EP0697149A4

EP0697149A4 - Active cancellation of noise or vibrations

Info

Publication number: EP0697149A4
Application number: EP19930909299
Authority: EP
Inventors: Jaime I Chait
Original assignee: Active Noise and Vibration Technologies Inc
Current assignee: Active Noise and Vibration Technologies Inc
Priority date: 1992-04-10
Filing date: 1993-04-09
Publication date: 1995-12-20
Also published as: AU3976493A; EP0697149A1; CA2117803A1; WO1993021688A1

Abstract

An active noise cancellation system processes a residual signal (r), generated by the interaction of a noise signal (p) and a cancelling signal (s), in the frequency domain so as to produce a new cancelling signal. A Fourier transformer (5, 8) operating in accordance with a moving discrete Fourier transform algorithm is used to produce a frequency domain representation of the residual signal.

Description

Active Cancellation of Noise or Vibrations

FIELD OF THE INVENTION The present invention relates to active cancellation of noise or vibrations.

BACKGROUND TO THE INVENTION

One method of effecting active noise cancellation is described in US Patent No. 4 490 841 which is hereby incorporated by reference. The system described therein transforms a residual signal, resulting from the superposition of a noise signal and a cancelling signal, from the time domain into the frequency domain wherein it is represented by fourier coefficients. The fourier coefficients are then used to calculate a further set of fourier coefficients from which the cancelling signal is generated by an inverse fourier transformer.

Many noise or vibration cancellation systems, including that referred to hereinbefore, employ fast fourier transforms to convert from the time domain to the frequency^* domain. The fast fourier transforms are digitally implemented and the transformation process is carried out on a block of N samples. Therefore, the system cannot respond properly until NΔ.t after the change __ has occurred, whereAt is the time between successive samples. Thus a step change in the noise signal results in a sharp rise in the amplitude of the residual signal which is then reduced in a stepwise manner as effective cancellation is re-established. This stepwise decay of residual signal has been found to be undesirable by users of such systems.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an improved active noise or vibration cancellation system which exhibits a non-stepwise decay of residual signal during establishment of effective cancellation.

According to the present invention, there is provided an active vibration cancellation system including means responsive to a residual vibration signal to produce an electrical signal representative thereof, sampling means for sampling said electrical signal and a fourier transformer means for processing the sampled electrical signal to produce a frequency domain representation of the residual vibration signal, wherein the fourier transformer means performs a moving discrete fourier transformation on the sampled electrical signal to produce said frequency domain representation of the residual vibration signal.

In an embodiment, the frequency domain representation is only a partial representation. The partial representation may comprise a limited number of, possibly predetermined, harmonics. This avoids the need for unnecessary processing where a particulax noise source includes only a limited number of harmonics which need to be suppressed.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is block diagram of a single-input/ single-output system according to the present invention;

Figure 2 is a block diagram of a first embodiment of a multi-input/multi-output system according to the present invention; and Figure 3 is a block diagram of a second embodiment of a multi-input/multi-output system according to the present ivnention.

DESCRIPTION OF EMBODIMENTS

A source of noise such as an internal combustion engine

1 generates primary vibrations p which propagate into the neighborhood of a microphone 2. A loudspeaker 3 generates secondary vibrations s which interact with the primary vibration p in the neighborhood of the microphone 2.

The microphone 2 outputs an electrical signal r which represents the residual sound wave produced by the interaction of the primary vibrations p and the secondary vibrations s. The output from the microphone

2 is amplified by an amplifier 10 filtered by a low pass filter 11. The filter output is then digitised by an A to D converter 4 to produce a signal r' at 15 which is transformed into the frequency domain by a first fourier transformer 5. An electrical signal representing the fourier coefficients of the signal r' is fed to a processor 6. The processor 6 also receives a synchronisation signal from a synchronisation signal generator 7 which generates the signal synchronisation signal in dependence on the operation of the internal combustion engine 1.

