Shynk, J.J.: `Frequency-domain and multirate adaptive filtering', IEEE Signal Process. Mag., 1997, 9, (1), pp. 14--37  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and widely used among these transforms. The DFT and other transforms have been used successfully to reduce the complexity of algorithms as well as to increase convergence rates. In this section we will present a brief overview of a few of these approaches. In the Frequency Domain Adaptive Filter [12] (FDAF) use is made of the fact that a cyclic convolution in the time domain can be represented as a product in the frequency domain. The filter is in the frequency domain, and the block update contains a correction matrix to compensate for the linear convolution that actually takes place. ....

J. Shynk. Frequency-Domain and Multirate Adaptive Filtering. IEEE Signal Processing Magazine, pages 15--36, Jan. 1992.

....1999 DRAFT IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 1999 3 transform domain techniques which use the singular value decomposition (SVD) as the transform. Fast Fourier Transform based techniques were developed which take advantage of the possibility of efficient convolution [13], 14] Another form of frequency domain adaptive filters are the subband adaptive filters which also involve decimators, and can hence be termed as multirate filters [15] 16] Adaptive filtering techniques are widely used in applications such as echo cancellation, system identification, ....

....unitary transformations are DFT and DCT, and an example of a data dependent transformation is the SVD. These transforms also decorrelate the data to various degrees and this property can be used to achieve performance as well as complexity gains. The FDAF (Frequency Domain Adaptive Filter [13]) is a different manifestation of the block LMS update, which uses the fact that a convolution in the time domain can be represented as a product in the frequency domain. The subband approaches use analysis filter banks to separate the signal into different frequency bins, each being adapted by a ....

J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, pp. 15--36, Jan. 1992.

.... slow convergence due to strong spectral dynamics at the input to the equaliser [4] These characteristics have previously triggered the application of subband techniques to FS equalisers [5] based on the computational reduction, prewhitening, and parallelisation properties of the subband approach [6, 7, 8]. In this contribution, we evaluate two di erent subband architectures for FS equalisers. This includes a novel scheme for including the equaliser s feedback section into the subband domain, and the incorporation of decision directed subband equaliser structures to track channel alterations after ....

J. J. Shynk, \Frequency-Domain and Multirate Adaptive Filtering," IEEE SP Mag., 9(1):14-37, Jan. 1992.

....Both methods require the couple utilization of all frequencies for LMS adaptation in spite of the fact that some of them contain almost no information. Alternatively, the Karhunen Loeve Transform (KLT) can be applied, which orders the components by energy, but the method is not an on line algorithm[10]. We propose, in this paper, an orthogonal transform using temporal PCA learning to implement an on line and efficient LMS algorithm. It is well known that the PCA can be implemented on line by Oja or Sanger s rules [7] 9] Furthermore, data reduction can be achieved with PCA transform since the ....

....orthogonal transformation, but FFT, and DCT are preferred because they can be applied in most real time applications and fast algorithms with O(KlogK) algebraic operations, where for some positive integer q, are available. The transversal filter weights are adjusted by the classical LMS algorithm [10]: U i n ( V i n ( W i Y i n ( K 2 q N = where is the step size. 3. Transform Domain LMS Algorithm Based on Temporal PCA Learning A transform domain LMS filter is given in Figure 2. The only difference with the conventional transform domain LMS filter given in Figure 1 is that the PCA ....

Shynk, J. J., "Frequency-domain and multirate adaptive filtering," IEEE SP Magazine, Jan. 1992.

.... conventional adaptive feedforward controller models the primary path w and consists of an FIR filter whose coefficients are adapted with the so called filtered x LMS algorithm [1] Large FIR filters, as is often the case in ANC systems, can be implemented very efficiently in the frequency domain [2]. Since the individual frequency components are approximately orthogonal to each other, such a filter can be adapted very fast, if the step size is selected optimally for each individual frequency component [3] However, such a scheme uses the FFT and therefore introduces a computational delay ....

John J. Shynk, Frequency-Domain and Multirate Adaptive Filtering, IEEE Signal Processing Magazine, Jan. 1992

....subband based methods for adaptive filtering offer an alternative for enhancing the performance of conventional time domain adaptive algorithms through the use of transformations and subbands. Subband adaptive processing typically finds application in echo cancelation [10] adaptive equalization [23, 26], and in particular advanced airborne radar systems [34] where there is a need to adaptively estimate filters with a large finite impulse response (FIR) Conventional adaptive techniques such as LMS, and SMI grow computationally expensive with increased adaptive degrees of freedom (DOF) and ....

