SENSOR ARRANGEMENT WITH VARIABLE CARRIER FREQUENCY AND GOERTZEL FILTERING

Abstract

A method for processing a signal modulated with a variable carrier frequency includes calculating a coefficient for demodulation of the signal. The method also includes demodulating the signal by calculating discrete intermediate values utilizing the coefficient for a predefined maximum number of steps and calculating the signal with the aid of the intermediate values of the coefficient. The value of the coefficient is respectively calculated on the basis of carrier frequencies for each step.

Claims

1. A method for processing a signal modulated with a variable carrier frequency, comprising: calculating a coefficient (c(n)) for demodulation of the signal, demodulating the signal by calculating discrete intermediate values (s, s1, s2) utilizing the coefficient for a predefined maximum number of steps (n_max), and calculating the signal with the aid of the intermediate values and the coefficient (c(n)), wherein the value of the coefficient (c(n)) is respectively calculated on the basis of the carrier frequencies (f_signal(n)) for each step.

2. The method as set forth in claim 1, wherein the coefficient is calculated as a function of the instantaneous frequency (f_signal(n)) of the carrier frequencies.

3. The method as set forth in claim 1, wherein at least one bandwidth of the carrier frequencies is predefined, the bandwidth lying outside predictable perturbation frequencies.

4. The method as set forth in claim 2, wherein a bandwidth of the carrier frequencies is predefined, the bandwidth being established as a function of a frequency or frequency bandwidth of the signal.

5. The method as set forth in claim 1, wherein the signal is modulated with a modulation unit, and in that the processing of the modulated signal is carried out by with a signal processing unit, the carrier frequencies or instantaneous frequencies being synchronized between the modulation unit and the signal processing unit.

6. The method as set forth in claim 1, wherein the values of the coefficient of the modulation of the signal are precalculated.

7. The method as set forth in claim 6, further comprising storage of the values of the coefficient in a nonvolatile memory.

8. The method as set forth in claim 6, further comprising storage of identical coefficient values in a memory location.

9. The method as set forth in claim 1, wherein the coefficients are calculated utilizing the equation
c(n)=2 cos(2*f_signal(n)/f_sample), where n=sampling step c(n)=coefficient for the sampling step n f_signal (n)=carrier frequency or instantaneous frequency for the nth sampling step f_sample=sampling frequency.

10. The method as set forth in claim 1, wherein the intermediate values are calculated by utilizing the following procedure s1=0 s2=0 repeat with n from 1 to n_max
s=signal(n)+c(n)*s1s2 s2=s1 s1=s end, where s, s1, s2=intermediate values of different sampling steps signal(n)=modulated signal value in step n n_max=total number of sampling steps for a procedure.

11. The method as set forth in claim 1, wherein the modulation of the signal is carried out by using precalculated values of the coefficient.

12. The method as set forth in claim 11, wherein the modulation of the signal is calculated utilizing the following procedure
s1=0
s2=sin(2*f_signal/f_sample) repeat with n from 1 to n_max
s=c(n)*s1s2 s2=s1 s1=s signal(n)=s end.

13. The method as set forth in claim 1, wherein an amplitude of the signal is calculated utilizing the equation
A=2*sqrt(s2*s2+s1*s1-c(n_max)*s1*s2)/n_max, where: s1, s2=intermediate values after n_max steps c(n_max)=coefficient value at step n_max.

14. A signal processing unit (5) for processing a signal modulated with a variable carrier frequency (signal(n)), comprising a summation element for calculating the demodulated signal values, a coefficient block containing at least one value of a coefficient (c(n)), at least one intermediate memory for storing the intermediate values, one of the intermediate memories being connected to the coefficient block, and a multiplier for multiplying the modified signal value by the coefficient, this value being deliverable to the summation element, wherein the coefficient block contains a plurality of values of the coefficient (c(n)), or a plurality of values of the coefficient can be calculated utilizing the coefficient block.

15. A sensor arrangement, comprising a modulation unit for modulating a sensor signal, a sensor element for generating the sensor signal, and a signal processing unit comprising a summation element for calculating the demodulated signal values, a coefficient block containing at least one value of a coefficient (c(n)), at least one intermediate memory for storing the intermediate values, one of the intermediate memories being connected to the coefficient block, and a multiplier for multiplying the modified signal value by the coefficient, this value being deliverable to the summation element, wherein the coefficient block contains a plurality of values of the coefficient (c(n)), or a plurality of values of the coefficient can be calculated utilizing the coefficient block.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Other advantages of the disclosed subject matter will be readily appreciated, as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

[0035] FIG. 1 shows an exemplary embodiment of a sensor arrangement according to the invention,

[0036] FIG. 2 shows an exemplary embodiment of a signal processing unit according to the invention,

[0037] FIG. 3 shows a profile of the values of the coefficients c,

[0038] FIG. 4 shows a profile of the amplitude spectrum according to the values of the coefficient in FIG. 3, and

[0039] FIG. 5 shows a comparison of the perturbation susceptibility of the method according to the invention in relation to the Goertzel algorithm from the prior art.