The fourier coefficients received by the processor 6 are modified in a manner described hereinafter to provide modified fourier coefficients which are fed to a second, inverse fourier transformer 8. The second fourier transformer generates a digital time domain signal s ' at 16 in dependence upon the fourier coefficients supplied to it. A D to A converter 9 constructs an analog signal from the digital time domain signal. The constructed analog signal is filtered by a low pass filter 13, amplified by an amplifier 14 and fed to the loudspeaker 3 which produces the secondary vibrations s in accordance therewith. The operation of the processor 6 is such that the secondary vibrations s will tend to be equal in amplitude but opposite in phase to the primary vibrations p in the neighbourhood of the microphone 2. The operation of the first fourier transformer 5 will now be described in more detail. The digitised residual signal r forms a set of N complex numbers r{k} where k -= 0, 1, 2 , ..., N-l. ^ t is selected such that the Nyquist criterion is satisfied for the highest frequency harmonic of interest. The well known discrete fourier transform (DFT) of r{k is the set of complex number R{m)-_Λ m =- 0, 1, 2, ..., N-l defined by:

N-l

R_m ^■= X, r_v W mk ^rk^W , = 0, 1, 2, ..., N-l (1)

k=0

where W = exp (-j 2 π/N) and m represents the harmonic being considered. Conventionally, the set of values R{m} would be calculated for each block of N samples. However, the set of complex numbers R{m} could be recalculated as each sample is digitised by adding the new sample to the set r{k} and discarding the oldest sample; that is create a "moving" DFT. In practice, recalculating the set R{m> in this way - 1 - introduces an unacceptable overhead into the processing. However, if R (k) is the mth frequency

component of the DFT of the kth sequence of r, i.e.

{r^, ..., r^, _N-_l-** ^{tnen R caπ} be expressed

( ]r ) recursively in terms of Rm ' as follows:

Rm (^k+l)₌ [ r*_R. ("") "_ ^rr_k, ^♦+ ^r. ^W^ W

Thus, it can be seen that producing the fourier coefficients of the residual signal in the manner defined by equation (2) eliminates much of the processing overhead which would be expected if the fourier coefficients were to be calculated directly from the N samples on each occasion. Furthermore, the new fourier coefficient for each harmonic is only dependent on the previous value for that harmonic, the kth sample of the residual signal r, and the (k+N)th sample of the residual signal r. The fact that the fourier transform for a given harmonic is not a function of any other harmonic makes this approach well suited to systems where only selected harmonics require cancellation.

Equation (2) is known from "Efficient DFT-Based Model Reductions for Continuous Systems", IEEE Transactions on Automatic Control, vol. 36, No. 10, ppll88-1193 and "On-Line Determination of Reduced-Order Models of Linear Systems Via the Moving Discrete Fourier Transform (MDFT)", ICAS "89, ppl796-1799. However, it has not been proposed, heretofore, to apply moving discrete fourier transforms to the active cancellation of noise or vibrations. The independance of the calculations for each harmonic from that of any others is a major benefit in noise cancellation systems which must process signals in real time. Reducing the amount of processing, required to produce a given effect, results in the extension of the cancelling capabilities of a system based on a particular processor or the option to use devices of a lower specification to achieve the same effect. A system embodying the present invention responds to a rapid change in the primary vibrations by producing a smooth decay in the resultant residual signal rather than the stepped decay found with the prior ar .

The operation of the processor 6 will now be described in more detail. The transfer function of the path between the output 16 of the second fourier transformer 8 and the input 15 of the first fourier transformer 5 is stored for use by the processor 6. The transfer function may be predetermined or dynamically determined by the processor from detected changes in the signal r' in response to known changes in the signal s ' . Thus the transfer function of the path between output 16 of the second fourier transformer 8 and input 15 of the first fourier transformer 5, TF, can be defined as follows:

TF = change in signal s ' resulting change in signal r' = a + jb m + jn where a is the amplitude change of the sine components - 10 - of the signal s' , b is the amplitude change of the cosine component of the signal s' , m is the resultant amplitude in the sine component of the signal r' and n is the amplitude change in the cosine component of the signal _^ r¹. Thus for a measured signal r' of (p+jq) where p is the amplitude of the sine component of r' and q is the amplitude of the cosine component of r'_r the required change in signal s' = pfam+bnl+qfan-bnrQ+ir fbm-an)+qfam-ι-bn) 1 m^z + n²

