United States Patent
`Eatwell
`
`[19]
`
`l|||||||||||||llllllll||||||||||||||||ll||l|l||||||||||||||||l|||||l||||||!
`USOO5553153A
`[11] Patent Number:
`[45] Date of Patent:
`
`5,553,153
`Sep. 3, 1996
`
`[75]
`
`[54] METHOD AND SYSTEM FOR ON-LINE
`SYSTEM IDENTIFICATION
`Inventor: Graham P. Eatwell Cambridge United
`Kjngdom
`[73] Assignee; Noise canceuation Tec1mo1ogies, Inc”
`Linthi
`, Md.
`Cum
`[2]] Appl_ No_. 15,195
`
`IEEE Transactions of Information Theory. “Polyphase
`Codes with Good Periodic Correlation Properties.” David
`Ch“ ’“1- 1972 PP- 531“535-
`Adaptive Signal Processing Bernard Widrow and Samuel
`Stearns. Prentice Hall, Inc. 1985, Table of Contents.
`Active Control ofSound. Nelson and Elliot. Academic Press.
`1992, Table of Contents.
`
`[22]
`
`Filed:
`
`Feb. 10, 1993
`
`Primary Examiner—Curtis Kuntz
`Assistant EW"'W—Pin8 W- L66
`
`
`
`A61F 11/06
`Int C15
`[51]
`.. ......... 381/71
`.... ... ..... . ....
`[52] U.S. Cl.
`[58] Field of Search ........................................ .. 381/71, 94
`
`[56]
`
`References Cited
`
`[57]
`
`ABSTRACT
`
`4,677 676
`4,953,217
`
`U.S. PATENT DOCUMENTS
`6,1987 Efikssom
`8/1990 Twiney et al.
`‘Ii; 1Z)‘e°1%":;eJ:-t
`
`............................ 381/71
`
`
`OTHER PUBLICATIONS
`IBM J. Research and Development “Periodic Sequences
`with Optimal Properties for Channel Estimation and Fast
`Start Up Equalization” A. Milewski. pp. 426-430. Vol. 27
`No. 5 Sep. 1983.
`
`This invention relates to an improved method of on-line
`system identification for use with active control systems
`which requires less computation and reduces the problem of
`coefficient jitter in the filters of the active control system by
`using a fixed test signal which is designed to have a
`particular power spectrum.
`
`18 Claims, 4 Drawing Sheets
`
`CONTROLLER
`DISTURBANCE
`OUTPUT
`
`STDRED
`TEST
`5 IGNAL
`
`
`
`
`uln)
`
`CONTROLLER
`OUTPUT
`
`DISTURBANCE
`dln)
`
`STORED
`TEST
`
`SIGNAL
`
`TO CONTROLLER
`
`1
`
`APPLE 1027
`
`1
`
`APPLE 1027
`
`

`
`U.S. Patent
`
`Sep. 3, 1996
`
`Sheet 1 of 4
`
`5,553,153
`
`34
`4
`I8
`
`6\
`FEEDBACK
`56
`ERROR
`cfiipur
`PATH
`~——-—
`
`,5
`
`“um
`'F I LTER
`
`RANDOM NOISE
`SOURCE
`
`48
`
`2
`
`

`
`U.S. Patent
`
`Sep. 3, 1996
`
`Sheet 2 of 4
`
`5,553,153
`
`u._oz<mmEma
`
`E6
`
`._<zu_mEm:
`
`E;
`
`
`
`.5...ézem$5
`
`
`
`m.Sn_z_mZ<w.2
`
`
`
`mmI._.oZO_.._.n_<D<
`
`mm.:oEzoo
`
`._.:n_._.:o
`
`3
`
`
`
`
`

`
`U.S. Patent
`
`Sep. 3, 1996
`
`Sheet 3 of 4
`
`5,553,153
`
`moz<mm3ma
`mm_._._oEz8
`
`.:%
`
`Sara
`
`H._m8.m
`
`._<z..:m
`
`Gm:
`
`oz:om9a<m
`
`zo_E<o<
`
`4
`
`

`
`U
`
`ma
`
`S
`
`m3:
`
`.m
`
`4
`
`
`
`p_as._.:n_.SoSm_oz<m%B:_mm.:oEz8
`
`Mzo_E<o<m oz=om9a<m
`
`%+
`
`m t+.:23“..E;n+
`+\-5..m_82
`
`
`
`fi,rjmo,
`
`
`
` 3%50M,E._._oEz8E{D0_n_5_
`
`.---r
`
`{LmE<.s_2:8<
`
`as.\+25
`
`5
`
`
`

`
`1
`METHOD AND SYSTEM FOR ON-LINE
`SYSTEM IDENTIFICATION
`
`5,553,153
`
`2
`
`BACKGROUND
`
`This invention relates to a technique for on-line system
`identification primarily for use with active control systems.
