analyzer contains at least one of: a generator, based on the field information generating an expansion matrix; wherein the expansion matrix uses a coordinate system which is aligned with position and orientation of the source under test or the symmetry of the sound field; and an estimator based on the scanned data set generating said direct wave coefficients by using said expansion matrix comprising expansion functions associated with solution of the wave equation.

9. The arrangement according to claim 1, wherein: said acquisition device, measuring a state variable of a sound field surrounding said source under test at a plurality of measurement points separated in two non-overlapping scanning ranges; the first scanning range generating a first scanned data set has a higher density of measurement points than the second scanning range generating the second scanned data set; and said analyzer, based on the first scanned data set and on the second scanned data set generating direct wave coefficients associated with the expansion of the direct sound.

10. The arrangement according to claim 9, wherein said analyzer comprises: a first sub-analyzer, based on second scanned data set generating second wave coefficients, wherein the number of measurement points in the second scanning range limits the maximal order of the second wave coefficients; an interpolator, based on the second wave coefficients generating an interpolated scanned data set, comprising a number of elements, which is higher than the number of measurement points in the second scanning range; a combiner, based on both the first scanned data set and the interpolated scanned data set generating a unified data set; a second sub-analyzer, based on the unified data set generating said direct wave coefficients, which provides at least one wave coefficient at a maximal order which is higher than the maximal order of the second wave coefficients.

11. An arrangement according to claim 1, wherein: said direct wave coefficients contain at least one coefficient having a maximal order, wherein at least one coefficient in said direct wave coefficients is approximated by zero, wherein said coefficient has an order which is smaller than said maximal order, or the number of measurement points in the scanned data set is smaller than the maximal number of coefficients in said direct wave coefficients.

12. The arrangement according to claim 11, wherein said analyzer comprises at least one of: an estimator, based on the scanned data set generating reduced wave coefficients by using a reduced expansion matrix; an inverse transformer, based on the reduced wave coefficients generating iterative wave coefficients by using a predefined selection matrix, wherein the number of elements in said iterative wave coefficients is larger than the number of elements in said reduced wave coefficients; an evaluator, based on iterative wave coefficients generating a contribution vector, which describes the contribution of an element of the iterative wave coefficients to the total sound power radiated by source under test; a selector, based on the contribution vector generating said predefined selection matrix and generating a maximal order of the expansion function; wherein at least one element is set to zero, if its contribution is below a critical threshold; a generator, generating a complete expansion matrix by using at least one of: maximal order of the expansion function, number and position of the measurement points in said scanning range, an expansion point representing the position of the acoustical center of the source under test, orientation information representing main direction of radiation of the source under test, rotational symmetry of the sound field generated by the source under test, and reflection symmetry of the sound field generated by the source under test; a transformer, based on the complete expansion matrix generating an updated value of said reduced expansion matrix, wherein the number of elements in the reduced expansion matrix is smaller than the number of elements in the complete expansion matrix; and a controller, based on iterative wave coefficients generating said direct wave coefficients, if the change of the iterative wave coefficients between two iterative steps of the iteration is below a predefined threshold.

13. An arrangement according to claim 1, wherein: said acquisition device contains: at least one scanning sensor, generating a scanning output representing the measured state variable of the sound field at a current position of the scanning sensor; a positioning device, which moves the scanning sensor to at least one measurement point located in a scanning range; an ambient noise sensor, generating an ambient noise output representing a state variable of the sound field at an ambient position outside the scanning range, wherein the distance between ambient noise sensor and the sound source under test is larger than the distance between the scanning sensor and the sound source under test; and said arrangement contains a noise identifier, based on the scanning output and the ambient noise output generating valid scanned data set, wherein said noise identifier detects an invalid part in the scanning output corrupted by said ambient noise source by analyzing the ambient noise output and excludes the detected invalid part from the scanned data set.

14. The arrangement according to claim 13, wherein: said noise identifier repeats the measurement of the state variable of the sound field at the measurement point if the scanning output contains invalid parts corrupted by said ambient noise source, or said noise identifier contains a storage device, which stores the valid parts of the scanning output of multiple measurements and generates a merged output assigned to the scanned data set containing valid and complete information at the measurement point.

15. The arrangement according to claim 1, wherein: said analyzer, based on the scanned data set generating direct wave coefficients associated with the expansion of the direct sound or generating sound error coefficients representing the error in the expansion of the scanned data set; and said extrapolator, based on the sound error coefficients generating information describing the error of the predicted quantity at the observation point.

16. A method for determining direct sound radiated by a sound source under test comprising: measuring a state variable of a sound field surrounding the sound source under test, wherein said state variable describes the superposition of the direct sound with at least one of the following other sound components: an incoming sound generated by an ambient noise source or by the direct sound reflected on an external boundary, and a secondary sound generated by an interaction of said incoming sound with the surface of the sound source under test; generating a scanned data set by collecting the state variable at a plurality of measurement points arranged in a scanning range; a filtered scanned data set by filtering the scanned data set, wherein said filtering preserves the direct sound and attenuates the other sound components which have a larger time delay than the direct sound; identifying parameter information based on the scanned data set wherein said parameter information comprises filtered wave coefficients associated with an expansion of the filtered scanned data set by using expansion function which are solutions of the wave equation, wherein the filtered wave coefficients is a valid representation of the direct sound for signal frequencies above a defined cut-off frequency; performing an expansion of the scanned data set for signal frequencies below the cut-off frequency by using separate expansion functions representing incoming sound and outgoing sound; generating separated direct wave coefficients associated with the expansion of the outgoing sound, wherein the separated direct wave coefficients is a valid representation of the direct sound for signal frequencies below said cut-off frequency; generating a crossover frequency corresponding to said cut-off frequency based on assessment and parameter information; generating direct wave coefficients associated with the expansion of the direct sound by: assigning the separated direct wave coefficients to the direct wave coefficients for signal frequencies below said crossover frequency, assigning the filtered wave coefficients to the direct wave coefficients for signal frequencies which are higher or equal to said crossover frequency, and and based on direct wave coefficients generating a predicted state variable describing the radiated direct sound field at a defined observation point outside the inner boundary of the scanning range.