The processor 6 receives the fourier components from the fourier transformer 5 and calculates the necessary change in fourier components of the signal s' based thereon and on the known transfer function of the path between the output 16 of the second fourier transformer 8 and the input 15 of the first fourier transformer 5. The fourier components of the changed signal s' are then fed to the second, inverse fourier transformer 8 in order to produce a digital time domain signal, which, after conversion to analog form by the D to A converter 9, is used to produce the cancelling signal s to effect cancellation. Referring to Figure 2, a two channel system is shown wherein a plurality of microphones 22 are associated with respective loudspeakers 23, for instance in the headrests of the seats in an airliner. Each of the microphones 22 is coupled to a respective analog to digital converter 24 via perspective amplifiers 30 and low-pass fitters 31. The first fourier transformer 5, operating in accordance with a MDFT algorithm, receives signals from the analog to digital converters 24 and outputs electrical signals representing the fourier coefficients of the signals r' at the inputs to the first fourier transformer 5, which are derived from the residual signals r detected by the microphones 22, to the processor 6. Since each microphone 22 is substantially only affected by its associated speaker 23, the processor 6 operates as described hereinbefore, carrying out the necessary processing of each signal r' independently. The modified fourier coefficients are fed to a second fourier transformer 8 which outputs time domain signals to respective digital to analog converters 29. The analog signals created by the digital to analog converters 29 are then passed through respective low-pass fitters 32 and amplifiers 33 to the speakers 13.

Referring to Figure 3, which shows a third embodiment of the,, present invention, suitable for cancelling noise within a volume such as the cabin of a car, a plurality of microphones 42 are distributed about a volume in which noise is to be cancelled. A similar number of loudspeakers 43 are also distributed around the volume. The arrangement of microphones 42 and speakers 43 is such that each microphone 42 is influenced by more than one of the loudspeakers 43. The outputs from the microphones 42 are again amplified and filtered by amplifiers 50 and low-pass filters 51 and then digitised by respective analogue to digital converters 44. However, a time division multiplexer 40 is interposed between the analogue to digital converters 44 and the first fourier transformer 5. The first fourier transformer operates in accordance with a MDFT algorithm. The signals output by the first fourier transformer 5 are again passed to a processor 6. The processor 6 processes these signals taking into account the fact that each microphone 42 responds to more than one speaker 43. The operation of the processor 6 will be described in more detail hereinafter.

The modified fourier coefficients output from the processor 6 are treated in substantially the same manner as described with reference to Figure 2. However, a demultiplexer 31 is interposed between the second fourier transformer 8 and the digital to analog converters 49. The constructed analog signals output from the digital to analog converters 49 are filtered and amplified by respective low-pass filters 52 and amplifiers 53.

Since each microphone 42 responds to more than one speaker 43, the processor 6 determines the desired change in the signals s ' at the output of the second fourier transformer 8, according to the following algorithm:

where s ' to si are the necessary changes in the

signals output by the second fourier transformer 8 to drive respective speakers 1 to i, r. to r. are the

signals r* derived from the residual signals r from the microphones 1 to j and TF-, to TF.. are the transfer

functions of each path from the output of the second fourier transformer 8 to the input of the first fourier transformer 5.

For instance, the first row of the transfer function atric contains ^"the transfer functions of the paths including speaker 1 and respectively each of the microphones 1 to j.

In certain circumstances, the functions of the fourier transformers 5, 8 and the processor 6 may be combined, for instance into a microcomputer running under the control of a suitable program.

It is appreciated that the system described with reference to Figure 2 may be implemented using a multiplexer and demultiplexer and that the system described with reference to Figure 3 may be implemented using the arrangement of elements shown in Figure 2.

Whilst the present invention has been described with reference to an internal combustion engine, microphones and loudpseakers, the present invention may be employed to cancel the noise or other cyclic vibrations from various signals and that other forms of transducers may be used in place of microphones and loudspeakers.

Claims

WHAT IS CLAIMED IS:

1. An active noise or vibration cancelling system for cancelling a substantially periodic noise signal, including: processing means for producing a cancelling signal for cancelling^' said noise signal in dependance on a frequency domain representation signal; means for producing a residual signal representative of the sum of said noise signal and said cancelling signal; means for sampling said residual signal to produce a sampled signal representative of said residual signal; and transformer means for transforming said sampled signal by moving discrete fourier transformation to produce a frequency domain representation signal of said residual signal to control said processing means.