`A review of systems for active control of sound is given in
`“Active Control of Sound" by P. A. Nelson and S. J. Elliott,
`Academic Press, London. Most of the control systems used
`for active control are adaptive systems, wherein the control-
`ler characteristics or output
`is adjusted in response to
`measurements of the residual disturbance. If these adjust-
`ments are to improve the performance of the system, then
`knowledge is required of how the system will respond to any
`changes. This invention relates to methods for obtaining that
`knowledge.
`Usually the system is characterized by the system impulse
`response, which is the time response at a particular control-
`ler input caused by an impulse at a particular output. The
`response therefore includes the response of the input and
`output processes of the system, such as actuator response,
`sensor response, smoothing and anti-aliasing filter responses
`etc. For multichannel systems, which have more than one
`input and/or output, a matrix of impulse responses is
`required, one for each input/output pair. For a sampled data
`representation the impulse response between the j-th output
`and the i-th input at the n-th sample will be denoted by a'7(n).
`Equivalently, the system can be characterized by a matrix
`of transfer functions which correspond to the Fourier trans-
`forms of the impulse responses. These are defined, for the
`k-th frequency, by
`_
`N—l
`ut'j(k) = 2 a'7(n) - exp(2z'kn1t/N),
`n=0
`
`(1)
`
`where the k-th frequency is (k/NT) Hz and T is the sampling
`period in seconds.
`The most common technique for system identification is
`to send a test signal from the controller output and measure
`the response at the controller input. In order to discriminate
`against other noise in the system, a random test signal is
`normally used, and this is correlated with the response.
`Other noises which are not correlated with the test signal are
`rejected.
`In “Adaptive Signal Processing” by B. Widrow and S. D.
`Stearns, Prentice Hall, (1985), several adaptive schemes for
`system identification (or plant modeling) are described.
`Provided that the test signal is uncorrelated with other
`system noise, the system identification can continue while
`an active control system is in operation. In U.S. Pat. No.
`4,677,676 by L. J. Eriksson this is described for a single
`channel active control system in a duct. This system is
`typical of the prior art and is summarized in FIGS. 1 and 2.
`FIG. 1 shows the system identification system and control
`system in a duct or pipe. FIG. 2 shows the equivalent block
`diagram. These correspond to FIGS. 19 and 20 in the
`original document.
`It is not recognized in Eriksson that the residual signal (44
`in the Figures) used to adapt the control filters is contami-
`nated by the test signal. This will cause the system to try to
`adapt
`to cancel
`the test signal—resulting in a random
`variation or ‘jitter’ in the filter coefiicients. This results in a
`reduced performance.
`A further aspect of Eriksson and similar approaches is that
`on-line system identification is an adaptive filter and at each
`sampling interval every coefficient of the impulse response
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`is updated. This is a computationally expensive operation
`and, since the signal processor has fixed processing power,
`this will slow down the maximum sampling rate of the
`controller and reduce its performance. Another aspect of
`Eriksson and similar approaches is that a random test signal
`(or noise source) is used.