DETAILED DESCRIPTION

[0040] Referring to the Figures, wherein like numerals indicate like parts throughout the several views, a sensor arrangement 1 is shown and described herein.

[0041] FIG. 1 shows the schematic structure of the sensor arrangement 1, which may be integrated into known sensors. The sensor arrangement 1 comprises a modulation unit 3 for modulating a signal, or a sensor signal. The sensor signal is generated by means of a sensor element 4. The invention may be carried out with different types of sensor elements, for example ohmic resistances, capacitances or inductances. A signal processing unit 5 demodulates the modulated signal signal(n) or carries out a part of the demodulation according to the method according to the invention. The modulation unit 3 and the signal processing unit 5 are connected to one another via a connection 6 so that synchronization of the carrier frequency, instantaneous frequency f_signal(n) or of the coefficients c is possible by means of this.

[0042] The modulation unit 2 generates a carrier signal having a carrier frequency, or within a selected frequency bandwidth. The signal is applied to the sensor after having been converted by means of a digital/analog converter (not shown in the figures). It is also conceivable to configure the modulation unit as an analog oscillator. On the part of the signal processing unit, the analog signal is again converted by means of an analog/digital converter.

[0043] FIG. 2 schematically represents an exemplary embodiment of the signal processing unit 5. The modulated sensor signal is fed in through the input of the signal processing unit 5. The signal processing unit 5 processes the modulated input signal over a plurality of iterations corresponding to a number of sampling steps.

[0044] The signal processing unit 5 comprises two intermediate memories 50, 51. The intermediate values of different sampling steps n-1and n-2are stored in the intermediate memories 50, 51. The intermediate memory 50 is connected, on the one hand, via a multiplier to a coefficient block 52 in which the different values of the coefficient c(n) are stored. The value of the intermediate memory 50 is multiplied by the respective n.sup.th coefficient value c(n) and added to the input signal. Furthermore, the intermediate memory 50 is connected to the second intermediate memory 51. The preceding intermediate value of the first intermediate memory (s2, or s(n-2)) is stored in the second intermediate memory. The value from the second intermediate memory 51 is subtracted from the input signal signal(n). On the input side, the first intermediate memory is connected to the output of the summation element 53. After each cycle, the result of the summation element 53 is stored in the first intermediate memory 50. This value corresponds to the output value of the signal processing unit 5.

[0045] A plurality of variants are provided for implementation of the coefficient block 52. On the one hand, the coefficient block may be configured as a simple memory in which the values of the coefficient which are to be used are stored. In particular, this variant is advantageous when the frequencies to be used, or the frequency band to be used, for modulation of the signal is fixed or known. It is in this case advantageous to select the frequencies, or the frequency band, in such a way that it does not cover the known perturbation frequencies. The calculation of the coefficients is preferably carried out by means of the equation

c(n)=2 cos(2*f_signal(n)/f_sample), [0046] where
n=sampling step
c(n)=coefficient for the sampling step n
f_signal(n)=carrier frequency or instantaneous frequency for the n.sup.th sampling step
f_sample=sampling frequency.

[0047] As an alternative thereto, it is possible to configure the coefficient block 52 as a computation unit, in which the values of the coefficient c(n) are calculated continuously according to the input value for the instantaneous frequency or carrier frequency f_signal(n) for each sampling step n.

[0048] The signal processing unit 5 may, as described above, be configured in terms of circuit technology in order to carry out the calculation of the intermediate steps according to the following procedure. As an alternative, however, it is also possible to configure the signal processing unit 5 as a programmable circuit and to embody the procedure by means of corresponding programming of the software. The procedure for calculating the intermediate values is carried out in the following steps:

s1=0
s2=0
repeat with n from 1 to n_max [0049] s=signal(n)+c(n)*s1s2 [0050] s2=s1 [0051] s1=s
end.
The procedure is essentially a loop, which is cycled through for the total number of sampling steps n_max.

[0052] As an initial condition, two intermediate values s1 and s2 are predefined with the values zero. A further intermediate value s is defined for the loop, the intermediate value being defined according to the equation indicated above. The term signal(n) corresponds to the modulated signal in the sampling step n, which is present here in discrete form.

[0053] The calculation of the amplitude of the signal, or of the useful signal, is carried out by means of the equation

A=2*sqrt(s2*s2+s1c(n_max)*s1*s2)/n.sub.13max.