17. The method according to claim 16, wherein the parameter information contains a transfer function between an incoming sound and a secondary sound; wherein identifying parameter information contains at least one of: generating a filtered scanned data set by filtering said scanned data set, wherein the reverberant sound part is preserved and the direct sound part is attenuated; generating late incoming wave coefficients based on the filtered scanned data set, wherein said late incoming wave coefficients represent the reverberant part of the incoming sound; generating late outgoing wave coefficients based on the filtered scanned data set, wherein the late outgoing wave coefficients represent the late parts of the secondary sound when the direct sound is decayed; generating total incoming wave coefficients based on scanned data set, wherein said total incoming wave coefficients represent the total incoming sound; generating total outgoing wave coefficients based on scanned data set, wherein said total outgoing wave coefficients represent the total outgoing sound comprising the secondary sound and direct sound; and generating primary wave coefficients based on the total incoming wave coefficients and the total outgoing wave coefficients and the late incoming wave coefficients and the late outgoing wave coefficients; wherein said primary wave coefficients represents the direct sound radiated from the sound source under test.

18. The method according to claim 17, wherein identifying parameter information further contains at least one of: generating a transparency parameter based on both the late incoming wave coefficients and the late outgoing wave coefficients, wherein the transparency parameter describes the acoustical transparency of the space enclosed by the scanning range; generating secondary wave coefficients based on the total incoming wave coefficients and the transparency parameter, wherein the secondary wave coefficients represents the secondary sound radiated from the sound source under test; and generating said direct wave coefficients based on the total outgoing wave coefficients and the secondary wave coefficients.

19. The method according to claim 17, wherein identifying parameter information further contains at least one of: generating a transmission parameter by correlating the total incoming wave coefficients and the late incoming wave coefficients, wherein the transmission parameter describes the concurrence of the directivity of the total incoming sound and the directivity of the reverberant part of the incoming sound; synthesizing secondary wave coefficients based on both the total incoming wave coefficients and the transmission parameter, wherein the secondary wave coefficients represent the secondary sound radiated from the sound source under test; and generating said direct wave coefficients based on the total outgoing wave coefficients and the secondary wave coefficients.

20. The method according to claim 16, wherein generating a crossover frequency comprises: generating a first error by assessing the mismatch between the scanned data set and an expanded data set based on said separated direct wave coefficients associated with said expansion functions; performing an expansion of the filtered scanned data set by using separate expansion functions for incoming filtered sound and outgoing filtered sound; generating a second error of the filtered wave coefficients by comparing the energy of the incoming filtered sound and the outgoing filtered sound; summarizing the first error and the second error to a total error; generating an optimal value of said cut-off frequency, which gives a minimum total error; and adjusting the crossover frequency to the cut-off frequency.

21. A method according to claim 16, further comprising: generating direct wave coefficients by using field information describing the properties of the sound field generated by the source under test, wherein direct wave coefficients are associated with the expansion of the direct sound; and based on the direct wave coefficients or the scanned data set generating said field information comprising at least one of: an expansion point associated with the position of the acoustical center of the source under test, orientation information associated with the main radiation direction of the source under test, rotational symmetry information of the sound field generated by the source under test, and reflection symmetry information of the sound field generated by the source under test.

22. The method according to claim 21, wherein said generating the scanned data set comprises at least one of: measuring the state variable of the sound field at the current position of the scanning sensor; generating a scanning vector based on the field information; wherein the scanning vector comprises the position of an additional measurement point which gives unique information about direct sound generated by the source under test; moving the scanning sensor to the additional measurement point defined by the scanning vector; and measuring a state variable of the sound field at the additional measurement point.

23. The method according to claim 21, wherein generating direct wave coefficients comprises based on the field information generating an expansion matrix; wherein the expansion matrix contains a minimum of elements by using a coordinate system in the expansion which is aligned with the position and the orientation of the source under test or the symmetry of the sound field; and based on the scanned data set generating said direct wave coefficients by using said expansion matrix.

24. The method according to claim 16, wherein measuring a state variable of the sound field surrounding said source under test at a plurality of measurement points separated in two non-overlapping scanning ranges; wherein a first scanning range has a higher density of measurement points than a second scanning range; and further comprising: generating a first scanned data set which represents the first scanning range; generating a second scanned data set which represents the second scanning range; and based on the first scanned data set and on the second scanned data set generating direct wave coefficients associated with the expansion of the direct sound.

25. The method according to claim 24, wherein generating direct wave coefficients comprises: based on the second scanned data set generating second wave coefficients, wherein the number of measurement points in the second scanning range limits the maximal order of the coefficients in the second wave coefficients; based on the second wave coefficients generating an interpolated scanned data set; wherein the interpolated scanned data set comprises a number of elements, which is higher than number of measurement points in the second scanning range; based on both the first scanned data set and the interpolated scanned data set generating a unified data set; and based on the unified data set generating said direct wave coefficients; wherein the direct wave coefficients contain at least one coefficient having a maximal order which is higher than the maximal order in the second wave coefficients.

26. The method according to claim 16, wherein: said direct wave coefficients have a maximal order; at least one coefficient in said direct wave coefficients is approximated by zero; said coefficient has an order which is smaller than said maximal order; or the number of measurement points in the scanned data set is smaller than the maximal number of coefficients in said direct wave coefficients.

27. The method according to claim 26, wherein said generating direct wave coefficients comprises at least one of: based on the scanned data set generating reduced wave coefficients by using a reduced expansion matrix; based on the reduced wave coefficients generating iterative wave coefficients by using a predefined selection matrix, wherein the number of elements in said iterative wave coefficients is larger than the number of elements in said reduced wave coefficients; based on iterative wave coefficients generating a contribution vector, which describes the contribution of a coefficient to the total sound power radiated by source under test; based on the contribution vector generating said selection matrix; wherein selection matrix set the coefficients to zero, if its contribution is below a critical threshold; based on the contribution vector generating a maximal order of the coefficients associated with the expansion; generating a complete expansion matrix by using at least one of: maximal order of the expansion, number and position of the measurement points in said scanning range, an expansion point representing the position of the acoustical center of the source under test, orientation information representing main direction of radiation of the source under test, rotational symmetry information of the sound field generated by the source under test, and reflection symmetry information of the sound field generated by the source under test; based on the complete expansion matrix generating an updated value of said reduced expansion matrix, wherein the number of elements in the reduced expansion matrix is smaller than the number of elements in the complete expansion matrix; based on iterative wave coefficients generating said direct wave coefficients, if the difference between the values of iterative wave coefficients at two iterative steps of the iteration is below a pre-defined threshold; and based on direct wave coefficients generating a predicted state variable describing the radiated direct sound field at a defined observation point outside the inner boundary of the scanning range.