`
`SUMMARY OF THE INVENTION
`
`This invention relates to an improved method and system
`of on-line system identification which requires less compu-
`tation and removes the problem of coeificient jitter.
`In contrast to the prior art, which describes the use of a
`random, uncorrelated test signal, the system of this invention
`uses a fixed test signal. The use of a fixed test signal reduces
`the computational requirement of the system identification.
`The model of the system response can be updated using an
`accumulated response signal or an accumulated error signal.
`In another aspect of the invention, a means is provided for
`estimating the effect of the test signal and subtracting this
`from the residual (error) signal used to adapt the control
`system This greatly reduces the problem of coefiicient or
`weight jitter.
`In another aspect of the invention, the system identifica-
`tion is performed at a rate which is diifcrent to the rate of the
`control filters.
`
`Accordingly, it is an object of this invention to provide an
`improved method of on-line system identification which
`requires less computation and removes the problem of
`coefiicient jitter.
`Another object of this invention is to use a fixed test signal
`to reduce the number of computations required in a system
`identification.
`
`A still further object of this invention is to estimate the test
`signal effect and subtract that from the error signal
`in
`adapting the control system.
`These and other objects of this invention will become
`apparent when reference is had to the accompanying draw-
`ings in which
`FIG. 1 is a diagrarrunatic View of the circuitry of US. Pat.
`No. 4,677,676,
`
`FIG. 2 is a diagrarrunatic view of the circuitry of U.S. Pat.
`No. 4,677,676,
`
`FIG. 3 is a diagrammatic view of the control system of
`this invention incorporating on-line system identification,
`FIG. 4 is a diagrammatic view of the system identification
`circuit using accumulated response, and
`FIG. 5 is a diagrammatic view of the circuit using
`accumulated error.
`
`DETAH_.ED DESCRIPTION OF THE
`INVENTION
`
`The system identification system of this invention is
`primarily for use with sampled data systems (either analog
`or digital).
`The invention will be described with reference to a single
`channel system, although it can be easily extended to
`multichannel systems.
`By way of explanation, we will first consider the case
`where the system can be modeled by a Finite Impulse
`Response (FIR) filter with coeflicieuts a(n).
`
`6
`
`

`
`3
`
`4
`
`5,553,153
`
`The response at sample n to a test signal produced from
`the sequence of controller outputs, y(n), is
`
`d
`— MEI
`u(n) —— m=O a(m) - y(n — m) + (n),
`
`i
`
`(2)
`
`Where M is the number of coeflicients in the filter and d(n)
`is the component of the response not due to the test signal,
`y(n). (d(n) also contains any unmodeled response.
`The Least Squares estimate of the system impulse
`response can be obtained by correlating the response, u, with
`tho output signal, this gives the cross-correlation
`
`M—l
`<y(i)u(It)> = "E0 a(m) ' <}’(i)y(n - m)> + <}’(l7d(n)>,
`
`(3)
`
`where the angled brackets <.> denote the expected value.
`The last term can be ignored provided that the test signal is
`uncorrelated with the noise d(n). Equation (3) is a matrix
`equation for the coelficients a(m) which can be solved
`directly or iteratively. The LMS iterative solution is given by
`
`a,-+1(k)=a,(k)—u.<r(n).y(n—k)>+u.<u(n)y(n—k)>,
`
`(4)
`
`where a,.(k) is the estimate of the k-th term in the impulse
`response at the i-th iteration and where r(n) is the estimated
`response to the test signal given by
`M—l
`r(n)= >2 a.(m)-y(n—m).
`m=O
`
`(5)
`
`and I1 is a positive convergence parameter.
