Frequency-domain Adaptive Filter Research Articles

Frequency domain adaptive filters using higher‐order statistics with application to adaptive time delay estimation

Frequency domain adaptive filters using higher‐order statistics with application to adaptive time delay estimation

Frequency domain adaptive filters using higher-order statistics with application to adaptive time delay estimation

Novel block-adaptive frequency domain filters based upon higher-order statistics are proposed for estimation of the parameters of a class of errors-in-variables models. The class includes moving average models as well as autoregressive models. The input to the system is restricted to be non-Gaussian with either non-vanishing bispectrum or non-vanishing trispectrum. The noise processes contaminating the input and the output measurements are assumed to be Gaussian if the input bispectrum vanishes, whereas they are allowed to be non-Gaussian with vanishing bispectra if the input has non-vanishing bispectrum. An integrated polyspectrum (bispectrum or trispectrum) of a random process is defined and exploited for adaptive parameter estimation. The integrated polyspectrum is computed as a cross-spectrum leading to substantial computational savings. Consistency of the proposed approaches is proved for the stationary case under certain mild sufficient conditions. The proposed approaches are applied to the problem of adaptive differential time delay estimation for non-Gaussian signals under spatially correlated Gaussian noise environment. Simulation results are presented to illustrate the proposed approaches.

A new method for efficient convolution in frequency domain by nonuniform partitioning for adaptive filtering

By using block processing, partitioning, and fast Fourier transforms (FFTs), large filters perform efficiently in the frequency domain. For small processing delay the complexity can still be too large for implementation on a digital signal processor (DSP). A solution is to partition the filter into unequal-length subfilters. Application in adaptive filtering yields the nonuniform partitioned block frequency domain adaptive filter (NU-PBFDAF).

A frequency domain quasi-Newton algorithm

In this paper a new frequency domain adaptive filtering (FDAF) algorithm is derived. The algorithm belongs to the quasi-Newton class of algorithms which are known to have better convergence properties as compared to gradient algorithms. The computational complexity of the new algorithm is comparable to that of the frequency-domain least mean square algorithm offering at the same time an improvement in performance, which may be significant in some practical cases.

The generalized multidelay adaptive filter: structure and convergence analysis

Frequency-domain adaptive filters have long been recognized as an attractive alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. New frequency-domain LMS adaptive schemes have been proposed. These algorithms essentially retain the attractive features of frequency-domain implementations, while requiring a processing delay considerably smaller than the length of the impulse response. The authors show that these algorithms can be seen as particular implementations of a more general scheme, the generalized multidelay filter (GMDF). Within this general class of algorithms, we focus on implementations based on the weighted overlap and add reconstruction algorithms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate of update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. We present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error are first derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained, and are translated into bounds for the stepsize parameter. Simulations are presented to support our analysis and to demonstrate the practical usefulness of the GMDF algorithm in applications where large impulse response has to be processed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frequency-domain adaptive filtering with applications to acoustic echo cancellation

In this paper an algorithm is presented for adaptive filtering in the frequency-domain with application to acoustic echo cancellation. This algorithm, called generalized multi-delay filter(GMDFα, is derived from the frequency-domain implementation of the time-domain block least mean square algorithm. Two different implementations are introduced, one based on the discrete Fourier transform(dft) and one based on the discrete Hartley transform(DHT); some results on fixed-point implementation of the algorithm are provided which are compared to results obtained from floating point implementation. Finally, the application of thegmdfα algorithm to acoustic echo cancellation, in hand-free telephone systems, is detailed. Some control strategies are presented; in particular a novel double-talk detector based on a spectral dissimilarity measure is introduced ; also, a twin-filter structure which significantly enhances the echo rejection is derived.

Adaptive cancellation of the respiratory artifact in surface recording of small intestinal electrical activity

In the human small intestine there is omnipresent electrical activity with a frequency of 0.15–0.2 Hz. The electrical activity of the small intestine can be measured by surface electrodes placed on the abdominal skin. The most annoying problem in the surface electrical recording is the respiratory artifact which is not discernible from the small intestinal signal. The frequency of the respiration is about 0.2–0.4 Hz, which is very close to that of small intestinal activity, making the use of the conventional bandpass filtering impractical. In this paper a selective frequency domain adaptive filter was proposed for the cancellation of the respiratory artifact. The basic principle of the selective frequency domain adaptive filter is that only selected filter weights are adapted based on the frequency characteristics of the respiratory artifact. Therefore, a substantial reduction of computation is achieved. A series of computer simulations was conducted for the optimization of the system parameters and for the investigation of the system performace. It was demonstrated in this paper that the selective frequency domain adaptive filter is as effective as, but more efficient than, the conventional frequency domain adaptive filter. The adaptive system for the cancellation of the respiratory artifact based on the selective frequency domain adaptive filter is very efficient in computation, has a fast convergence (about 100 adaptations), substantial reduction of the respiratory artifact and little effect (or distortion) on the small intestinal electrical signal.