28. The method according to claim 16, wherein generating a scanned data set comprises: moving a scanning sensor to at least one measurement point located in a scanning range; generating a scanning output representing the measured state variable of the sound field at the current position of a scanning sensor; generating an ambient noise output representing a state variable of the sound field at an ambient position outside the scanning range, wherein the distance between ambient noise sensor and the sound source under test is larger than the distance between the scanning sensor and the sound source under test; analyzing the ambient noise output and the scanning output; separating an invalid part of in the scanning output corrupted by said ambient noise source from valid parts; and collecting the valid parts of the scanning output in a scanned data set.

29. The method according to claim 28, wherein said collecting the scanning output comprises: repeating the measurement of the state variable of the sound field at the measurement point if the scanning output contains at least one invalid part corrupted by said ambient noise source; storing the valid parts of the scanning output; generating a merged output by merging the valid parts of multiple measurements; and assigning the merged output to the scanned data set, if the merged output contains valid and complete information at the measurement point.

30. The method according to claim 16, further comprising: generating sound error coefficients representing the error in the expansion of the scanned data set; based on direct wave coefficients generating a predicted state variable describing the radiated direct sound field at a defined observation point outside the inner boundary of the scanning range; and based on the sound error coefficients generating information describing the error of the predicted quantity at the observation point.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further details, aspects and embodiments of the invention will be described, by way of example only, with reference to the drawings. Elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale.

(2) FIG. 1 schematically shows a holographic measurement of the direct sound using a IOFS-method.

(3) FIG. 2 shows a PSFS-method based on acoustical impedance of the surface to separate the scattered wave.

(4) FIG. 3 shows a PSFS-method based on a perturbation by an external source Q.sub.2.

(5) FIG. 4 schematically shows a holographic measurement based on a modified PSFS-method.

(6) FIG. 5 shows an embodiment of the identifier generating the transfer parameter P based on the reverberant sound.

(7) FIG. 6 shows an embodiment of the analyzer using the IOFS-method and the modified PSFS-method.

(8) FIG. 7 shows an embodiment of the measurement system determining the optimal expansion point.

(9) FIG. 8 shows an embodiment of the measurement system using two scanning ranges G.sub.1 and G.sub.2 with density of the measurement points.

(10) FIG. 9 shows an embodiment of the analyzer using selected expansion functions.

(11) In all figures of the drawings elements, features and signals which are the same or at least have the same functionality have been provided with the same reference symbols, unless explicitly stated otherwise.

DETAILED DESCRIPTION OF EMBODIMENTS

(12) FIG. 1 shows an IOFS-method for measuring the direct sound p.sub.rad.sup.Q.sup.0(r) at an observation point r radiated by the source Q.sub.0 under test 2 excited by an excitation signal u(t) generated by the generator 8. An acquisition device 4 uses a sensor 1 to measure the sound pressure p.sub.t(r.sub.m) or another acoustical state variable on two spherical scanning surfaces S.sub.1 and S.sub.2 close to the source under test 2 and collects the sound pressure signals in two scanned data sets p.sub.S.sub.1.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 and p.sub.S.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 by using the storage devices 7 and 9, respectively.

(13) Reverberant sound w.sub.ref generated by room reflections of the direct sound w.sub.rad at boundary S.sub.B and noise w.sub.noise generated by an external source Q.sub.1 passes the scanning surfaces in an incoming wave w.sub.in and generates a secondary sound w.sub.sec by reflection, diffraction and scattering at the surface S.sub.0 of the device under test 2. The superposition of the secondary sound w.sub.sec and the direct sound w.sub.rad gives the outgoing wave w.sub.out at both scanning surfaces.

(14) The total sound pressure at point r in the sound field at frequency

(15) $\begin{array}{cc}\begin{array}{c}{p}_t\left(r,\right)=p_t\left(r,,,\right)\\ =p_{\mathrm{out}}^{Q_0,Q_1}\left(r,,,\right)+p_{\mathrm{in}}^{Q_0,Q_1}\left(r,,,\right)\\ \underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m,\mathrm{out}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)+\\ \underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{in}}\left(\right)h_n^{\left(2\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\\ =\underset{j=1}{\overset{J}{.Math.}}{C}_{j,\mathrm{out}}^{Q_0,Q_1}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)+\\ \underset{j=1}{\overset{J}{.Math.}}{C}_{j,\mathrm{in}}^{Q_0,Q_1}\left(\right){}_{j,\mathrm{in}}\left(r,,,\right)\end{array}& \left(23\right)\end{array}$
is expanded into sound pressure components p.sub.out.sup.Q.sup.0.sup.,Q.sup.1 and p.sub.in.sup.Q.sup.0.sup.,Q.sup.1, corresponding to outgoing wave w.sub.out and incoming wave w.sub.in, respectively. Both components are expanded in a series comprising expansion function .sub.j,out and .sub.j,in weighted by coefficients C.sub.j,out and C.sub.j,in.

(16) The solutions of the wave equation in Cartesian, cylindrical or spherical coordinates are perfect candidates for expansion functions. For example, the expansion function describes the angular dependency by spherical harmonics Y.sub.n.sup.m(,) and the radial dependency from the expansion point by the Hankel function of the first and second kind, h.sub.n.sup.(1)(kr) and h.sub.n.sup.(2)(kr) in spherical coordinates. The expansion point r.sub.0 is in the origin of the coordinate system.