`In the stochastic or noisy LMS adaption algorithm the
`correlations are estimated over a single sample, and the
`angled brackets in equation (4) can be removed to give
`
`10
`
`15
`
`20
`
`25
`
`30
`
`arbitrary. They can be chosen to minimize the peak value of
`the signal, for example. Two articles describing this are
`“Polyphase Codes with Good Periodic Correlation Proper-
`ties”, by D. C. Chu, IEEE Transactions on Information
`Theory, July 1972, pp 531-532, and “Periodic Sequences
`with Optimal Properties for Channel Estimation and Fast
`Start—Up Equalization”, by A. Milewski, IBM Journal of
`Research and Development, Vol. 5, No. 5, Sept. 1983, pp
`426—431. Alternatively, the coeflicients ej can be chosen to
`shape the spectrum of the test signal so as to make it less
`noticeable or to give a more uniform signal to noise ratio.
`According to one aspect of this invention an impulsive
`test signal is used. This test signal is zero unless n is a
`multiple of M, in which case y(n)=+/—L. Here L is the level
`of the test signal and the sign of the signal is varied in a
`random or prescribed manner. This signal is obtained by
`setting all of the phase angles in equation (9) to zero.
`In equation (2) only one value of y(n~m) is non-zero, at
`m:k say, so the input is
`
`u(n)=a(k)-y(n—k)+d(n),
`
`(10)
`
`As indicated by the “+” symbol shown in FIG. 5, u(n) is
`always added to r(n) signal to produce e(n). The estimate of
`a(k) can then be adjusted using
`
`a.‘+r(k)=(1—ll)l1.(k)+l1-'4(n)/}’("‘k)-
`
`or, equivalently
`
`am(k)=a,(k)+1.1.e(n)/y(n—k).
`
`(11)
`
`(12)
`
`am(k)=a;(k)-LL[r(n)-u(n)]-y(n-k).
`
`35
`
`(6)
`
`where e(n) is the diflerence between the actual response and
`the expected response
`
`or, if the test signal is a random sequence with an autocor-
`relation which is a delta function,
`
`€(n)=u(n)-a.(kJy(n-k)-
`
`(13)
`
`a.+1(k)=(1-H)-a.(k)+u.u(n).y(n—k).
`
`(7)
`
`The algorithm in (6) is described in the “Adaptive Signal
`Processing” article, for example, and a similar approach is
`used in Eriksson’s patent. At each step (i), the response r(n)
`must be calculated, which requires M multiplications and
`additions, and all M coefficients are adjusted which requires
`a further M multiplications and additions.
`According to one aspect of the invention, a test signal is
`used which satisfies
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`Only one coeflicient of the impulse response is being
`updated at each sample time. This requires 2 multiplications
`and additions, compared to the 2><M multiplications and
`additions of previous methods.
`.
`The update can be performed in every sample interval if
`required. Alternatively, the update can be performed at a
`slower rate. The update can be done as a background task,
`where the update rate is determined by the processing power
`of the system identification circuit shown in FIG. 4.
`One embodiment of the system described by equations
`(12) and (13) and incorporated into an active control system,
`is shown in FIG. 3. In contrast to the prior art, the signal e(n)
`is used to adapt the control system rather then the signal
`u(n). This reduces the problem of weight jitter.
`Alternatively,
`the system can be estimated using the
`general block white signal. This same signal is sent out
`repeatedly, except that the sign is changed in some random
`or predetermined manner in order to decorrelate the test
`signal with any other signals. Additionally, or alternatively,
`the test signal can be delayed by varying amounts to aid
`decorrelation. Preferably, this delay is a whole number of
`sample periods. It can be achieved either by varying the
`number of samples (the gap) between each block of mea
`surcments, or by starting the test signal from a dilferent point
`within the block. Account is taken of this delay when the
`response to the signal is accumulated.
`If the sign of the test signal is changed, then two blocks
`of the signal are sent out with the same sign, and measure-
`
`L2
`0
`
`'fm=0
`‘
`otherwise
`
`M_1
`(— >=
`<
`2
`n=oyn)yn in
`This condition relates to the circular autocorrelation of the
`test signal.
`A test signal of this form is called ‘block white’ since a
`finite Fourier transform of the signal over M points will
`result in a flat spectrum. It is said to be ‘delta-correlated’
`since its autocorrelation over a block of M samples, as
`expressed by (8), is zero except at one point. One way of
`constructing such a sequence is to use
`M/2
`.