2. A system according to claim 1, wherein said processing means includes a processor for producing a frequency domain representation signal of a cancelling signal in dependance on said frequency domain representation signal of said residual signal, and inverse transformer means for producing said cancelling signal from said frequency domain representation signal of a cancelling signal.

3. A system according to claim 1, wherein the frequency domain representation signal is a partial representation of said residual signal in the frequency domain.

4. A system according to claim 3, wherein the frequency domain representation signal represents the components of said residual signal at predetermined harmonics of a noise fundamental frequency.

5. A system according to claim 1, wherein said means for sampling includes means for digitizing said sampled signal, whereby said sampled signal is in digital form.

6. A system according to claim 1, wherein the means for processing said sampled signal processes said sampled signal according to the algorithm:

m ^• =[R (*), m ^"rk^+r(k+N)j W where: R ' is the mth frequency component of the

discrete fourier transform of the kth sequence of r which is a sampled signal representative of a residual noise signal,

R ^• ' is the mth frequency component of the

discrete fourier transform of the (k-KL)th sequence of r, r, is kth sample of the residual noise signal,

r., _N. is the (k+N) the sample of the residual

noise signal, and

7. An active noise or vibration cancelling system for cancelling a substantially periodic noise signal including: processing means for producing a plurality of cancelling signals for cancelling substantially periodic noise signals, having a common source, at different respective locations in dependance upon frequency domain representation signals; a plurality of means for producing respective residual signals representative of the sum of said cancelling signals and one of said noise signals at each of said locations; a plurality of means for sampling respective said residual, signals to produce a plurality of sampled signals; and transformer means for transforming said sampled signals by moving discrete fourier transformation to- produce a frequency domain representation signal for each of said residual signals for controlling said processing means.

8. A system according to claim 7, wherein said processing means includes a processor for producing frequency domain representative signals of a cancelling signal in dependance upon said frequency domain representative signals of said residual signals and inverse transformer means for producing said cancelling signals from said frequency domain representing signals of a cancelling signal. 9. A system - according to claim 7, wherein the frequency domain representation signals are partial representations of said residual signals in the frequency domain.

10. A system according to claim 9, wherein the frequency domain representation signals represent the components of said residual signals at predetermined harmonics of a noise fundamental frequency.

11. A system according to claim 7, wherein said means for sampling includes means for digitizing said sampled signals, whereby said sampled signals are in digital form.

12. A system according to claim 7, wherein the means for processing said sampled signals processes said sampled signals according to the algorithm:

where: R C^■k)' is the mth frequency component of the

discrete fourier transform of the kth sequence of r which is a sampled signal representative of a residual noise signal ,

R ^• ' is the mth frequency component of the

discrete fourier transform of the ( k+l ) th sequence of r, r, is kth sample of the residual noise signal ,

r ., _+N. is the ( k+N) the sample of the residual

noise signal , and

13. An active noise or vibration cancelling system for cancelling a substantially periodic noise signal including: processing means for producing a plurality of cancelling signals for cancelling a substantially periodic noise signal in a predetermined space in dependence upon frequency domain representation signals; a plurality of means for producing respective residual signals representative of spacially distributed sums of said cancelling signals and said noise signal; and transformer means for processing said sampled signals by moving discrete fourier transformation to produce a frequency domain representation signal for each of said residual signals to control said processing means.

14. A system according to claim 13, wherein said processing means includes a processor for producing frequency domain representative signals of cancelling signals in dependence upon said frequency domain representative signals of said residual signals, and inverse transformer means for producing said cancelling signals from said frequency domain representing signal of a cancelling signal.

15. A system according to claim 13, wherein the frequency domain representation signals are partial representations of said residual signals in the frequency domain.

16. A system according to claim 15, wherein the frequency domain representation signals represent the components of said residual signals at predetermined harmonics of a noise fundamental frequency. 17. A system according to claim 13, wherein said means for sampling includes means for digitizing said sampled signals, whereby said sampled signals are in digital form.