(17) The sound pressure of the outgoing wave w.sub.out

(18) $\begin{array}{cc}\begin{array}{c}{p}_{\mathrm{out}}^{Q_0,Q_1}\left(r,\right)=p_{\mathrm{out}}^{Q_0,Q_1}\left(r,,,\right)\\ =p_{\mathrm{rad}}^{Q_0}\left(r,,,\right)+p_{\sec }^{Q_0,Q_1}\left(r,,,\right)\\ =\underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m,\mathrm{rad}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)+\\ \underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\sec }\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\\ =\underset{j=1}{\overset{J}{.Math.}}{C}_{j,\mathrm{rad}}^{Q_0}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)+\\ \underset{j=1}{\overset{J}{.Math.}}{C}_{j,\sec }^{Q_0,Q_1}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)\end{array}& \left(24\right)\end{array}$
comprises a sound pressure p.sub.rad.sup.Q.sup.0 of the direct sound wave and a sound pressure p.sub.sec.sup.Q.sup.0.sup.,Q.sup.1 of the secondary wave w.sub.sec.

(19) An alternative expansion describes the total sound pressure

(20) $\begin{array}{cc}\begin{array}{c}{p}_t\left(r,\right)=p_t\left(r,,,\right)\\ =p_{\mathrm{sw}}^{Q_0,Q_1}\left(r,,,\right)+p_{\mathrm{ex}}^{Q_0,Q_1}\left(r,,,\right)\\ =\underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m,\mathrm{sw}}\left(\right)\left(h_n^{\left(1\right)}\left(\mathrm{kr}\right)+h_n^{\left(2\right)}\left(\mathrm{kr}\right)\right)Y_n^m\left(,\right)+\\ \underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{ex}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\\ \underset{n=0}{\overset{N_1}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m,\mathrm{sw}}\left(\right)2j_n\left(\mathrm{kr}\right)Y_n^m\left(,\right)+\\ \underset{n=0}{\overset{N_2}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{ex}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\\ =\underset{j=1}{\overset{J_1}{.Math.}}{C}_{j,\mathrm{sw}}^{Q_0,Q_1}\left(\right){}_{j,\mathrm{sw}}\left(r,,,\right)+\\ \underset{j=1}{\overset{J_2}{.Math.}}{C}_{j,\mathrm{ex}}^{Q_0,Q_1}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)\end{array}& \left(25\right)\end{array}$
as a superposition of the standing wave w.sub.sw represented by coefficients C.sub.j,sw.sup.Q.sup.0.sup., Q.sup.1 and excess wave w.sub.ex represented by coefficients C.sub.j,ex.sup.Q.sup.0.sup.,Q.sup.1.
The excess sound pressure

(21) 0$\begin{array}{cc}\begin{array}{c}{p}_{\mathrm{ex}}^{Q_0,Q_1}\left(r,\right)=p_{\mathrm{ex}}^{Q_0,Q_1}\left(r,,,\right)\\ =p_{\mathrm{rad}}^{Q_0}\left(r,,,\right)+p_{\mathrm{scat}}^{Q_0,Q_1}\left(r,,,\right)\\ =\underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{rad}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)+\\ \underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{scat}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\\ =\underset{j=1}{\overset{J}{.Math.}}{C}_{j,\mathrm{rad}}^{Q_0}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)+\\ \underset{j=1}{\overset{J}{.Math.}}{C}_{j,\mathrm{scat}}^{Q_0,Q_1}\left(\right){}_{j,\mathrm{out}}\left(r,,,\right)\end{array}& \left(26\right)\end{array}$
comprises the direct sound w.sub.rad radiated by the source under test Q.sub.0 and the sound w.sub.scat scattered and reflected on the surface S.sub.0.

(22) The total pressure p.sub.S,t.sup.Q.sup.0.sup.,Q.sup.1 at the measurement points r.sub.m with m=1, . . . , M, on the scanning surface S{S.sub.1, S.sub.2, . . . } can be summarized to a scanned data set

(23) $\begin{array}{cc}\begin{array}{c}{p}_{S,t}^{Q_0,Q_1}=p_{S,\mathrm{in}}^{Q_{0,}{Q}_1}+p_{S,\mathrm{out}}^{Q_{0,}{Q}_1}\\ ={}_{S,\mathrm{in}}{C}_{\mathrm{in}}^{Q_0,Q_1}+{}_{S,\mathrm{out}}{C}_{\mathrm{out}}^{Q_0,Q_1}\\ =p_{S,\mathrm{in}}^{Q_0,Q_1}+p_{S,\mathrm{rad}}^{Q_0}+p_{S,\sec }^{Q_0,Q_1}\\ ={}_{S,\mathrm{in}}{C}_{\mathrm{in}}^{Q_0,Q_1}+{}_{S,\mathrm{out}}\left(C_{\mathrm{rad}}^{Q_0}+C_{\sec }^{Q_0,Q_1}\right)\\ =p_{S,\mathrm{sw}}^{Q_0,Q_1}+p_{S,\mathrm{ex}}^{Q_0,Q_1}\\ =\left({}_{S,\mathrm{out}}+{}_{S,\mathrm{in}}\right)C_{\mathrm{sw}}^{Q_o,Q_1}+{}_{S,\mathrm{out}}{C}_{\mathrm{ex}}^{Q_0,Q_1}\\ =p_{S,\mathrm{sw}}^{Q_0,Q_1}+p_{S,\mathrm{ex}}^{Q_0,Q_1}\\ ={}_{S,\mathrm{sw}}{C}_{\mathrm{sw}}^{Q_0,Q_1}+{}_{S,\mathrm{out}}{C}_{\mathrm{ex}}^{Q_0,Q_1}\\ =p_{S,\mathrm{sw}}^{Q_0,Q_1}+p_{S,\mathrm{rad}}^{Q_0}+p_{S,\mathrm{scat}}^{Q_0,Q_1}\\ ={}_{S,\mathrm{sw}}{C}_{\mathrm{sw}}^{Q_0,Q_1}+{}_{S,\mathrm{out}}\left(C_{\mathrm{rad}}^{Q_0}+C_{\mathrm{scat}}^{Q_0,Q_1}\right)\end{array}& \left(27\right)\end{array}$
where the expansion uses the sound pressure vector
p.sub.S,d.sup.Q=[p.sub.d(r.sub.1,)p.sub.d(r.sub.2,) . . . p.sub.d(r.sub.M,)].sup.T(28)
the wave coefficients
C.sub.d.sup.Q=[C.sub.1,d()C.sub.2,d() . . . C.sub.J,d()].sup.T(29)
and the expansion matrix