....blocks of input data, followed by adaptation in the frequency domain. The blocks are inverted back into the time domain to form the time domain output. Because of wrap around effects inherent in circular convolution, the adaptive algorithm typically converges to a suboptimal solution [26]. More sophisticated algorithms, such as the overlap save and overlap add methods implement linear convolution by a combination of sequence manipulations and FFT operations. The principle involved is that a circular convolution contains at least some samples which correspond to a linear ....

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J.J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, vol.9, no.1, pp. 14-37, Jan. 1992.

....adaptive structures, such as echo cancellation where filters with hundreds or even thousands of taps are necessary to model the echo path. Frequency domain and subband adaptive filters have been proposed to reduce the computational requirements inherent to such applications (see, e.g. 1] 2] [3], 4] These techniques not only result in more efficient structures (due to the use of efficient block signal processing methods) but they also improve the convergence rate of an adaptive algorithm (due to a decrease in the eigenvalue spread of the correlation matrix of the transformed signals) ....

....III. THE DFT BASED ADAPTIVE STRUCTURE In this section we show how the pseudocirculant structure of G(z) can be exploited to derive a well known frequency domain adaptive filter that relies on the DFT, and which is known in the literature as the multidelay adaptive filter (or MDF see [1] 2] [3]) The original derivation of this structure is different from the approach we present in this section. Our derivation is based on exploiting in a direct way the PC nature of G(z) As a fallout, the argument will suggest immediate extensions that rely on other signal transformations (such as the ....

J. Shynk, "Frequency-domain and multirate adaptive filtering," Signal Processing Mag., vol. 1, pp. 15-37, 1992.

....idea of transform domain signal processing proved to x(n) Input Block oriented preprocessing N 1 M z 1 z M Decimation y(m 1) y(m) Output 1 Figure 2. Block recursive sliding window averager scheme, n = mN , window size: MN be very efficient especially in adaptive filtering (see e.g. [2]) The contribution of this paper is directly applicable for the majority of these intensively cited algorithms. The most important practical advantage here compared to other methods is the early availability of rough estimates which can orientate in making decisions concerning further processing. ....

J.J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering", IEEE Signal Processing Magazine, pp. 15-37, Jan. 1992.

....are versions where this delay does not hurt the capabilities of the adaptation technique applied. 1. INTRODUCTION In recent years transform domain adaptive filtering methods became very popular especially for those applications where filters with very long impulse responses are to be considered [1]. The basic idea is to apply the fast Fourier Transformation (FFT) for signal segments and to perform adaptation in the frequency domain controlled by the FFT of an appropriate error sequence. There are several algorithms based on this approach [1] and further improvements can be achieved ( 2] ....

....very long impulse responses are to be considered [1] The basic idea is to apply the fast Fourier Transformation (FFT) for signal segments and to perform adaptation in the frequency domain controlled by the FFT of an appropriate error sequence. There are several algorithms based on this approach [1] and further improvements can be achieved ( 2] The formulation of the available methods follows two different concepts. The first one considers transformations as a single operation to be performed on data sequences (block oriented approach) while the other emphasizes the role of multirate ....

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J. J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering", IEEE Signal Processing Magazine, pp. 15-37, Jan. 1992.

....adaptive structures, such as acoustic echo cancelation where filters with hundreds or even thousands of taps are necessary to model the echo path. Frequency domain and subband adaptive filters have been proposed to reduce the computational requirements inherent to such applications (see, e.g. [1, 2, 3, 4]) These techniques not only result in more efficient computations (due to the use of efficient FFT implementations and block signal processing) but they also improve the convergence rate of an adaptive algorithm (due to a decrease in the eigenvalue spread of the correlation matrix of the signals ....

....0 0 0 z Gamma1 0 3 7 7 7 7 5 . 3) 3 The DFT Based Adaptive Structure The pseudocirculant structure of G(z) can be exploited to derive a known frequency domain adaptive filter that relies on the DFT, and which is known in the literature as the multidelay adaptive filter (or MDF see [1, 2, 3]) The original derivation of this structure is considerably different from the approach we present in this paper. Our derivation is based on exploiting in a direct way the PC structure of G(z) As a fallout, the argument will suggest immediate extensions that rely on other signal transformations ....