[0054] The overall procedure comprising the calculation of the coefficient c(n), of the intermediate values s, s1, s2 and of the signal A is in each case carried out for the demodulation of a signal value. In the case of a continuous measurement, for example in the case of a sensor, the overall procedure is to be carried out for each value determined and modulated by the sensor. Since the measurement rate or a measurement cycle of a sensor lies in the range of a few milliseconds, it is advantageous to calculate the coefficients beforehand.

[0055] Advantageously, the modulation of the signal is carried out by means of the following procedure in order to achieve synchronization of the carrier frequency or instantaneous frequency between the modulation unit and the signal processing unit. The nomenclature of the terms corresponds to the definitions indicated above.

s1=0
s2=sin(2*f signal/f_sample)
repeat with n from 1 to n_max [0056] s=c(n)*s1s2 [0057] s2=s1 [0058] s1=s [0059] signal(n)=s
end.

[0060] A simulation was carried out with the method according to the invention. Some visualizations of the simulation are shown in FIGS. 3 and 4. FIG. 5 shows a comparison of the deviations of the demodulated signal according to the method according to the invention and according to the already known Goertzel algorithm.

[0061] A sampling rate of 1 MHz (A/D and D/A converters) and a measurement cycle of 1 ms were selected for the simulation. The total number of sampling steps is n_max =1MHz*1 ms =1000 sampling steps per measurement cycle. The frequency of the amplitude-modulated carrier and the central frequency of the variable carrier are selected around 200 kHz. The Goertzel coefficient for the conventional solution is cAM =0.6180. For the solution according to the invention, the instantaneous frequency should oscillate around the central frequency, and the average value of the coefficient field cFM(1 nmax) is therefore likewise cAM. This formally corresponds to frequency modulation.

[0062] For the simulation, a curve shape was selected for the coefficient and the carrier signal was established as a function of the curve shape of the coefficients. A triangular oscillation was selected as the curve shape for the frequency modulation, because this oscillation leads to a uniform spectral density of the resulting oscillation. When using a sinusoidal oscillation, the instantaneous frequencies at the ends of the spectrum used would be more frequent than those in the middle, while equidistribution can be achieved inter alia with the triangular shape. The triangular shape is in no way a prerequisite for the solution according to the invention, although uniform use of the spectrum used is always to be regarded as advantageous when there is no information about the system (application system, transmission medium, expected perturbations, etc.) leading to different metrological use of different frequencies in the spectrum used. The values of the coefficient field cFM(1 . . . nmax) may be selected freely, and the amplitude of the triangular shape is therefore also freely selectable. Higher amplitudes lead to the use of a broader spectrum. For the reasons discussed above, it is necessary to carry out an appraisal between the advantages and disadvantages of a broadband configuration. The compromise selected for this exemplary embodiment is graphically represented in FIG. 3. The cFM values as a function of the index n can be found in the figure. The associated amplitude spectrum is shown in FIG. 4. The choice of the coefficient field therefore leads to approximately uniform use of a band of about 60 kHz at 20030 kHz.

[0063] The coefficient field is now used in order to determine the sample values of the excitation function with the aid of the inverse Goertzel algorithm. The result is stored and the values are sent successively to a D/A converter. When the end of the field is reached (which is equivalent to the end of the measurement cycle), in the case of continuous operation of the system a start is made again at the beginning of the field. The excitation signal is sent to the sensor via an amplifier. For example, a current may be given to the sensor as excitation and a voltage may be tapped from the sensor, or a voltage may be applied and the current may be measured. The signal modulated by the sensor is sent to an A/D converter. A Goertzel filter is then implemented with the samples by using the same coefficient field. If the same coefficient (i.e. the one with the same index) is used for each step (A/D and D/A), then the two parts are synchronized in terms of their instantaneous frequency, as represented in FIG. 1.

[0064] Compared with conventional AM with sinusoidal excitation, only the memory and the indexing are to be listed as additional outlay. The requirement of achieving a reduction of the perturbations with low circuit outlay is therefore satisfied.

[0065] The advantage may be shown by carrying out calculation of the signal processing steps in a Monte Carlo simulation. To this end, in each cycle, a perturbation that is determined by a random generator is added to the signal of the sensor. In the present case, the perturbation is the sum of white noise (broadband) and a sinusoidal signal (narrowband), the phase and frequency of which (between 150 and 250 kHz) are random. This signal has an amplitude which is 5% of the amplitude of the sensor signal. The noise has an equally large RMS value. After 106 cycles, the frequency distribution of the error (i.e. the deviation from the sensor signal) of FIG. 5 is obtained.

[0066] Although the solution E according to the invention numerically has a higher number of deviations in the range of up to 2%, the number of deviation tends toward zero in the range above 2%.

[0067] The Goertzel algorithm G known from the prior art also has a low number of deviations above 2%. The deviations range up to about 6%. For the application in measurement technology, this is a substantial disadvantage in comparison with the method according to the invention. The invention is not however restricted to application in sensors, even though this application field is particularly advantageous.