(24) $\begin{array}{cc}{}_{S,d}=\left[\begin{array}{cccc}{}_{1,d}\left(r_1,\right)& {}_{2,d}\left(r_1,\right)& \mathrm{.Math.}& {}_{J,d}\left(r_1,\right)\\ {}_{1,d}\left(r_2,\right)& {}_{2,d}\left(r_2,\right)& \mathrm{.Math.}& {}_{J,d}\left(r_2,\right)\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ {}_{1,d}\left(r_M,\right)& {}_{2,d}\left(r_M,\right)& \mathrm{.Math.}& {}_{J,d}\left(r_M,\right)\end{array}\right]& \left(30\right)\end{array}$
with the indices representing the sound components
d{t,in,out,ex,scat,sw,sec,rad}(31)
and the indices representing the sound sources
Q{Q.sub.0,Q.sub.1,Q.sub.2, . . . }(32)

(25) The expansion in Eq. (27) corresponds to the following relationship between the wave coefficients:
C.sub.out.sup.Q.sup.0.sup.,Q.sup.1=C.sub.sec.sup.Q.sup.0.sup.,Q.sup.1=C.sub.rad.sup.Q.sup.0=C.sub.sw.sup.Q.sup.0.sup.,Q.sup.1+C.sub.ex.sup.Q.sup.0.sup.,Q.sup.1=C.sub.sw.sup.Q.sup.0.sup.,Q.sup.1+C.sub.scat.sup.Q.sup.0.sup.,Q.sup.1+C.sub.rad.sup.Q.sup.0(33)
The wave coefficients C.sub.out.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.in.sup.Q.sup.0.sup.,Q.sup.1 are determined in the IOFS-method 13 by

(26) $\begin{array}{cc}\left[\begin{array}{c}{C}_{\mathrm{ex}}^{Q_0,Q_1}\\ C_{\mathrm{sw}}^{Q_0,Q_1}\end{array}\right]={\left[\begin{array}{cc}{}_{S_1,\mathrm{ex}}& {}_{S_1,\mathrm{sw}}\\ {}_{S_2,\mathrm{ex}}& {}_{S_2,\mathrm{sw}}\end{array}\right]}^{-1}\left[\begin{array}{c}{p}_{S_1,t}^{Q_0,Q_1}\\ p_{S_2,t}^{Q_0,Q_1}\end{array}\right]& \left(34\right)\end{array}$
or by performing an integration over spherical scanning surfaces S.sub.1 and S.sub.2 described by E. Williams in Fourier Acoustics, Academic Press 1999, chapter 7.4.

(27) An extrapolator 11 determines the sound pressure of the direct sound

(28) $\begin{array}{cc}\begin{array}{c}{p}_{\mathrm{rad}}^{Q_0}\left(r,\right)=p_{\mathrm{rad}}^{Q_0}\left(r,,,\right)\\ =\underset{n=0}{\overset{N}{.Math.}}\underset{m=-n}{\overset{n}{.Math.}}{c}_{n,m.\mathrm{rad}}\left(\right)h_n^{\left(1\right)}\left(\mathrm{kr}\right)Y_n^m\left(,\right)\end{array}& \left(35\right)\end{array}$
at any observation point r beyond the scanning surface by using the coefficients C.sub.rad.sup.Q.sup.0C.sub.ex.sup.Q.sup.0.sup.,Q.sup.1 of the excess sound in analyzer 55.

(29) FIG. 2 shows a holographic measurement combining the IOFS-method and a PSFS-method. The coefficients C.sub.ex.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.sw.sup.Q.sup.0.sup.,Q.sup.1 estimated by the IOFS-method 13 are supplied to the following PSFS-method 10 which generates the coefficients C.sub.rad.sup.Q.sup.0 in the expansion of the direct sound pressure:

(30) $\begin{array}{cc}\begin{array}{c}{p}_{S,\mathrm{rad}}^{Q_0}=p_{S,t}^{Q_0,Q_1}-p_{S,\mathrm{sw}}^{Q_0,Q_1}-p_{S,\mathrm{scat}}^{Q_0,Q_1}\\ =p_{S,\mathrm{ex}}^{Q_0,Q_1}-p_{S,\mathrm{scat}}^{Q_0,Q_1}\\ ={}_{S,\mathrm{out}}\left[C_{\mathrm{out}}^{Q_0,Q_1}-C_{\mathrm{sw}}^{Q_0,Q_1}-C_{\mathrm{scat}}^{Q_0,Q_1}\right]\\ ={}_{S,\mathrm{out}}\left[C_{\mathrm{ex}}^{Q_0,Q_1}-C_{\mathrm{scat}}^{Q_0,Q_1}\right]\\ ={}_{S,\mathrm{out}}{C}_{\mathrm{rad}}^{Q_0}\end{array}& \left(36\right)\end{array}$

(31) The coefficients associated with the scattered sound w.sub.scat are estimated by
C.sub.scat.sup.Q.sup.0.sup.,Q.sup.1=(Y.sub.S.sub.0.sub.S.sub.0.sub.,out.sub.S.sub.0.sub.,out.sup.v).sup.1(v.sub.S.sub.0.sub.,swY.sub.S.sub.0p.sub.S.sub.0.sub.,sw.sup.Q.sup.0.sup.,Q.sup.1)(37)
using the velocity on the surface S.sub.0 of the source under test 2
v.sub.S.sub.0.sub.,sw=.sub.S.sub.0.sub.,sw.sup.vC.sub.sw.sup.Q.sup.0.sup.,Q.sup.1,(38)
the expansion matrix of the standing wave

(32) $\begin{array}{cc}{}_{S_0,\mathrm{sw}}^v=\frac{1}{j{}_{0}c}\frac{{}_{S_0,\mathrm{sw}}}{r},& \left(39\right)\end{array}$
the expansion matrix of the outgoing wave

(33) $\begin{array}{cc}{}_{S_0,\mathrm{out}}^v=\frac{1}{j{}_{0}c}\frac{{}_{S_0,\mathrm{out}}}{r}& \left(40\right)\end{array}$
and acoustical admittance Y of the surface S.sub.0.