J. Shynk, "Frequency-domain and multirate adaptive filtering, " Signal Processing Mag., vol. 1, pp. 15-37, 1992.

....with respect to the desired frequency response (in terms of the behavior in various frequency bands) There has also been work on adaptive filters using a collection of frequencydomain based ideas dissimilar to those to be used here. For example, consider the frequency domain implementations [10] of adaptive filters, including LMS. The present contribution, however, assesses the frequency domain performance of a standard time domain implementation of LMS and not the time domain performance of a frequency domain LMS adaptive filter. A similarity between the behaviors of time and ....

J. J. Shynk "Frequency domain and multirate adaptive filtering" IEEE Signal Processing Magazine, vol. 9, no. 1, pp. 14--37, January 1992.

....an increase in the critical gain of 14dB has been obtained (for each phone) by using an adaptive echo canceler with 1152 taps. 1 INTRODUCTION Due to their excellent convergence behavior and their computational efficiency, frequency domain adaptive FIR filters have gained increased attraction [Shy92, Som92]. They are especially promising for real time applications where a large number of coefficients have to be adapted. In this paper, we describe the realization of a robust hands free phone using a partitioned frequency domain adaptive FIR filter with a new adaptive step size control allowing for ....

John J. Shynk. Frequency-domain and multirate adaptive filtering. IEEE SP Magazine, pages 14--37, January 1992.

....to multichannel blind deconvolution (MBD) problem. The well known cocktail party problem is one of typical examples of the MBD task. Time domain multichannel adaptive FIR filters with a number of filter coefficients need much computation if they employ sample by sample updating strategy [2] 3] [4]. One way to reduce the computational complexity is to use adaptive infinite impulse response (IIR) filters. However, they suffer from instability and local minima problems. An alternative approach is to employ block updating strategy in which the filter coefficients are kept fixed during a block ....

....(FFT) THIS WORK IS SUPPORTED BY BRAIN SCIENCE RESEARCH CENTER (BSRC) based block processing. Considerable savings in the computational complexity are achieved by performing fast convolution and correlation with a proper data sectioning technique such as the overlap save and overlap add methods [4]. In general, there are two approaches in obtaining those frequency domain adaptive filters. One is to derive them directly in the frequency domain and the other is to realize time domain block adaptive filters equivalently in the frequency domain [4] For least mean square (LMS) adaptive filters, ....

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J. J. Shynk, "Frequency-domain and multirate adaptive filtering", IEEE Signal Processing Magazine, vol. 9, no. 1, pp. 15--37, Jan. 1992.

....underlying dataflow model. We present a PCSDF model of this application in Section 6.2. 5.2. Block Adaptive Filtering In certain applications, like acoustic echo cancellation in teleconferencing, the necessity of frequency domain block adaptive filtering for computational efficiency is well known [21, 31, 16]. In Section 2.4, we had presented a PSDF model of a linear LMS adaptive filter. In this section we augment that by presenting a PSDF model of a time domain block adaptive filter and the corresponding frequency domain block adaptive filter. In a block adaptive filter, the incoming data sequence ....

....be speeded up by performing fast convolution using the overlap save or overlap add methods. It has been shown that the most efficient implementation of the fast LMS algorithm is obtained by using 50 percent overlap in the overlap save method [14] 21] describes a fast LMS algorithm, adapted from [31], that uses the overlap save method with 50 percent overlap, and with the block size chosen equal to the filter length ( A PSDF model of the fast LMS algorithm implemented in this manner is shown in Fig. 45. According to this method, the tap weights (filter coefficients) of the FIR filter are ....

J. J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, Vol. 9, No. 1, January, 1992.

.... e Gammaj2ml=L x(k Gamma m) 1) where l is an integer in the range 0 l (L Gamma 1) This system computes the lth bin value of the sliding discrete Fourier transform (DFT) of the signal x(k) Such a system is useful in spectral estimation [1] as well as in transformdomain adaptive filtering [2]. When l = 0, 1) computes the running sample average of a signal across an L element window. This ubiquitous system is useful for numerous signal processing tasks [3] 10] In addition, if x(k Gamma m) represents the squared estimation error of an N coefficient FIR adaptive filter, the ....