`,
`_m
`y(n)+/-2-M -L- e,- cos(2n}7t/M+¢,-)
`
`<8)
`
`(9)
`
`where eJ=1/2 if j=0 or j=M/2 and eJ=l otherwise. The phase
`angles dpj are zero for j=0 and j=M/2 otherwise they are
`
`7
`
`

`
`5,553,153
`
`5
`ments are only made in the second block. This ensures that
`real convolutions can be replaced by circular convolutions
`and so use can be made of the property in equation (8).
`Limiting the length of the block to exactly M points, so
`that it has the same length as the model filter, means that a 5
`maximum amount of time is spent measuring (which makes
`adaption to changes quicker) and a minimum of storage is
`required.
`The response at the controller input is accumulated, with
`the appropriate sign and/or delay, and then used to adapt the 10
`model of the system. One embodiment of this approach is
`shown in FIG. 4 and will now be described in more detail.
`' Variable delay is not used in this example.
`We define a number sj which is 0 if the sign has changed
`from one block to the next and otherwise is equal to +/-1 15
`depending on the sign of the j-th block. We denote the
`accumulated response at the n-th point in the block by U(n).
`We denote by uj(n) the value of the input at the n-th point in
`the j-th block. U(n) can be accumulated over N consecutive
`blocks of M samples. Using equation (2) this gives
`
`20
`
`(14)
`
`N—1
`
`S; - u,-(rt)
`
`NE1
`N—21ME1
`"=0 mzo a(m) As,-y,-(n — m) + ":0 s,--
`
`d
`,-(n),
`
`)
`NME1 (
`m=0am)-y(rL—m,
`
`U(n)
`
`=
`
`—
`
`—
`
`where
`
`N—1
`N‘: _>:
`F0
`
`Is,-I
`
`is the number of non-zero accumulations made and y(n) is
`the fixed test sequence.
`There are two ways in which the accumulated response
`U(n) can be used to calculate the coefiicients a(m). The first
`way is to correlate U with the test signal. This gives
`
`25
`
`3°
`
`35
`
`from which
`
`53;+1(k)=(1—H)5i(k)+(u/N)‘ (7(k)/§(k).
`
`(19)
`
`The coefiicients a(n) can be found from an inverse transform
`of (19), or the Fourier coeflicients can be used directly.
`The amplitudes ej can be chosen so that
`the power
`spectrum of the response to the test signal and the power
`spectrum of the residual noise have a fixed ratio. For
`example, with L=l,
`
`[ekl2=}. l?(k)|2 /lE(k)|2+min(k)
`
`(20)
`
`where 2. is a positive factor and rnin(k) is a low-level
`spectrum which can be included to ensure that the test signal
`is not zero in any frequency band and that any quantization
`errors in the digital system do not have too large an effect.
`The estimates of the modulus of the residual signal f(k)
`can be obtained recursively to cope with changing signal
`statistics.
`
`Alternatively, the coeflicients ej can be chosen so that the
`response to the test signal is white, but the power level, L,
`can be chosen to be proportional to the power in the residual
`signal. Alternatively, the coeflicients can be chosen to give
`any other desired frequency spectrum.
`The averaging process used in the above techniques
`allows for small test signals to be used, which reduces the
`effects of weight jitter in the cancellation filters.
`In an altemative approach, the efiect of the test signal is
`subtracted from the response signal.
`This new signal is used for the adaption of the cancella-
`tion filters and is accumulated for use in the adaption of the
`system model. One embodiment of this approach is shown
`in FIG. 5.
`For the adaption of the model, the difference between the
`expected response and the actual response is accumulated.
`This gives an accumulated error defined by
`
`k —m2 t
`k)—zvME1ME1
`MEI U
`M (nu-y(n— —
`n:0m=0a<m>-y(n—m)-y<n—>— .a<)
`
`(15)
`
`and so the coefiicients can be updated using
`
`a.«+1(k)=(1_—+l)a.»(k)++1a‘(k).