(34) FIG. 3 shows a perturbation method using an external sound source Q.sub.2 placed at a plurality of points r.sub.e with e=1, . . . , E in the space between outer surface S.sub.out of the scanning range G.sub.m and the room boundary S.sub.B. A switch 27 provides a stimulus generated by a generator 8, either to the source under test Q.sub.1 or the external sound source Q.sub.2. The switch 29 supplies the pressure signal p.sub.t(r.sub.m) either to the storage devices 7 and 9 generating the scanned data set p.sub.S,t.sup.Q.sup.0.sup.,Q.sup.1 or to the storage devices 15 and 216 generating the scanned data set p.sub.S,t.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup..sup.) depending on the position r.sub.e.

(35) The IOFS-module 19 provided with p.sub.S,t.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.E.sup.) generates the wave coefficients

(36) $\begin{array}{cc}\left[\begin{array}{c}{C}_{\mathrm{out}}^{Q_1,Q_2\left(r_e\right)}\\ C_{\mathrm{in}}^{Q_1,Q_2\left(r_e\right)}\end{array}\right]={\left[\begin{array}{cc}{}_{S_1,\mathrm{out}}& {}_{S_1,\mathrm{in}}\\ {}_{S_2,\mathrm{out}}& {}_{S_2,\mathrm{in}}\end{array}\right]}^{-1}\left[\begin{array}{c}{p}_{S_1,t}^{Q_1,Q_2\left(r_e\right)}\\ p_{S_2,t}^{Q_1,Q_2\left(r_e\right)}\end{array}\right]e=1,\mathrm{.Math.},E& \left(41\right)\end{array}$
which are supplied to subsystem 21 to identify the transfer matrix
H=Z.sub.outZ.sub.in.sup.1(42)
with
Z.sub.out[C.sub.1,out.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.1.sup.) . . . C.sub.j,out.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.e.sup.) . . . C.sub.J,out.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.E.sup.)](43)
and
Z.sub.in[C.sub.j,in.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.1.sup.) . . . C.sub.j,in.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.e.sup.) . . . C.sub.j,in.sup.Q.sup.1.sup.,Q.sup.2.sup.(r.sup.E.sup.)](44)
The IOFS-module 18 generates the wave coefficients

(37) $\begin{array}{cc}\left[\begin{array}{c}{C}_{\mathrm{out}}^{Q_0,Q_1}\\ C_{\mathrm{in}}^{Q_0,Q_1}\end{array}\right]={\left[\begin{array}{cc}{}_{S_1,\mathrm{out}}& {}_{S_1,\mathrm{in}}\\ {}_{S_2,\mathrm{out}}& {}_{S_2,\mathrm{in}}\end{array}\right]}^{-1}\left[\begin{array}{c}{p}_{S_1,t}^{Q_0,Q_1}\\ p_{S_2,t}^{Q_0,Q_1}\end{array}\right]& \left(45\right)\end{array}$
based on the scanned data sets p.sub.S.sub.1.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 and p.sub.S.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 provided by the storage devices 7 and 9.

(38) The following PSFS-module 23 generates the coefficients of the direct sound
C.sub.rad.sup.Q.sup.0=C.sub.out.sup.Q.sup.0.sup.,Q.sup.1C.sub.sec.sup.Q.sup.0.sup.,Q.sup.1=C.sub.out.sup.Q.sup.0.sup.,Q.sup.1HC.sub.in.sup.Q.sup.0.sup.,Q.sup.1(46)
by using the results of the IOFS-method and the transfer matrix H.

(39) FIG. 4 shows schematically one embodiment of the holographic measurement method according to the present invention. The acquisition device 14 generates the stimulus u(t) exciting the device under test 2 with the source Q.sub.0 and places the sensor 1 at the measurement points r.sub.m located in a scanning range G.sub.m. Contrary to the prior art the scanning range G.sub.m depends on the shape of the surface S.sub.0 of the device under test 2. An identifier 16 provided with the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 generates a parameter P describing the acoustical properties of the device under test 2. Based on this parameter P and the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 the analyzer 55 generates wave coefficients C.sub.rad.sup.Q.sup.0 representing the direct sound w.sub.rad and error coefficients E.sub.rad representing the error of the direct sound prediction. Based on this information the extrapolator 11 generates the sound pressure P.sub.rad.sup.Q.sup.0 (r) of the direct sound according to Eq. (35) and the relative error e.sub.rad(r) at observation point r according to Eq. (18).

(40) FIG. 5 shows an embodiment of the identifier 16 using scanned data set p.sub.G.sub.m.sub.,w.sup.Q.sup.0.sup.,Q.sup.1 which is contrary to prior art the only input information. A linear filter 39 generates a filtered scanned data set p.sub.G.sub.m.sub.,w.sup.Q.sup.0.sup.,Q.sup.1, according to Eq. (4). The following IOFS-module 19 generates the wave coefficients C.sub.in,w.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.out,w.sup.Q.sup.0.sup.,Q.sup.1 according to Eq. (6) which represent the incoming and outgoing fields of the reverberant sound, respectively. The wave coefficients C.sub.in,w.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.out,w.sup.Q.sup.0.sup.,Q.sup.1 are supplied as parameter P to PSFS-module 24 in the analyzer 55, which generates the wave coefficients C.sub.ps.sup.Q.sup.0 of the primary sound according to Eqs. (7), (9), (11) using the wave coefficients C.sub.in.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.out.sup.Q.sup.0.sup.,Q.sup.1 generated from the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 by the IOFS-module 18.

(41) Based on the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 a linear filter 111 generates according to Eq. (14) a filtered scanned data set p.sub.G.sub.m.sub.,w.sub.dir.sup.Q.sup.0.sup.,Q.sup.1, which comprises components having a small group time delay. A free field expander 113 generates according to Eq. (15) the wave coefficients C.sub.w.sup.Q.sup.0.sup.,Q.sup.1 and error vector e.sub.w supplied as a parameter P to the analyzer 55. The analyzer 55 contains an evaluator 117 generating the crossover frequency .sub.c and the error coefficients E.sub.rad according to Eq. (17) based on the error vector e.sub.w from the free field expander 113 and the error vector e.sub.io from the IOFS-module 18. A crossover 115 receives the crossover frequency .sub.c and the wave coefficients C.sub.ps.sup.Q.sup.0 and generates according to Eq. (15) the wave coefficients C.sub.rad.sup.Q.sup.0.