....the federal government, and no official endorsement should be inferred. marginally stable, and thus finite precision errors will linearly accumulate in the value of y(k) over time. If left unchecked, such errors can make (2) useless. For this reason, the following approximate system is proposed [2]: by(k) L Gamma1 X m=0 ( b e Gammaj2l=L ) m x(k Gamma m) 3) where 0 b 1. The recursive implementation of (3) is b y(k) i b e Gammaj2l=L j b y(k Gamma 1) Gamma b L x(k Gamma L) x(k) 4) which requires two multiplies and two additions per time instant. While this ....

J.J. Shynk, "Frequency-domain and multirate adaptive filtering, " IEEE Signal Processing Mag., vol. 9, no. 1, pp. 14-37, Jan. 1992.

....affine projection of the error vector E k as shown in Table 1. In our efficient implementation, we compute an approximate version of this vector using orthogonal transforms. The methods we describe are similar in both spirit and implementation to those used in frequency domain adaptive filtering [5]. We show that the approximate FAP algorithm based on the discrete cosine transform (DCT) provides similar performance to that of the original FAP algorithm while using about half the number of operations to compute the affine projection. In addition, in a finite precision environment, the ....

....worthy of further exploration in this case. 2.2. Efficient Implementations We now develop efficient implementations of the transforms to further reduce the complexity of the new adaptive filter. Our methods invoke the concept of a sliding window transform as a bank of frequency sampling filters [5]. Considering the DCT as an example, it is well known that i;k , the (i 1)th element of the DCT of the vector X k , can be calculated by passing xk through a linear, time invariant filter with transfer function H i (z) c i B i (z) A i (z) 8) where A i (z) 1 Gamma a i z Gamma1 ....

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J.J. Shynk, "Frequency-domain and multirate adaptive filtering, " IEEE Signal Processing Mag., vol. 9, no. 1 pp. 14-37, January 1992.

....x(n) Interpolation Filter A (z) 0 L Analysis Filter Bank I Decimation Filter y(n) 0 Synthesis Filter Bank A (z) 1 L Fig. 1. Subband Adaptive Filter Structure paper, present the architectural synthesis of lowpower computational engines for a subband based adaptive filtering algorithm [12] [16] Among the various adaptive filtering algorithms [6] 7] the least mean squares (LMS) algorithm [8] 9] has been extremely popular and successful. This is primarily due to the fact that the algorithm is simple and robust. However, this full band LMS adaptive filtering algorithm is con ....

J. J. Shynk, "Frequency-domain and multirate adaptive filtering," IEEE Signal Processing Magazine, pp. 14-37, Jan. 1992.

....h(k 1) h(k) XM ThetaN Gamma X T M ThetaN XM ThetaN Delta Gamma1 eN : 12) 2. TRANSFORM DOMAIN ADAPTIVE FILTERING Transform domain filtering involves a unitary transformation of the input data, and then using the transformed data as input to a normal adaptive filtering implementation [2, 4, 6]. Some of the most commonly used data independent transformations are DFT and DCT and the most commonly used data dependent transformation is SVD (or EVD) The advantages of transform domain adaptive filtering depend on exactly how transform domain filtering is implemented, but they can be either ....

J. J. Shynk. Frequency-domain and multirate adaptive filtering. Signal Processing Magazine, pages 14--37, 1992.

....of the POCS might be detrimental. Further research is required to determine the potential of this idea. ffl A frequency domain LMS algorithm was proposed in order to achieve a reduction in the computations required in the LMS algorithm. This idea is well known in the field of adaptive filters [41], and was shown to be also capable of improving the convergence properties of the adaptive algorithm. This is done by using different step size for each bin of the transformed update vector. Such an idea seems to be suitable for our implementation of the LMS, and further tests should be done in ....

J. J. Shynk, "Frequency-domain and multirate adaptive filtering," IEEE Signal Proc. Magazine, pp. 14--37, January 1992.

.... of long impulse responses, as required for acoustic echo cancellation, is unlikely to be implemented as a fullband FIR system due to computational limitations [4] Strategies to lower the computational complexity of adaptive DSP algorithms include the application of decimated subband structures [7, 3, 13], where both input and desired signal are split into a number of frequency bands, as depicted in Fig. 1. The reduced spectra allow a downsampling of the subband signals, which enables computational savings when applying adaptive filtering to the subbands. Via a synthesis bank operation, a fullband ....

J. J. Shynk. "Frequency-Domain and Multirate Adaptive Filtering". IEEE Signal Processing Magazine, Vol.9:pp.14--37, Jan. 1992.