18. A system according to claim 13, wherein the means for processing said sampled signals processes said sampled signals according to the algorithm:

where ::: RR <^k>' ii:s the mth frequency component of the

R ' ^•' is the mth frequency component of the

discrete fourier transform of the (k+l)th sequence of r, r, is kth sample of the residual noise signal,

r.*, ... is the (k+N) the sample of the residual

noise signal, and W is exp(-j2ττ/N) . 19. An active noise or vibration cancelling system including: processing means for producing a plurality of cancelling signals for cancelling substantially periodic, noise signals, having a common source, at different respective locations in dependence upon frequency domain representation signals; a plurality of means for producing respective residual signals representative of the sum of said cancelling signals and one of said noise signals at each of said locations; a plurality of means for sampling respective said residual signals to produce a plurality of sampled signals; means for time division multiplexing said sampled signals to form a multiplex signal; and transformer means for transforming said multiplex signal by discrete fourier transformation to produce a frequency domain representation of each of said residual signals to control said processing means. 20. A system according to claim 1, wherein said processing means includes a processor for producing frequency domain representative signals of cancelling signals in dependance upon said frequency domain representative signals of said residual signals and inverse transformer means for producing said cancelling signals from said frequency domain representing signals of said cancelling signals.

21. A system according to claim 19, wherein the frequency domain representation signals are partial representations of said residual signals in the frequency domain.

22. A system according to claim 21, wherein the frequency domain representation signals represent the components of said residual signals at predetermined harmonics of a noise fundamental frequency.

23. A system according to claim 19, wherein said means for sampling includes means for digitizing said sampled signals, whereby said sampled signals are in digital form. 24. A system according to claim 19, wherein the means for processing said multiplex signal processes said multiplex signal according to the algorithm:

Rm(^k+1> = TLRm ⁾-r^rk+r^r(k+N)1] W^W"m

where: R ( ^•k ' is the mth frequency component of the

R ^•' is the mth frequency component of the

discrete fourier transform of the (k+l)th sequence of

r, is kth sample of the residual noise signal,

r., _+N. is the (k+N) the sample of the residual

noise signal, and

25. An active noise or vibration cancelling system including: processing means for producing a plurality of cancelling signals for cancelling a substantially periodic noise signal in a predetermined space in dependence upon frequency domain representation signals; a plurality of means for producing respective residual signals representative of spatially distributed sums of said cancelling signals and said noise signal; a plurality of means for sampling respective said residual signals to produce a plurality of sampled signals; means for time division multiplexing said sampled signals to form a multiplex signal; and transformer means for transforming said multiplex signal by moving discrete fourier transformation to produce a frequency domain representation signal for each of said residual signals to control said processing means.

26. A system according to claim 1, wherein said processing means includes a processor for producing frequency domain representative signals of cancelling signals in dependance uponsaid frequency domain representative signals of said residual signals and inverse transformer means for producing said cancelling signals from said frequency domain representing signals of said cancelling signals.

27. A system according to claim 25, wherein the frequency domain representation signals are partial representations of said residual signals in the frequency domain.

28. A system according to claim 27, wherein the frequency domain representation signals represent the components of said residual signals at predetermined harmonics of a noise fundamental frequency.

29. A system according to claim 25, wherein said means for sampling includes means for digitizing said sampled signals, whereby said sampled signals are in digital form.

30. A system according to claim 25, wherein the means for processing said multiplex signal processes said multiplex signal according to the algorithm:

where: R ' is the mth frequency component of the

R ' ' is the mth frequency component of the

r., _N. is the (k+N) the sample of the residual

noise signal, and

31. An active noise or vibration cancelling system for cancelling a substantially periodic noise signal, including: means for producing a cancelling signal for cancelling said noise signal in dependence upon a controlling signal; means for producing a residual signal representative of the stim of said noise signal and said cancelling signal; means for sampling said residual signal to produce a sampled signal representative of the residual signal; transformer means responsive to said sample signal to produce a frequency domain representation signal of said residual signal utilising a moving discrete fourier transform; processing means for operating on said frequency domain representation signal to produce frequency domain representation of noise cancellation signals for cancelling said residual signal; and inverse transformer means to produce in response to said frequency domain representation of the cancellation signals a time domain representation thereof, whereby to produce said cancelling signal.