Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H21/00—Adaptive networks
  • H03H21/0012—Digital adaptive filters
  • H03H21/0025—Particular filtering methods
  • H03H21/0027—Particular filtering methods filtering in the frequency domain

Definitions

• the invention relates to a method of adaptive digital filtering, in the frequency domain, of digital signals.
• Such methods are implemented in signal processing, to adapt the reception devices to changes in a time-changing transmission channel.
• Adaptive filters are therefore generally used in receivers, that is to say filters with weighting coefficients that vary over time.
• the variations in time of the weighting coefficients are defined according to an optimization criterion and these coefficients are produced by devices (generally signal processing processors or DSPs) implementing an adaptation algorithm.
• J (n) E ⁇
• this matrix is the inverse of the autocorrelation matrix of the input signals, then we obtains the recursive least squares algorithm (or RLS, from English recursive least squares).
• RLS recursive least squares algorithm
• This algorithm presents a better convergence than the LMS algorithm (the input signals being taken into account), at the cost of a much greater complexity.
• a problem with the implementation of this adaptation algorithm is the time necessary for carrying out the calculations of tf m -1 and G for each block of input signals.
• An example of implementation of this algorithm is described in document US-A-4 658 426.
• Another document IEEE, Acoustics Speech and Signal Processing Magazine, Vol. 34 No. 6 December 1986, New York, US, pages 1573-1582, entitled "Self orthogonalizing efficient block adaptive filters” proposes a block-type RLS algorithm in the time domain.
• Adaptive filtering in the frequency domain has the advantage, compared to adaptive filtering in the time domain, of considerably reducing the complexity of the implementation of adaptation algorithms. This comes from the fact that the temporal convolution is replaced in the frequency domain by a multiplication and two Fourier transforms. Consequently, a calculation in the frequency domain makes it possible to reduce both the production times of the weighting coefficients and the size of the circuits calculating these coefficients.
• the frequency domain adaptation algorithms implement adaptive block filtering, with a block dimension generally equal to the order of the filter, i.e. the number of filter weights.
• Most of the existing algorithms are of the gradient algorithm type. Examples of implementation of LMS algorithms in the frequency domain are already known.
• ER Ferrara "Frequency Domain Adaptive Filtering", Adaptive Filters, CFN Cowan and PM Grant, Eds, Englewood Cliffs, Prentice Hall, 1985, Chapter 6, pages 145-179 offers adaptive filters in the frequency domain. More particularly, figure 6.2 and the corresponding description present an adaptive filter of the LMS type in the frequency domain.
• An object of the invention is to propose an adaptive filtering method, in the frequency domain, but having a higher convergence than LMS block filtering in the frequency domain. To do this, the invention proposes to modify the calculation method blocks of weighting coefficients by taking a Hessian estimate different from the identity (that is to say from producing the input signals a model of the input, which makes it possible to improve convergence), and which does not require the recursion processing inherent in the RLS type formulation.
• the invention proposes to transpose into the frequency domain a simplified version of the method illustrated above by equation (2).
• the invention is based on the assumption that the input autocorrelation matrix practically does not change during a time interval equivalent to at least m samples, that is to say that an estimate of the autocorrelation matrix of input which is exact at a time n will be exact for at least m to 2 m time intervals later (a time interval corresponding to the time distance between two successive input signals).
• Many applications meet this hypothesis for much longer time intervals (for example the cancellation of echoes induced by a multipath propagation in the radio transmission).
• R ⁇ n is constant for at least m or 2m time intervals, then R_ (n) will be also.
• B m (k) is a matrix m * p defined by
• c m l (k) [(X p * (k) .e m (k)) H: O m _ p H] H with X p * (k) a matrix p. m including the first p rows of X m * (k).
• equation (6) the first corrective term of equation (6) is treated in a similar way to the LMS process. If we ignore the corrective term c m 2 (k) in equation (6), we find an equation of LMS type (with the only difference that the gradient constraint in the case of c m 1 (k) is different because only p elements of this vector are non-zero).
• linear convolutions of equations (4) to produce the error block and (7) for the first corrective block can be easily implemented in the frequency domain using the technique of recovery of partial recovery called overlap-save, well known in the art. skilled in the art.