Efficient scheme of pole-zero system identification based on multilayer neural network

A novel scheme to identify adaptive pole-zero filters, based on the multilayer neural network approach, is proposed using the conventional back propagation algorithm. The performance of the neural network is studied in a system identification application and simulation results are presented showing identical performance but computational superiority over a frequency domain adaptive pole-zero filter reported in the literature.

On the implementation of a partitioned block frequency domain adaptive filter (PBFDAF) for long acoustic echo cancellation

The growing demand of communication systems incorporating hands-free audioterminals has multipled the efforts of developing efficient and reduced size acoustic echo cancellers. This work deals with the implementation of a wideband acoustic echo canceller using only a single DSP chip. The complete implementation takes advantage of two interesting features of a partitioned block frequency technique for the filtering operation:its good computational burden, and reduced and user-bounded delay. Essentially, this technique makes a sequential partition of the impulse response in the time domain prior to a frequency domain implementation of the filtering operation. Furthermore, this time segmentation allows to set up individual coefficient updating strategies concerning to different sections of the adaptive canceller, thus avoiding the need of disabling the adaption in the complete filter. The adaptive algorithm is based on the known frequency domain adaptive filter (FDAF) for every section of the filter, but the adaptation step computation procedure differs from other usual ones because it introduces an additional measure of the input spectral uniformity. Finally, a real time prototype is implemented with the help of a commercial floating-point DSP board. It is able to satisfy the needs of any wideband hands-free audioterminal working in reverberant environments with acoustic echoes of length up to 200 ms (≈3000 filter coeffients).

On the implementation of the frequency-domain LMS adaptive filter

Alternative implementations for the frequency-domain LMS adaptive filter are presented. One of the implementations uses an LMS steepest-descent algorithm to compute the discrete Fourier transform (DFT). Therefore, the frequency-domain LMS adaptive filter is implemented as a cascade of two parts, with each one running the LMS adaptive algorithm. This requires fewer computations than the FFT for large filter lengths. Simulations of practical applications of frequency-domain LMS adaptive filters are carried out to determine their suitability, and comparisons are made with simulations using the FFT. For real input data, another frequency-domain LMS adaptive filter is suggested based on the discrete Hartley transform (DHT). >

Normalised frequency-domain adaptive filter based on optimum block algorithm

A fast-convergence frequency-domain adaptive filter is described. A simple normalisation scheme in the frequency-domain optimum block algorithm (FOBA) is used to set the convergence factor separately in each frequency bin. This normalised FOBA (NFOBA) yields significant convergence improvements.

Frequency-domain and multirate adaptive filtering

An overview is presented of several frequency-domain adaptive filters that efficiently process discrete-time signals using block and multirate filtering techniques. These algorithms implement a linear convolution that is equivalent to a block time-domain adaptive filter, or they generate a circular convolution that is an approximation. Both approaches exploit the computational advantages of the FFT. Subband adaptive filtering is also briefly described. Here the input data are first processed by a bank of narrowband bandpass filters that are approximately nonoverlapping. The transformed signals are then decimated by a factor that depends on the degree of aliasing that can be tolerated, resulting in a large computational savings. Several performance issues are considered, including convergence properties and computational complexities of the adaptive algorithms and the effects of circular convolution and aliasing on the converged filter coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the complexity of frequency-domain adaptive filtering

In frequency-domain adaptive filtering (FDAF), the 'crossover point' where the frequency domain becomes more efficient than the time domain is asymptotically 1.5 times as high for a DSP software realization as for a VLSI hardware realization. However, actual software realizations of FDAF may require as much as twice the computation predicted by theory, depending on the processor chosen. The approach can be extended to analyze other FDAF structures, such as multirate filters. >

A multistep size (MSS) frequency domain adaptive filter

A multistep size frequency-domain adaptive filter capable of tracking both stationary and nonstationary signals is proposed. This algorithm makes use of the simple structure of the least mean square error algorithm to update the filter coefficients and process the signal. It then proceeds further by incorporating a set of three step sizes and a knowledge-based strategy to select the best set of filter coefficients and the optimum step size iteratively. The main advantage of the MSS algorithm over the conventional LMS algorithm is that better performance is achieved without the knowledge of the input signal characteristics, such as signal power, degree of nonstationarity, signal-to-noise ratio, and stability bounds. Experimentally, the MSS algorithm is tested under various signal environments. The transient characteristics of the step sizes are found to be in agreement with previous theoretical studies of nonstationary characteristics of the LMS algorithm. In order to reduce the complexity, the conventional frequency-domain block LMS structure is also modified so that the MSS algorithm can be embedded more efficiently by exploiting the block structure. >