.... advantages, as it consists of modulated versions of a single prototype filter and can be very efficiently realized, although there is a persistent opinion that polyphase implementations are only viable for integer oversampling ratios N K 2 Z [1, 8] and usually frequency domain realizations [10] of the filter banks are preferred if larger computational savings for N close to K are to be achieved. In Sec. 2 an efficient polyphase implementation extended to arbitrary integer decimation ratios N K of a complex valued oversampled generalized DFT (GDFT) is derived based on the work in [2] ....

J. J. Shynk. "Frequency-Domain and Multirate Adaptive Filtering". IEEE Signal Processing Magazine, 9:14--37, Jan. 1992.

....is the poor adaptation speed and tracking ability due to the large eigenvalue disparity typically arising in such a system. These two problems can be circumvented by using a frequencydomain LMS (FDLMS) algorithm where both filtering and adaptation are carried out in the frequency domain [2]. The linear convolution (filtering) in the time domain is derived from a cyclic convolution using the overlap save method for fast filtering. This can be implemented efficiently in the frequency domain using fast Fourier techniques [3] As is known, the DFT generates signals that are ....

....are valid only for m = 2. M . The incremental updates of the frequency domain weight vectors are: #H m [k] m [k] # X # m [k] # E [k] 13) where # denotes the complex conjugate. X # m [k] # E [k] corresponds to a cyclic correlation between the input and the error sequence [2]. The step size of the adaptation can be controlled in each frequency bin by m [k] The update equation for the adaptive coefficients is H m [k 1] H m [k] P H #H m [k] 14) where P H = F # I N 0 00 C N # F 1 (15) sets the last C N elements of #h m [k] F 1 ....

J.J. Shynk, " Frequency-domain and multirate adaptive filtering, " IEEE SP Magazine, Jan. 1992, pp. 14--37.

....Figure 1. Permutation tree structure for the ranking of 3 samples. resulting z[k] s are z[1] x 1(1) x 2(2) x 3(3) T ; z[2] x 1(1) x 2(3) x 3(2) T ; z[3] x 1(2) x 2(1) x 3(3) T ; z[4] x 1(2) x 2(3) x 3(1) T ; z[5] x 1(3) x 2(1) x 3(2) T ; z[6] = x 1(3) x 2(2) x 3(1) T : For our example, the z[k] s are given by z[1] 0; 0; 0] T ; z[2] 0; 0; 4] T ; z[3] 0; 1; 0] T ; z[4] 0; 0; 0] T ; 4) z[5] 5; 1; 4] T ; z[6] 5; 0; 0] T : In order to decompose xL into the permutation vector ensemble, we define ....

.... ] T ; z[4] x 1(2) x 2(3) x 3(1) T ; z[5] x 1(3) x 2(1) x 3(2) T ; z[6] x 1(3) x 2(2) x 3(1) T : For our example, the z[k] s are given by z[1] 0; 0; 0] T ; z[2] 0; 0; 4] T ; z[3] 0; 1; 0] T ; z[4] 0; 0; 0] T ; 4) z[5] 5; 1; 4] T ; z[6] = 5; 0; 0] T : In order to decompose xL into the permutation vector ensemble, we define a family of transformations fQ[k] j k = 1; 2; N g, where Q[k] 2 6 6 6 4 R ae 1 [k] 0 T Delta Delta Delta 0 T 0 T R ae 2 [k] 0 T Delta Delta Delta 0 T R ae N ....

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J. J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, vol. 9, pp. 14-37, Jan. 1992.

....that case, the inputs are perfectly uncorrelated and have equal power. As the eigenvalue spread 1 of the input autocorrelation matrix increases, the convergence speed of LMS deteriorates. Transform domain (also called frequency domain) LMS algorithms offer two types of solutions to this problem [4]. In block frequency domain algorithms, a block of several input data is Fourier transformed and inputted in an LMS filter. Each adaptive weight in the filter is responsible for a given frequency band, and is updated independently from the other weights as if there were many one weight LMS ....

....can also be estimated based on a sliding rectangular window, or with the help of an arbitrary linear weighting filter. More details can be found in [9] 10] 11] 3 This description of real time frequency domain algorithms differs slightly from the one often found in the literature (see e.g. [4]) In general, power normalization is included in the LMS algorithm instead of being performed on its inputs. The signals v k (i) are equal to the DFT DCT outputs, u k (i) but the learning constant in Eq. 6 is replaced by a diagonal matrix whose elements are proportional to the inverse of the ....