(42) FIG. 6 shows an embodiment of the PSFS-module 24 in accordance with the invention. The correlator 97 generates the transmission parameter k.sub.x according to Eq. (8) based on the wave coefficients C.sub.in,w.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.in.sup.Q.sup.0.sup.,Q.sup.1, wherein the transmission parameter k.sub.x describes the concurrence of the directivity of the total incoming sound w.sub.in and the directivity of the reverberant part of the incoming sound w.sub.in.

(43) The comparator 99 generates a transparency parameter k.sub.t according to Eq. (10) based on the wave coefficients C.sub.in,w.sup.Q.sup.0.sup.,Q.sup.1 and C.sub.out,w.sup.Q.sup.0.sup.,Q.sup.1, which describes the acoustical transparency of the space enclosed by the scanning range (G.sub.m). A synthesizer 93 generates the secondary wave coefficients C.sub.sec.sup.Q.sup.0.sup.,Q.sup.1 associated with the expansion of the secondary sound w.sub.sec according to Eq. (9) based on the total incoming wave coefficients C.sub.in.sup.Q.sup.0.sup.,Q.sup.1, the transparency parameter k.sub.t and transmission parameter k.sub.x. The combiner 95 generates the direct wave coefficients C.sub.rad.sup.Q.sup.0 according to Eq. (15) based on total outgoing wave coefficients C.sub.out.sup.Q.sup.0.sup.,Q.sup.1 and the secondary wave coefficients C.sub.sec.sup.Q.sup.0.sup.,Q.sup.1.

(44) FIG. 7 shows an embodiment of the measurement system applied to a multi-way loudspeaker system 2, comprising a woofer 41, midrange transducer 43 and a tweeter 45. The inner and outer surfaces S.sub.in and S.sub.out, respectively, of the scanning range G.sub.m are cylinders to fit the slim shape of the loudspeaker. The sensor 1 is placed at the measurement point r.sub.m by a positioning device 49 using three actuators 11, 47, 51 in cylindrical coordinates r, z and . A second sensor 76 is placed outside the scanning range G.sub.m at a larger distance from the source under test Q.sub.0 than the sensor 1 to monitor an ambient sound signal p.sub.t(r.sub.a) representing acoustical disturbances w.sub.noise generated by a noise source Q.sub.1. An noise identifier 77 compares the scanning signal p.sub.t(r.sub.m) with the ambient sound signal p.sub.t(r.sub.a) and detects an invalid measurement corrupted by the noise source Q.sub.1. After storing the valid parts of the scanning signal p.sub.t(r.sub.m) in the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 the noise identifier 77 repeats the measurement at the current sensor position r.sub.m until the collected valid parts are complete.

(45) The analyzer 55 is embedded in an iterative process beginning with the determination of wave coefficients C.sub.rad.sup.Q.sup.0[l] based on the preliminary scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1[l] in the first step l=1. An expansion point identifier 59 detects the acoustical center z.sub.0() of the device under test 2 as a function of frequency and determines the coordinates of an expansion point r.sub.0[l+1]. A symmetry identifier 60 generating symmetry parameters A[l+1] representing the axial and reflection symmetry of the sound field and the orientation of the device under test 2 associated with the direction of main radiation. Based on the identified expansion point r.sub.0[l+1] and symmetry parameters A[l+1] in wave coefficients C.sub.rad.sup.Q.sup.0[l] a generator 53 extends the scanning vector R[l+1] by introducing additional measurement points placed at optimal positions in the scanning range G.sub.m. Based on the extended scanning vector R[l+1] the positioning device 49 performs an adaptive scanning process considering the identified properties of the device under test 2. Thus the scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1[l] provides sufficient information for the wave expansion while using a minimum number of measurement points.

(46) FIG. 8 shows an embodiment of the analyzer 55 using two scanning ranges G.sub.1 and G.sub.2, having a different density of measurement points. The acquisition device 14 collects the measured sensor output p.sub.t(r.sub.m) in the first scanned data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 and in the scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1. The first sub-analyzer 63 generates a second wave coefficients C.sub.G.sub.2.sub.,rad.sup.Q.sup.0.sup.,Q.sup.1 according to Eq. (15) based on second scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1, wherein the number of measurement points M.sub.2 in the second scanning range G.sub.2 limits the maximal order N.sub.2 of the second wave coefficients C.sub.G.sub.2.sub.,rad.sup.Q.sup.0.sup.,Q.sup.1. An interpolator (65) generates an interpolated scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 by extrapolation in accordance with Eq. (35) based on the second wave coefficients C.sub.G.sub.2.sub.,rad.sup.Q.sup.0.sup.,Q.sup.1. The number M.sub.2S of elements in the interpolated scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 is higher than the number of measurement points M.sub.2 in the second scanning range G.sub.2. A combiner 67 generates a unified data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 merging the first scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 and the interpolated scanned data set p.sub.G.sub.2.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 wherein the density of samples in the second scanning range G.sub.2 equals the density of measurement points in first scanning range G.sub.1. A second analyzer 69 generates the wave coefficients C.sub.red.sup.Q.sup.0 of the direct sound according to Eq. (15) based on the unified data set p.sub.G.sub.m.sub.,t.sup.Q.sup.0.sup.,Q.sup.1 wherein the order N.sub.rad of the expansion is larger than the order N.sub.2 of the second wave coefficients C.sub.G.sub.2.sub.,rad.sup.Q.sup.0.sup.,Q.sup.1. However, the interpolation cannot increase the resolution of the identified directivity pattern in the second scanning range G.sub.2.

(47) FIG. 9 shows an alternative embodiment of the analyzer 55 for getting a maximum resolution of the directivity pattern based on a minimum number M of measurement points. An estimator 81 generates a reduced wave coefficients C.sub.red.sup.Q.sup.0[l] according to Eq. (15) by using expansion matrix .sub.d,red[l] determined in the l.sup.st-step.

