Method for the synthetic generation of a digital audio signal

Abstract

A method for the synthetic generation of a digital audio signal by means of periodic sampling of a waveform shall permit the user a particularly simple and intuitive access to the changing and creative transformation of the waveform on which the sampling is based. For this purpose, according to the invention, the waveform is specified by using control points, which, in addition to position parameters, may contain further attributes, of which the parameters and attributes can be changed individually over time by means of control signals or spontaneouseous intervention. The control-point values which result in this way can be interpreted either as direct amplitude-period phase or as magnitude-frequency or phase-frequency pairs. A continuous waveform is generated by interpolation or approximation of the control points and the parameters/attributes of the latter, which assume a time-specific value depending on the current control signals and other influences, and is used for further processing, e.g. spectral band limiting.

Claims

1. A method for synthetic generation of a digital audio signal, the method comprising: providing, by a synthesizer, a number of control points, each of which is given by an amplitude-period phase, a magnitude-frequency, or a phase-frequency value pair, wherein the control points are changeable by respective associated control signals; and on the basis of the control points, repeatedly performing, by the synthesizer, the further steps of: defining a wave function by interpolating or approximating between the control points; calculating amplitude values of the wave function; and using the amplitude values for generating the digital audio signal.

2. The method of claim 1, wherein the amplitude, magnitude, or phase values of the control points and period-phase or frequency values of the control points are each changeable by individually associated control signals, independently from each other.

3. The method of claim 2, wherein at least one other attribute of the control points is changeable by at least one other individually associated control signal, independently of at least one of the amplitude, magnitude, or phase values or the period-phase or frequency values of the control points.

4. The method of claim 1, wherein polynomial-based interpolation, Bzier curves, b-splines, or NURBS are used for approximation or interpolation of a course between the control points, the basic conditions of the interpolation method being adapted when at least one of the control points or their attributes change.

5. The method of claim 1, wherein: the wave function is composed of a number of wave segments (32) which follow each other within a period phase or a frequency band and are each defined by a segment-specific linear combination of a number of basic functions, the wave segments (32) being connected at segment edges (34) thereof, via one of the control points each, with the respective adjacent wave segment (32); for each wave segment (32), linear coefficients are determined with which the respective wave segment (32) has at its segment edges (34), within the framework of a local control point, predefinable changeable amplitude or magnitude or phase edge values; and the values of respective updated linear coefficients are determined for the respective wave segment (32) during the repeated calculation of the amplitude values of the wave function and are taken as a basis for the calculation of the amplitude values.

6. The method of claim 5, wherein for each wave segment (32), the linear coefficients are determined and taken as a basis for calculating the values in the subsequent calculation period, with which the respective wave segment (32) has on its segment edges (34) a predefinable, changeable edge gradient.

7. The method of claim 5, wherein polynomial functions are used as the basic functions.

8. The method of claim 1, wherein the wave function is composed of a number of wave segments (32) which succeed each other within a period phase or a frequency band and are each defined by a segment-specific linear combination of a number of basic functions and control points, the wave segments (32) being connected on segment edges (34) thereof near one of the control points each with the respective adjacent wave segment (32) and the linear combination of the current control point with the basic functions assigned thereto being taken as a basis during the repeated calculation of the amplitude values of the wave function.

9. The method of claim 1, wherein the wave function is displayed on a display unit (22) for processing purposes.

10. The method of claim 1, wherein the control points are changed via an input device (20).

11. The method of claim 1, wherein the control points are temporally changed in accordance with a modulation function stored in a storage unit (4).

12. The method of claim 11, wherein: the modulation function is generated by use of the repeatedly calculated amplitude values of the wave function that are determined by a period-phase or frequency-dependent amplitude course formed by the control points, the control points being formed by approximation or interpolation between a number of amplitude-period phase or amplitude-frequency value pairs over a predefined interval; and at least one of the parameter values or other attributes of the control points are changeable by respective associated control signals and the interpolation or approximation of the wave function determined by currently existing control signals is taken as a basis for the calculation of the amplitude values.

13. The method of claim 1, wherein at least two control signals which are independent of each other are provided.

14. The method of claim 7, wherein the polynomial functions are of the third degree.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) An exemplary embodiment of the invention is explained in detail by means of a drawing, in which

(2) FIG. 1 shows a synthesizer for the synthetic generation of a digital audio signal

(3) FIGS. 2-9 each show a sequence of a waveform displayed on a display unit of the synthesizer of FIG. 1 and edited there, and

(4) FIG. 10 is a flowchart of an exemplary method for synthetic generation of a digital audio signal.

(5) Identical parts are identified in all figures by the same reference numbers.

