Frequency-domain Adaptive Filter Research Articles

On least square frequency-domain adaptive filters

This paper presents a least square approach to the Dentino et al. [1] frequency-domain adaptive filter by minimizing a frequencydomain error criterion. The constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu</tex> that controls the LMS convergence behavior is replaced by an adaptive <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu</tex> that every new iteration achieves this least squared error. The proposed approach can be extended and then applied to modify other frequency-domain adaptive algorithms. For example, a modified version of the unconstrained frequency domain adaptive algorithm proposed by Mansour and Gray in [2] is presented. The advantage of our modified unconstrained frequency-domain adaptive algorithm is that it has only one convergence parameter as compared to two in the original algorithm.

The block-processing FTF adaptive algorithm

A new block-type adaptive-filtering algorithm is presented. This new block adaptive filter differs from the frequency-domain block adaptive filters of Ferrara (1980), and of Clark, Mitra, and Parker (1980), in that the new method applies a deterministic time-domain least-squares criteria within each of the data blocks. Information is carried from block to block via a weighted initial condition. This new block fast transversal filters (BFTF) algorithm is a numerically stable algorithm and can also be used to perform efficient least-squares system identification on any one data block, in which case it shows a moderate computational advantage over the previous most-efficient single-data-block algorithms of Morf et al. (1977), of Marple (1981), and of Kalouptsidis, Manolakis, and Carayannis (1984-1985). Mechanisms for tracking and varying block length from block to block are also presented and evaluated. Finally, we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters, after computation of the sample correlation lags.

A method for detection of signals using frequency-domain adaptive filter

The detection performance of the frequency-domain adaptive filter is compared with the time-domain one. Comparisons are based on the computer digital simulation with a sinusoidal signal and white Gauss noise. The performance of the frequency and time-domain adaptive filters are shown to be the same for an unknown frequency signal, but for the detection of known frequency the frequency-domain adaptive filter length is much shorter to get the same detection probability.

Wide-band hybrid analog/Digital frequency domain adaptive filter

This paper describes a hybrid adaptive filter which employs a cascade of analog forward and inverse Fourier transform processors interconnected via a digital interface. The interface multiplies the transformed input, sample by sample, by a set of weights stored in RAM and compares the products against a desired complex spectrum. The resulting error is used to update the RAM weights via a feedback loop, which forces the multiplied output to converge towards the desired complex spectrum. The use of frequency domain processing in the adaptive filter offers faster, more controlled convergence than conventional time domain adaptive transversal filters. We present simulations and practical results on a frequency domain adaptive filter based on 100 point surface acoustic wave chirp transform processors which give the adaptive filter a 4 MHz real-time bandwidth capability. Thus, this new processor is likely to find potential application in equalization, echo, and interference suppression in high bandwidth communications and radar systems.

A reduced structure of the frequency-domain block LMS adaptive digital filter

In this letter, it is shown that the frequency-domain block LMS (FBLMS) adaptive digital filter (ADF) for the block length of one reduces to the frequency-domain LMS (FLMS) ADF. Using the relation between the two convergence factors of the FBLMS and FLMS ADFs, it is possible to predict the steady-state performance of the former from that of the latter.

A fast convergence frequency domain adaptive filter

This correspondence presents a new fast convergence algorithm for frequency domain adaptive filter and its applicability to acoustic noise cancellation in speech signals.

A unified approach to time- and frequency-domain realization of FIR adaptive digital filters

Specific implementations of the finite impulse response (FIR) block adaptive filter in the frequency domain are presented and some of their important properties are discussed. The time-domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency-domain adaptive filter (derived in the frequency domain), provided data sectioning is done properly. All of the known time- and frequency-domain adaptive filters [1]-[12], [16]-[18] are contained in the set of possible block adaptive filter structures. Thus, the block adaptive filter is generic and its formulation unifies the current theory of time- and frequency-domain FIR adaptive filter structures. A detailed analysis of overlap-save and overlap-add implementations shows that the former is to be preferred for adaptive applications because it requires less computation, a fact that is not true for fixed coefficient filters.

Frequency-domain adaptive filtering using continuous transfer functions

A continuous-time frequency-domain adaptive filtering approach is described. The adaptive filter is required to allow independent control of its transfer function coefficients. A sequential-linear-search (SLS) adaptation algorithm is presented and its convergence properties are investigated. It is shown analytically that the algorithm converges to a global solution with respect to the numerator coefficients of any adaptive transfer function order. The error surface as a function of the denominator coefficients is studied numerically for orders up to the third. Practical considerations for implementation purposes are presented. The filter configuration suggested is shown to be MOS integrable using switched capacitor techniques. The proposed algorithm was applied successfully to adapt to rational and irrational unknown systems using second and third order adaptive filters.

Correlation function for the weight sequence of the frequency domain adaptive filter

The statistical behavior of the single complex adaptive weight in the frequency domain adaptive filter is further investigated. In a previous note [8], an expression was evaluated for the expected value of the magnitude square of the weight sequence at any time. In this note, the covariance of the weight at different times is evaluated and, in steady state, shown to be geometric with the same time constant as the frequency domain adaptive filter algorithm itself. Using these results, the reduction in the fluctuations of the weight values are computed for an exponentially decaying post-algorithm filter.

Unconstrained frequency-domain adaptive filter

An unconstrained frequency-domain least mean-squares (UFLMS) algorithm is presented. The algorithm is based on the "overlap-save" technique used in frequency-domain filtering. The proposed algorithm converges to the Wiener solution without the time-domain constraint on the impulse response as proposed by Ferrara. For a large number of taps ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\geq32</tex> ), the UFLMS algorithm offers a significant reduction in computation. Another advantage is its fast convergence for highly correlated input signals. The performance of the algorithm is illustrated by a simulation.

Frequency domain adaptive filter for detection of sonar signals

An adaptive filter for sonar signals which operates on the complex spectral components of the received signal, which signal has been transformed into the frequency domain by means such as the Fast Fourier Transform. The adaptive filter consists of a plurality of component filters, each of which operates on a single spectral component of the received signals. The transfer coefficient of each component filter is described by a complex number and is adaptively adjusted by means of a computational feedback loop. The feedback loop compares the product of the transfer coefficient and the complex spectral component of the received signal from a prior frequency transformation cycle, with the present spectral component to obtain an error signal. The error signal, in turn, adaptively alters the magnitude and phase of the transfer coefficient. A plurality of such component filters operate together to adaptively filter, in the frequency domain, the entire spectrum of the received signal.

Frequency domain least-mean-square algorithm

Frequency domain adaptive filtering can be performed by Fourier transforming the input-signal vector and weighting the contents of each frequency bin. By reducing the eigenvalue spread of the data autocorrelation matrix, frequency domain filtering promises great improvements in covergence rate over the conventional time-domain adaptive filtering.

Analysis of the frequency domain adaptive filter

The purpose of this note is to demonstrate significant analytical simplifications for studying the behavior of adaptive filtering in the frequency domain as opposed to studying the behavior of adaptive filtering in the time domain. A closed form expression, for the single complex weight in the frequency domain adaptive filter, is presented which allows significant statistical analysis to be performed. The mean-square error of the filter is evaluated as a function of the algorithm step size and the signal and noise powers.