(48) Based on the reduced wave coefficients C.sub.red.sup.Q.sup.0[l] an inverse transformer 85 generates iterative wave coefficients
C.sub.rad.sup.Q.sup.0[l+1]=S[l+1].sup.TC.sub.red[l+1](47)
by using a predefined selection matrix S[l], wherein the number of elements in said iterative wave coefficients C.sub.rad.sup.Q.sup.0[l] is larger than the number of elements in said reduced wave coefficients C.sub.red.sup.Q.sup.0[l].

(49) Based on iterative the wave coefficients C.sub.rad.sup.Q.sup.0[l] an evaluator 87 generates a contribution vector [l] comprising the contribution ratio .sub.j[l] in accordance with Eq. (22). A selector 89 generates the selection matrix S[l] by using the contribution vector [l] and generates a maximal order N[1+1] of the coefficients associated with the expansion function, wherein coefficients c.sub.j,rad are set to zero, if its contribution .sub.j[l]) is below a critical threshold .sub.0.

(50) A generator 84 generates a complete expansion matrix .sub.d[l+1] by considering maximal order N[1+1] of the expansion function and/or number and position R[1] of the measurement points (r.sub.m) in said scanning range (G.sub.m) and/or an expansion point r.sub.0[1] representing the position of the acoustical center of the source under test Q.sub.0 and/or orientation information A[1] representing main direction of radiation of the source under test Q.sub.0 and/or rotational and/or reflection symmetry A[1] of the sound field generated by the source under test Q.sub.0.

(51) Based on the complete expansion matrix .sub.d[l+1] and the selection matrix S[l+1] a transformer 83 generates an updated value of the reduced expansion matrix
.sub.d,red[l+1]=S[l+1].sub.d[l+1](48)
wherein the number of elements in the reduced expansion matrix .sub.d,red[l+1] is smaller than the number of elements in the complete expansion matrix .sub.d[l+1]. The reduced expansion matrix .sub.d,red[l+1] is the basis for a sparse wave expansion comprising a reduced number of coefficients in C.sub.red.sup.Q.sup.0, which can be estimated by limited number of measurement points.

(52) Based on iterative wave coefficients C.sub.rad.sup.Q.sup.0[l] a controller 91 generates a direct wave coefficients C.sub.rad.sup.Q.sup.0, if the difference between the values of iterative wave coefficients C.sub.red.sup.Q.sup.0[l+1]C.sub.rad.sup.Q.sup.0[l] at two iterative steps of the iteration is below a predefined threshold.

Advantages of the Invention

(53) The invention measures the direct sound radiated by a device under test Q.sub.0 in a non-anechoic acoustical environment under the influence of ambient noise. Dispensing with an anechoic room reduces the cost and gives more flexibility in the development of loudspeakers and other acoustical devices. The new measurement techniques provide a comprehensive data set C.sub.rad.sup.Q.sup.0 describing the radiated sound field at any point outside the scanning range G.sub.m. The near-field information are important for assessing mobile phone, laptops and other personal audio devices. Further benefits are the simplicity, robustness and increased speed of the measurement compared to techniques known in prior art. The new PSFS-method dispenses with a time-consuming perturbation and requires no information about the shape and acoustical properties of the surface of the device under test Q.sub.0. The measurement technique exploits redundant information provided in the scanned data set and describes the consistency and accuracy of the measurement results at any observation point by a relative error measure. The invention performs the field separation and wave expansion by using a minimum number of measurement points associated with a short measurement time.

(54) In the foregoing specification, the invention has been described with reference to specific examples of embodiments of the invention. It will, however, be evident that various modifications and changes may be made therein without departing from the broader spirit and scope of the invention as set forth in the appended claims. For example, the connections may be a type of connection suitable to transfer signals from or to the respective nodes, units or devices, for example via intermediate devices. Accordingly, unless implied or stated otherwise the connections may for example be direct connections or indirect connections.

(55) Because the apparatus implementing the present invention is, for the most part, composed of electronic components and circuits known to those skilled in the art, details of the circuitry and its components will not be explained in any greater extent than that considered necessary as illustrated above, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention.

(56) Some of the above embodiments, as applicable, may be implemented using a variety of different circuitry components. For example, the exemplary topology in the figures and the discussion thereof is presented merely to provide a useful reference in discussing various aspects of the invention. Of course, the description of the topology has been simplified for purposes of discussion, and it is just one of many different types of appropriate topologies that may be used in accordance with the invention. Those skilled in the art will recognize that the boundaries between logic blocks are merely illustrative and that alternative embodiments may merge logic blocks or circuit elements or impose an alternate decomposition of functionality upon various logic blocks or circuit elements.

(57) Thus, it is to be understood that the architectures depicted herein are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In an abstract, but still definite sense, any arrangement of components to achieve the same functionality is effectively associated such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as associated with each other such that the desired functionality is achieved, irrespective of architectures or intermediate components. Likewise, any two components so associated can also be viewed as being operably connected, or operably coupled, to each other to achieve the desired functionality.

(58) Also, the invention is not limited to physical devices or units implemented in non-programmable hardware but can also be applied in programmable devices or units able to perform the desired device functions by operating in accordance with suitable program code. Furthermore, the devices may be physically distributed over a number of apparatuses, while functionally operating as a single device. Devices functionally forming separate devices may be integrated in a single physical device.

(59) In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word comprising does not exclude the presence of other elements or steps then those listed in a claim. Furthermore, the terms a or an, as used herein, are defined as one or more than one. Also, the use of introductory phrases such as at least one and one or more in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles a or an limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases one or more or at least one and indefinite articles such as a or an. The same holds true for the use of definite articles. Unless stated otherwise, terms such as first and second are used to arbitrarily distinguish between the elements such terms describe. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage. The order of method steps as presented in a claim does not prejudice the order in which the steps may actually be carried, unless specifically recited in the claim.

(60) Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily drawn to scale. For example, the chosen elements are only used to help to improve the understanding of the functionality and the arrangements of these elements in various embodiments of the present invention. Also, common but well understood elements that are useful or necessary in a commercial feasible embodiment are mostly not depicted in order to facilitate a less abstracted view of these various embodiments of the present invention. It will further be appreciated that certain actions and/or steps in the described method may be described or depicted in a particular order of occurrences while those skilled in the art will understand that such specificity with respect to sequence is not actually required. It will also be understood that the terms and expressions used in the present specification have the ordinary meaning as it accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise be set forth herein.