DETAILED DESCRIPTION OF THE INVENTION

(6) The synthesizer 1 according to FIG. 1 comprises a central unit 2, in particular a computer, in which a so-called oscillator or a waveform can be processed, which can be modified as required, depending on the desired adaptation regarding tone pitch, tone color or other musical effects. The oscillator or the waveform is generated from the construction of piecewise basic functions and control points in the context of the system (components, temporal changes, etc), which is stored as a data set in the storage 4. As the control points can be evaluated continuously, the resulting construct can also be evaluated continuously. Therefore, a sampling of the underlying construct is possible in any frequency, so that any tone pitches can be generated. Sampling takes place at a constant sample rate, and the sampled values are stored with a constant bit depth in a storage 4 and/or directly output as a digital audio signal, possibly after a spectral band limiting and further processing, which digital audio signal is transformed into an analog audio signal in a downstream digital-analog transducer 10. The analog audio signal is then used for selecting a downstream loudspeaker unit 12 and supplied to the latter.

(7) The synthesizer 1 is specifically designed for offering the user a particularly simple and intuitive access for changing and creatively transforming the waveform on which the sampling is based. For this purpose, a processing unit 20, i.e. in particular an editor, is associated with the central unit 2, via which processing unit 20 a modification or processing of the oscillator read into the central unit or of the waveform available in the central unit 2 is possible. Furthermore, a display unit 22, i.e. in particular a screen or a display, is connected to the central unit 2, via which display unit 22, the processing of the waveform in question is directly displayed and made reconstructable to the user. In the exemplary embodiment, the processing unit 20 is designed as a separate unit, separated from the display unit. Alternatively, however, in a particularly preferred embodiment, it can also be integrated in the display unit 22, in particular when designed as a touch screen.

(8) In order to particularly simplify the processing of the waveform and to enable also novel effects, for example through extrapolation of values or the like, the waveform is provided for being processed in the central unit 2 in a particularly processing-friendly manner. For this purpose, the waveform is subdivided into a number of wave segments following each other temporally, so that the waveform as a whole can be obtained by composing the wave segments following each other temporally (or, in case of processing in the frequency domain, following each other in frequency). Each wave segment is in this case reproduced, in the manner of a mathematical decomposition, by means of a segment-specific linear combination from a number of basic functions and control points, the particularly preferred cubic polynomials, or, in other words, polynomial functions of the third order, being used as basic functions in the exemplary embodiment. The linear coefficients for each wave segment are chosen in the interpolation-based exemplary embodiment in such a way that each wave segment has at each of its segment edges predefinable, changeable amplitude edge values and gradients.

(9) In this way, a user-prompted changing or processing of the waveform through a corresponding modification of the respective linear coefficients is possible, so that even highly complex changes can be made with a relatively limited number of parameters.

(10) The number of segments in this decomposition of the waveform can be predefined and also modified by the user. It can in particular be taken into consideration whether, and if so, to which degree sections are present or shall be present in the waveform, which shall be characterized by a particular characteristic or a particular behavior; it can be expedient for the user to associate with each of such individualized sections in the waveform a wave segment of its own, so that a specific and selective modification of the respective section is possible.

(11) Examples of waveforms which can be modified in this way are shown in FIGS. 2 to 9 in the form of sequences of screenshots of the display unit 22. The waveform represented there in each case as an amplitude line 30 comprises the wave segments 32, which at their segment edges 34, in so-called touching points 36, merge into the respective adjacent wave segment 32. The linear coefficients for each wave segment 32 are in the particularly preferred exemplary embodiment chosen such that each wave segment 32 has at each of its segment edges 34 a predefinable, changeable edge gradient. The amplitude edge values and the edge gradients can in this case directly be changed via the processing unit 20, i.e. in particular via the touch screen, by selecting the touching points 36 and inputting the corresponding values via a context-related menue or a context-related editor.

(12) The amplitude edge values and the edge gradients can also be changed temporally in accordance with a modulation function stored in the storage 4, in addition to the direct changing through the user. In this case, for example, a periodic change of the respective parameters in the manner of an oscillation or else a linear change in the sense of a continuous enlargement of the respective parameters or any other changes might be provided.

(13) In the exemplary embodiment, it is provided, in a very particularly preferred embodiment, that each modulation function, for its part, is composed of a number of wave segments which follow each other temporally and are each defined by a segment-specific linear combination of a number of basic functions and control points, the linear coefficients for each wave segment being chosen in the exemplary embodiment such that each wave segment has at each of its segment edges predefinable, changeable amplitude edge values and/or edge gradients. After a change of an amplitude edge value and/or an edge gradient, the linear coefficients for the wave segment limited thereby can be newly calculated.

(14) By means of the sequences shown in FIGS. 2 to 9, some possible modifications are represented by way of example. These can be used individually or in any combination with each other for a desired and creative modification of the waveform.

(15) The sequence according to FIG. 2 is an example of a change of the waveform by means of a horizontal shift of a control or touching point 36. In the initial state according to FIG. 2a, the waveform available in the form of the amplitude line 30 is designed in the manner of a symmetrical embodiment regarding the x-axis or period-phase axis and comprises two wave segments 32, which are connected with each other at their common segment edge 34 via the control or touching point 36 and merge into each other. In each of the wave segments 32 following each other temporally, of which the waveform is composed, the amplitude line 30 in each wave segment 32 is calculated in the central unit 2 by means of a segment-specific cubic polynomial, i.e. a segment-specific linear combination of a number of polynomials used as basic functions, and shown on the display unit. In this way, in each wave segment 32, the part of the waveform corresponding thereto is mathematically defined and characterized by means of a relatively low number of four coefficients (i.e. the linear coefficients for the polynomials up to the third order). With these, the respective wave segment 32 can be described for its current state, but can, if required, also be extrapolated into the future. Thus, the corresponding partial waveform is generated constructively or additively, within each wave segment 32 by means of linear superposition of a number of polynomials provided as basic wave functions.

