Structural Subband Decomposition Research Articles

Structural sub-band decomposition of sequences and its applications in signal processing

The authors present a tutorial paper in which they review the concept of structural sub-band decomposition of sequences, a generalisation of polyphase decomposition. The idea of using a very simple analysis-synthesis structure allows for computational efficiency. It is applicable both for signals and for systems, which may thus be designed and realised advantageously. The use of such decomposition is shown, in terms of theory and applications, for transform-based spectral analysis, FIR filter design and implementation, and adaptive filtering. Advantages are demonstrated for cases of narrow-band signals and systems.

Efficient frequency-sampling design of one-and two-dimensional FIR filters using structural subband decomposition

A new method is presented for the fast and efficient design of one-dimensional (1D) and two-dimensional (2D) linear phase FIR filters. In this approach, the concept of structural subband decomposition of 1D and 2D sequences is applied to an improved method for frequency-sampling FIR filter design. Using this decomposition the filter is implemented as a parallel connection (bank) of sparse subfilters cascaded with interpolators. An algebraic relationship is then developed to determine the frequency samples of the subband filters from the original specified frequency samples. Filter designs based on various types of interpolators derived from transform matrices such as the Hadamard, binomial, and DCT are investigated. Significant computational savings arise from discarding subbands that contribute little to the overall frequency response and selectively quantizing the wordsize of the coefficients of the remaining subfilters. In addition to implementation advantages over traditional techniques, the proposed method enables a more accurate specification of filter design parameters, near optimal responses, and a design time considerably faster than that of the Parks-McClellan algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive FIR filters based on structural subband decomposition for system identification problems

LMS (least-mean-square) adaptive filtering algorithms using FIR (finite-impulse-response) filter structures based on structural subband decomposition are developed. It is shown that the subband decomposition is equivalent to transformation of input data by orthogonal matrices of which the Walsh-Hadamard transform (WHT) is a special case. The proposed method is a generalization of WHT-based transform domain adaptive filtering, which is known to enhance the convergence speed of adaptive filters. It is also shown that the interpolator network of the subband structure is a fast implementation of the required transform and is therefore attractive from a practical standpoint. The convergence properties of subband FIR adaptive filters are studied for system identification applications. The results demonstrate the advantages of the proposed structure compared to conventional adaptive filters. >

A generalized structural subband decomposition of FIR filters and its application in efficient FIR filter design and implementation

It is shown that any FIR (finite-impulse-response) transfer function can be realized as a parallel connection of interpolated FIR (IFIR) sections consisting of a cascade of a subfilter with a sparse impulse response and an FIR interpolator which fills in the missing samples of the corresponding subfilter. The set of interpolators can be realized as a subband filter bank, and as a result, each IFIR section contributes to the overall frequency response essentially within a given band of frequencies. The proposed decomposition can be considered as a generalization of the polyphase decomposition. It results in a computationally efficient structure in sampling rate alteration applications and also leads to faster FIR filter design algorithms. Examples are included to demonstrate the improvements in the speed of least-squares and minimax design algorithms based on the suggested structure. >

Adaptive FIR filter structure based on the generalized subband decomposition of FIR filters

An adaptive structure based on a generalized structural subband decomposition of FIR (finite-impulse-response) filters is presented. The proposed structure implements an adaptive FIR filter of length N as a parallel connection of L branches, with each branch composed of a cascade of a fixed interpolator and a sparse adaptive subfilter containing at least L nonzero coefficients. There is no sampling rate alteration in this structure, and therefore no problems with aliasing occur. The interpolators are implemented by a computationally efficient transform (e.g., DCT, DFT). The proposed structure presents superior convergence performance for colored input signals when compared to the conventional direct-form LMS (least-mean-square) structure, with a very small increase in the number of operations. The advantages of using the subband structure in the adaptive line enhancer, acoustic echo canceller, and channel equalizer applications are shown through computer simulations. >