Analysis of a frequency-domain adaptive IIR filter

Convergence of frequency-domain adaptive pole-zero IIR (infinite impulse response) filter is studied. The algorithm is shown to converge in probability to an associated ordinary differential equation (ODE) which in turn converges to a local minimum of its performance surface. An analysis of the performance surface shows that the algorithm converges to one of N-factorial members in an equivalence class of global minimum points, where N is the number of adaptive poles. Saddle points exist on manifolds that separate members in the equivalence class. This explains 'shoulders' in the MSE convergence curves and also suggests one way of avoiding these shoulders which cause slow convergence. A second-order simulation example confirms the above results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multidelay block frequency domain adaptive filter

A flexible multidelay block frequency domain (MDF) adaptive filter is presented. The distinctive feature of the MDF adaptive filter is to allow one to choose the size of an FFT tailored to the efficient use of the hardware, rather than the requirements of a specific application. The MDF adaptive filter also requires less memory and thus reduces the hardware requirements and cost. In performance, the MDF adaptive filter introduces smaller block delay and is faster, making it ideal for a time-varying application such as modeling an acoustic path in a teleconference room. This is achieved by using a smaller block size, updating the weight vectors more often, and reducing the total execution time of the adaptive process. The MDF adaptive filter compares favorably to other frequency-domain adaptive filters when its adaptation speed and misadjustment are tested in computer simulations. >

The application of frequency‐domain adaptive filters to speech enhancement

Several authors have applied the time‐domain least‐mean‐squares adaptive filter to the problem of (voiced) speech enhancement. Generally, these efforts have achieved only limited success due, in part at least, to the nonuniform convergence of the adaptive filter when faced with frequency components of highly disparate spectral power (the so‐called “eigenvalue disparity” problem). This problem is addressed by employing the normalization capacity of the frequency‐domain adaptive filter (FDAF). The first part of this paper deals with the analysis of the FDAF for strictly harmonic signals (this reflects the quasiperiodic nature of voiced speech). It is shown that the behavior of the filler for each weight of the FDAF can be described by a linear transfer function relating the desired input to the output signal. It is further shown that the product of the input power and the feedback component (in each frequency bin) determines the stability and convergence of the filter. Normalization can be achieved by adjusting this product for each weight. Simulations comparing time‐ and frequency‐domain approaches have shown that the FDAF enhancer significantly improves performance.

Adaptive IIR filtering using parallel-form realizations

Several parallel-form adaptive IIR (infinite impulse response) filters are presented, including a frequency-domain implementation based on the discrete Fourier transform and a recursive frequency-sampling structure. The performance of the frequency-domain adaptive IIR filter is investigated in a system identification application, which includes an analysis of its modeling capabilities and a discussion of the mean-square-error performance surface. Computer simulation results are presented to illustrate the robust convergence properties of the adaptive algorithm and to demonstrate the stability of the filter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Convergence analysis of a frequency-domain adaptive filter with exponential power averaging and generalized window function

One of the advantages of a Frequency-Domain Adaptive Filter (FDAF) is that one can achieve convergence at a constant rate over the whole frequency range by choosing the adaptation constant for each frequency bin <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</tex> equal to the overall adaptation constant divided by an estimate of the input power at this frequency bin. A commonly used method, applied in this paper, to estimate the input power is to do an exponentially weighting with smoothing constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta</tex> on the magnitude squared of the input values at each frequency bin <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</tex> . Furthermore, it is known that a correctly implemented FDAF, using the overlap-save method, contains five 2 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -points Fast Fourier Transforms (FFT). Two of these are used to force the last <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> points of the time-domain augmented impulse response to zero by applying a particular window function. In this paper, an analysis is given of the FDAF where the window function is generalized. Using these results, the convergence behavior of FDAF's with various window functions is compared. Furthermore, the analysis describes the influence of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta</tex> on the convergence behavior of the FDAF over the whole convergence range.

Recirculation of input data in frequency-domain adaptive filtering

The recirculation of input data is proposed in the application of frequency-domain adaptive filtering when the supply of input data is limited. An analysis of the performance of such an algorithm is presented and it indicates that superior performance can be achieved. Examples of its applications in adaptive filtering confirm the results of analysis and demonstrate the effectiveness of the proposed algorithm.