(16) The linear coefficients for each wave segment 32 are chosen such that the amplitude line 30 in each wave segment 32 has at each of its segment edges 34 predefinable, changeable amplitude edge values. At the transition point defined by the control or touching point 36 shown in FIG. 2c between the adjacent wave segments 32, said wave segments 32 are suitably chosen for a steady transition between the adjacent wave segments 32 in the example shown.

(17) To modify the waveform, for example to implement artistic or creative effects, the control or touching point 36 can be shifted or an automatic shifting by means of control signals can be specified via a context menue, with the help of the processing unit 20. Accordingly, the linear coefficients of the cubic polynomials in the wave segments 32 are newly calculated and determined, in order to correctly reproduce the modified design. The waveform modified in this way is then made available by means of its mathematic definition via the constructive synthesis for the sampling provided for generating the tone.

(18) The sequence according to FIG. 2 shows a modification of the wave function by shifting the control or touching point 36 in the x-direction, corresponding to the time axis of the wave function. As compared with FIG. 2a, FIG. 2b shows the wave function after the shifting of the control or touching point 36 to the left, FIG. 2c, however, to the right. Such a shifting in the x-direction also means that the limit between the wave segments 32 is shifted accordingly, i.e. that, from the temporal point of view, in each case one of the wave segments 32 has after the shift a correspondingly larger part in the temporal interval of the wave function as a whole.

(19) Accordingly, the sequence according to FIG. 3 shows a modification of the wave function by shifting the control or touching point 36 in the y-direction, corresponding to the amplitude of the wave function. As compared with FIG. 3a, FIG. 3b shows the wave function after the shifting of the control or touching point 36 upwards, FIG. 3c, however, downwards. Such a shifting in the y-direction substantially means a corresponding change of the amplitude of the wave function as a whole.

(20) The linear coefficients of the cubic polynomials in the wave segments 32 are, on the one hand, chosen such that each wave segment 32 has at its segment edges 34 the respective amplitude edge values which are predefinable and possibly changeable by means of the control or touching points 36. Furthermore, the linear coefficients of the cubic polynomials for each wave segment 32 are, however, also chosen such that each wave segment 32 has at each of its segment edges 34 a predefinable edge gradient. The latter can individually be changed by the user, which is made possible in the exemplary embodiment through a suitable configuration of the editor by means of a rotation of the respective control or touching point 36, as a whole or else independently for each segment edge 34. The sequence according to FIG. 4 is an example of such a rotation of the control or touching point 36, in which on both sides of the segment edge 34 between the wave segments 32, the edge gradients are changed corresponding to each other. By contrast, the sequence according to FIG. 5 is an example of a change of the edge gradients on both sides of the segment edge 34 between the wave segments 32 separately from each other. Such a separate change of the edge gradients results in a change of the angulation in the control or touching point 36.

(21) The number of control or touching points 36 and, thus, the number of wave segments 32 from which the wave function is composed, can also be changed by the user. FIG. 6 shows an example of adding or removing control or touching points 36 and, consequently, modifying at the same time the number of the wave segments 32.

(22) By suitable superposition, modulations of a wave function as such can analogously be edited and changed. Examples thereof are shown in the sequences according to FIG. 7 (amplitude modulation of a constructive waveform by shifting a control or touching point 36 of another constructive waveform, FIG. 8 (frequency modulation of a constructive waveform by rotating a control or touching point 36 of another constructive waveform), and FIG. 9 (frequency modulation with a change (over time) of rotation on the basis of a sinusoidal constructive waveform).

(23) FIG. 10 is a flowchart of an exemplary method 100 for synthetic generation of a digital audio signal. The method begins at Step 102 in which a number of control points are provided. Each control point may be given by an amplitude-period phase, a magnitude-frequency, or a phase-frequency value pair. The control points are changeable by respective associated control signals. The method continues by repeatedly performing, on the basis of the control points, the steps of defining a wave function by interpolating or approximating between the control points at Step 104, calculating amplitude values of the wave function at Step 106, and using the amplitude values for generating the digital audio signal at Step 108. If additional samples are needed, the method 100 returns to Step 104. If no more samples are needed, the method 100 terminates.

LIST OF REFERENCE NUMBERS

(24) 1 Synthesizer

(25) 2 Central unit

(26) 4 Storage

(27) 10 Digital-analog transducer

(28) 12 Loudspeaker unit

(29) 20 Processing unit

(30) 22 Display unit

(31) 30 Amplitude line

(32) 32 Wave segment

(33) 34 Segment edge

(34) 36 Touching point