`
`where
`
`M—1
`a'(k)=(1/N‘L2) 2 U(n)-y(n—k).
`n=0
`
`45
`
`(16)
`
`17
`
`(
`
`) 50
`
`E(n)=N;.‘.1s'-e-(n)
`i=0 1
`I
`
`where
`
`€,~(n)=u,-(H)-r,~(n)
`
`(21)
`
`(22)
`
`The correlation and update can be done in the processor as
`a background task or by a separate processor.
`The level, L, of the test signal can be chosen with
`reference to the power in the residual signal, or the power in 55
`the cancellation signal and/or the response of the system.
`Additionally, or alternatively, it can be chosen with refer-
`ence to quantization errors in the digital system.
`The other way of calculating a(k) is via a Discrete Fourier
`transform of the accumulated values U(n) as shown in FIG. 50
`4. This approach can also be used even when the coeflicients
`of the test sequence, ej in equation (9), are not chosen to give
`a flat spectrum.
`The Fourier transform of (14) gives
`
`65
`
`l_1(k)=N'E(k)-§(k).
`
`(18)
`
`is the ‘corrected’ error signal at the n-th point in the j-th
`block and is used for the adaption. The accumulated error
`signal is related to the difference between the actual impulse
`response and the current estimate, since
`
`E(n)
`
`=
`
`=
`
`N—1
`N—1 M—1
`"310 mg) la(m) - at-(m)l - Sm-(n - m) + "530 s;- d;-(n),
`M—1
`
`(23)
`
`N‘ "F20 [a(m) -ar(m)l -y(n - In).
`
`where a,.(m) is the current estimate of the impulse response,
`which is used to calculate r(m).
`Correlating the accumulated error E(n) with the test signal
`gives
`
`M—1
`
`"E0 E(n) - y(n - k) = NU [a(k) - as(k)l
`
`(24)
`
`8
`
`

`
`7
`
`8
`
`5,553,153
`
`and the update equation for the impulse response is
`
`M—l
`a,«,1(k) = a,-(k) + (p/N'L2) - ":20 E00 - y(n — k)
`where 0<p<2 and p is chosen with reference to the ratio of
`the test signal level to the noise level.
`The corresponding frequency domain update is
`
`(25)
`
`5
`
`E;+r(k)=Ii,(k)+(pIN‘).F (k)/§.,(k)
`
`10
`
`(25)
`
`This update is performed only once every N blocks of M
`points, and so for N>l it represents a considerable saving
`over the previous methods. The update can be performed as
`a background task.
`The signal e(n) is used to update the coefiicients of the
`control filter. This is in contrast to previous methods which
`use the signal u(n) and so try to adapt to cancel the test
`signal.
`Some physical systems are more efliciently modeled as
`recursive filters rather than FIR filters. The response at the
`input is then modeled by
`M—l
`Z
`mzo a(m) -y(n -— m) +
`
`£53 1107) - r01-1?) + d(n),
`u(n) =
`where b(p) are the coefficients of the feedback filter and r(n)
`is given by equation (5). The total number of computations
`involved in calculating the estimated response to the test
`signal can often be reduced by using this type of filter.
`The techniques for adapting this type of filter are well
`known (see “Adaptive Signal Processing", Widrow and
`Stearns, for example). These techniques can easily be modi-
`fied to use test signals of the type described above.