J. J. Shynk. Frequency-domain and multirate adaptive filtering. IEEE Signal Processing Magazine, pages 14--35, January 1992.

....to converge in a long term sense. The spectra of the frames are already computed in the feature extraction module of the speech recognition system. A frequency domain implementation of the adaptive filter was therefore more appropriate. A circular convolution frequency domain adaptive fil Z. ter Shynk, 1992 was implemented. This choice was motivated by the simplicity of this algorithm with respect to more exact algorithms. Fig. 1 describes the block diagram of the BEAF system. Assuming that the speech to additive noise ratio is relatively high and that the transmission channel acts Z. as a Linear ....

Shynk, J.J., 1992, Frequency-domain and multirate adaptive filtering.

....vector manipulations (zero padding, truncation, concatenation of vectors, to calculate one convolution. Since two convolutions are calculated at each weight update (one for the error gradient and one for the filter output) frequency domain block LMS algorithms are quite involved (see e.g. [52] for a detailed description of the algorithms) The main advantage of these algorithms in addition to their computational efficiency is their potentially very fast convergence. By attributing to each transformed weight a learning rate that is inversely proportional to the energy of the ....

J. J. Shynk. Frequency-domain and multirate adaptive filtering. In IEEE Signal Processing Magazine, pages 14--37, January 1992.

....using for generally non integer oversampling ratios K=N . This will prove an often stated misconception wrong that polyphase implementations are only viable for integer oversampling ratios (OSR) N K 2 Z [1, 8] while otherwise frequency domain realizations of the filter banks are preferred [10]. This is particularly important, since subband processing shows its highest reduction in computational complexity for OSRs close to 1. Further, we will adopt an iterative least squares method method [9, 6] to design prototype lowpass filters for GDFT modulated oversampled filter banks appropriate ....

J. J. Shynk. "Frequency-Domain and Multirate Adaptive Filtering". IEEE Signal Processing Magazine, 9:14--37, Jan. 1992.

....smaller than expected. C. Frequency Domain Adaptive Filters C.1 FDAF By applying block processing techniques, implementation cost can be exchanged for extra delay. BLMS is a block version of LMS. When it is translated in frequency domain it leads to the frequency domain adaptive filter (FDAF)[6]. The FDAF is only computationally attractive if the block length equals the filter length approximately. In practice this leads to unacceptable input output delays. C.2 PBFDAF By partitioning the adaptive filter a canceller with acceptable delay and low implementation cost can be obtained. It was ....

J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering, " IEEE Signal Processing Magazine, pp. 15--37, January 1992.

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Shynk, J.J.: `Frequency-domain and multirate adaptive filtering', IEEE Signal Process. Mag., 1997, 9, (1), pp. 14--37

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J.J. Shynk, " Frequency-domain and multirate adaptive filtering, " IEEE SP Magazine, Jan. 1992, pp. 14--37.

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J. J. Shynk, "Frequency-domain and multirate adaptive filtering," IEEE Signal Processing Mag., pp. 14--37, Jan. 1992.

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J. Shynk. Frequency--Domain and Multirate Adaptive Filtering. IEEE Signal Processing Magazine, 9(1):15-- 37, January 1992. 19

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J. J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, pp. 15--37, Jan. 1992.

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J. Shynk, 'Frequency-domain and multirate adaptive filtering,' IEEE Signal Processing Magazine, pp. 1439, Jan. 1992.

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J.J. Shynk, "Frequency-domain and multirate adaptive filtering, " IEEE SP Magazine, pp. 14-37, Jan. 1992

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J. J. Shynk, "Frequency-domain and multirate adaptive filtering," IEEE Signal Processing Magazine, pp. 14--37, Jan. 1992.

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J. Shynk, "Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, pp.15-37, January 1992.

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J.J. Shynk, "Frequency-domain and multirate adaptive filtering," IEEE SP Magazine, pp. 14-37, Jan. 1992

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J. J. Shynk, \Frequency-Domain and Multirate Adaptive Filtering," IEEE Signal Processing Magazine, vol. 9, pp. 14-37, January 1992.

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J. J. Shynk. "Frequency-Domain and Multirate Adaptive Filtering". IEEE Signal Processing Magazine, Vol.9:pp.14--37, Jan. 1992.

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Shynk, J.J., 1992. "Frequency-domain and multirate adaptive filtering", IEEE Signal Processing Magazine, Vol. 9, No. 1, pp. 14-37.

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