• the basic idea is to treat linear convolutions by means of circular convolutions of double size, these convolutions being implemented using fast discrete Fourier transforms.
• equation (8) If we look at the second corrective term of equation (6), we can verify from equation (8) that this term has a particular structure and can be written in the form of a succession of three linear convolutions. In frequency terms, we can bring back the following formulation:
• B 2m (k) diag ⁇ FFT [b * p + 1/1 0 m _ p _ ⁇ b * p + l, p + l "* Vl, 2] T > with p + l, i the i-th element of the vector b * p + 1
• equation (10) implies five additional Fourier transforms compared to the transposition of the LMS algorithm in the frequency domain, these transforms being used to implement temporal constraints in the frequency domain.
• W 2m '(k + 1) W ? M (k) + 2 ⁇ C' 2ml (k) + 2 ⁇ C 2m 2 (k) (12) with
• the invention relates to an adaptive filtering method of time input signals, in which the filtering is carried out on blocks of m successive signals, by multiplication in the frequency domain of the Fourier transform of blocks of input signals by blocks of weighting coefficients, these blocks of coefficients being computed recursively from blocks of previous coefficients and from first and second corrective terms obtained from output signals corresponding to the filtered input signals and from the transform of Fourier of an input model, characterized in that the input model is calculated by autocorrelation.
• FIG. 1 schematically represents an adaptive filtering process in the frequency domain, according to the invention.
• FIG. 1 schematically illustrates an example of implementation of the adaptive filtering method according to the invention.
• An application of such a method is for example the cancellation of echoes in audioconference.
• Another possible application is adaptive identification in general, and in particular the identification of channels disturbed by echoes during radio transmissions.
• the order of the predictors as well as the stationarity conditions fall exactly within the hypotheses of the invention.
• the input signals x (n) are processed in blocks of m successive signals (x (n), ..., x (n + m-l)), with m integer.
• a block k of input signals (x (n), ..., x (n + ml)) will correspond to a block of m weighting coefficients (w n (k), ..., w n + m _ 1 (k)).
• the method according to the invention proposes to carry out, in the frequency domain, the adaptation of the coefficients on the one hand from a block of errors produced from the output signals (analogously to the realization in the frequency domain of an LMS type method) and on the other hand from a predictor of input signals.
• the input signals x (n) are grouped, by a series-parallel transformation 1, into signal blocks [x (km), ..., x (km + m-l)].
• Each k-th block x m (k) is grouped by a concatenation 2, with the previous block x ⁇ n (kl), then the block of 2m signals obtained is transposed in the frequency domain, by a fast Fourier transform 3 (denoted FFT).
• FFT fast Fourier transform
• X 2m (k) diag ⁇ FFT [x (km-m) .... x (km + ml)] ⁇ ⁇ and
• W 2m (k) a vector, of dimension 2m, of weighting coefficients.
• the 2m direct Fourier transform operator The 2m direct Fourier transform operator.
• W 2m (k + 1) W 2m (k) + 2 ⁇ C 2m 1 (k) + 2 ⁇ C 2m 2 (k) (12), with
• E 2m (k) an error block vector in the frequency domain, of dimension 2m, X 2m H ( k ) a diagonal matrix of dimension 2m.2m obtained by Hermitian transposition 8 of X2m ( k ) '
• I D identity matrix of dimension p 0 0 p integer less than m
• B 2m (k) matrix of dimension 2m defined by:
• the corrective term C 2 m 2 ( k ) corresponds to a modeling of the input signals.
• the invention is based on the assumption that the input autocorrelation matrix practically does not change during a time interval equivalent to at least m samples, that is to say that an estimate of the autocorrelation matrix of entry which is exact at a time n will be exact for at least m to 2.
• m later time intervals (a time interval corresponding to the duration between two successive input signals), or even more.
• Many applications meet this hypothesis for number 1.
• m much longer time intervals for example the cancellation of echoes induced by a multipath propagation in the hertzian transmission). Consequently, we consider groupings in a concatenator 16 of 1 successive blocks of input signals.
• correlator 17 a known method known as autocorrelation is used in a correlator 17 (described for example in "Digital Spectral Analysis with Applications", by S.L. Marple, Prentice Hall, New Jersey, 1987).

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• 1995
  • 1995-09-08 FR FR9510568A patent/FR2738692B1/fr not_active Expired - Fee Related
• 1996
  • 1996-09-09 WO PCT/FR1996/001378 patent/WO1997009782A1/fr not_active Application Discontinuation
  • 1996-09-09 EP EP96931093A patent/EP0848867A1/de not_active Ceased

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