`Having described the invention it will be obvious to those
`of ordinary skill
`in the art that many modifications‘ and
`' changes can be made without departing from the scope of
`the appended claims in which
`I claim:
`
`(27)
`
`1. An active noise or vibration control system with on-line
`system identification for identifying the response of a physi-
`cal system, said control system comprising
`control means producing control signals, said control
`means including control adaption means responsive to
`residual signals,
`
`test signal generating means for generating test signals,
`wherein the test signal generating means includes
`means for delaying or inverting a fixed test signal of
`length determined by the response time of the physical
`system, including actuator means and sensing means,
`said actuation means responsive to a combination of the
`control signals and the test signals and producing a
`canceling noise or vibration, one component of which
`counters or partially counters an unwanted first noise or
`vibration,
`said sensing means responsive to the combination of said
`canceling noise or vibration and said first noise or
`vibration and producing input signals,
`compensation filter means responsive to said test signals
`and producing compensation signals, said compensa-
`tion filter means including a filtcr adaption means
`responsive to said test signals and said residual signals
`and configured to minimize the correlation between the
`residual signals and the test signals,
`signal subtraction means for subtracting said compensa-
`tion signals from said input signals to produce said
`residual signals,
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`characterized in that the compensation signals substan-
`tially cancel the components of the input signal due to
`the test signals.
`2. An active noise or Vibration control system as in claim
`1 and including means f°r delaying the residual Signals by
`the same amount as the test signals and inverting the residual
`signals whenever the test signals the inverted so as to
`produce delayed or inverted residual signals.
`3. An active noise or vibration control system as in claim
`2, said control system including accumulation means for
`accumulating said delayed or inverted residual signals so as
`to produce accumulated residual signals.
`4. An active noise or vibration control system as in claim
`3 wherein the compensation filter means is adapted in
`response to said accumulated residual signals and said fixed
`test signal.
`5. An active noise or vibration control system as in claim
`4 wherein the compensation filter means is adapted in
`response to the product of said accumulated residual signals
`and said fixed test signal.
`6. An active noise or vibration control system as in claim
`1 and including means for delaying the input signals by the
`same amount as the test signals and inverting the input
`signals whenever the test signals are inverted so as to
`produce delayed or inverted input signals.
`7. An active noise or vibration control system as in claim
`6, said control system including accumulation means for
`accumulating said delayed or inverted input signal so as to
`produce accumulated input signal.
`8. An active noise or vibration control system as in claim
`7 wherein predicted responses to said fixed test signal are
`produced by passing said test signals through said compen-
`sation filter means and wherein the compensation filter
`means is adapted in response to said accumulated input
`signals and the predicted responses.
`9. An active noise or vibration control system as in claim
`8 wherein the compensation filter means is adapted in
`response to a Fourier Transform of said accumulated input
`signals and a Fourier transform of said test signals.
`10. An active noise or vibration control system as in claim
`8 wherein the compensation filter means is adapted in
`response to said accumulated input signals, said fixed test
`signal and said predicted responses.
`11. An active noise or vibration control system as in claim
`1 wherein said fixed test signal, y(n) at time sample n,
`satisfies
`
`M—l
`":30 .V(n)y(n - m) =
`
`L2
`0
`
`if m = 0
`otherwise
`
`wherein M is the length of said fixed test signal and L is a
`constant.
`
`12. An active noise or vibration control system as in claim
`1 wherein said fixed test signal, y(n) satisfies
`
`y(0)=L
`
`Y(n)=0. n=1,2,3, .
`
`.
`
`.
`
`, M-1
`
`where M is the length of said fixed test signal and L is a
`constant.
`
`13. An active noise or vibration control system as in claim
`1 wherein one compensation filter means is used to couple
`each actuator output with each sensor input.
`14. An active noise or vibration control system as in claim
`1 wherein said compensation filter means is a Finite Impulse
`Response filter.
`
`9
`
`

`
`9
`
`5,553,153
`
`10
`
`15. An active noise or vibration control system as in claim
`1 wherein said compensation filter means is an Infinite
`Impulse Response or recursive filter.
`16. An active noise or Vibration control system as in claim
`1 wherein said compensation filter means is a Lattice filter.
`17. An active noise or vibration control system as in claim
`1 wherein said compensation filter means is adapted less
`frequently than said control means.
`
`18. An active noise or vibration control system as in claim
`1 wherein the control adaption means and the compensation
`filter adaption means operate at a different rate to the control
`means and the adaption rate of said compensation filter
`means is determined by the processing power of said active
`noise control system.
`
`5
`
`10
`
`10