# PDF SUBBAND ADAPTIVE FILTERING THEORY AND IMPLEMENTATION

Subband adaptive filtering: theory and implementation / by Kong-Aik Lee, .. This book covers the fundamental theory and analysis of commonly used subband. View Table of Contents for Subband Adaptive Filtering. Subband Adaptive Filtering: Theory and Implementation. Author(s). Kong‐Aik Lee. Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate.

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PDF | Subband adaptive filtering has attracted much attention lately. In this paper, we recent years, there has been a marked interest in the application. of adaptive ﬁltering to simulation results support the theoretical predictions. A. Subband Adaptive Filtering. Theory and Implementation. Kong-Aik Lee. Institute for Infocomm Research, Singapore. Woon-Seng Gan. Nanyang Technological. Abstract: Subband adaptive filtering (SAF) generally employs multirate filter banks for signal decomposition .. filtering. However, if implementation cost is not an issue,. Subband . Such a filter bank design method is based on a theoretical.

Kuo received the B. He is the leading author of four books: He holds seven US patents, and has published over technical papers.

## Journal of Applied Mathematics

His research focuses on active noise and vibration control, real-time DSP applications, adaptive echo and noise cancellation, digital audio and communication applications, and biomedical signal processing. Kuo received the IEEE first-place transactions Consumer Electronics paper award in , and the faculty-of-year award in for accomplishments in research and scholarly areas.

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Subband Adaptive Filtering: Theory and Implementation Author s: Eng 1st Class Hons , Ph. Kuo B.

First published: Print ISBN: About this book Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications.

This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap—weight adaptation, delayless architectures, and filter—bank design methods for reducing band—edge effects are included.

Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. Key Features: Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications.

Bridges the gaps between two distinct domains: In addition, as the length of the adaptive filter increases, the computational complexity increases. This can be a serious problem in acoustic applications such as echo and noise cancellation, where long adaptive filters are required to model the response of the noise path. This issue is of great importance in the hands-free application where processing power is kept low.

An alternative approach to reduce the computational complexity of long adaptive FIR filters is to incorporate block updating strategies and frequency domain adaptive filtering. These techniques reduce the computational complexity, because the filter output and the adaptive weights are computed only after a large block of data has been accumulated. However, the application of such approaches introduces degradation in the performance, including a substantial signal path delay corresponding to one block length, as well as a reduction in the stable range of the algorithm step size.

Therefore for nonstationary signals, the tracking performance of the block algorithms generally becomes worse. As far as speed of convergence is concerned, it has been suggested to use the Recursive Least Square RLS algorithm to speed up the adaptive process. The convergence rate of the RLS algorithm is independent of the eigenvalue spread.

Unfortunately, the drawbacks that is associated with RLS algorithm including its O N2 computational requirements, which are still too high for many applications, where high speed is required, or when a large number of inexpensive units must be built. As a result, adaptive filtering using subband processing becomes an attractive option for many adaptive systems to reduce these problems [4]. Multirate DSP consists of: www. A signal is down sampled only when it is "oversampled" i.

To down sample by a factor of M, we must keep every Mth sample as it is and remove the M-1 samples in between. Adaptive filter using the NLMS algorithm is applied in each band. Subband Adaptive Filtering in a Noise Cancellation Scenario Subband adaptive filtering belongs to two fields of digital signal processing, namely, adaptive filtering and multirate signal processing.

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The basic idea of SAF is to use a set of parallel filters to divide the wideband signal input of the adaptive filter into narrower subband signals, each subband serving as an input to an independent adaptive filter. Subband decomposition greatly reduces the adaptive filter update rate through parallel processing of shorter filters. Furthermore, subband signals are usually downsampled in a multirate system. A multirate DSP system uses multiple sampling rates within the system.

Whenever a signal at one rate has to be used by a system that expects a different rate, the rate has to be increased or decreased, and some processing is required to doso. Therefore "Multirate DSP" refers to the art or science of changing sampling rates.

Resampling is done to interface two systems with different sampling rates [5].

Multirate DSP consists of: 1. Decimation: It is a process to decrease the sampling rate. Interpolation: It is a process to increase the sampling rate. Block diagram of a decimator "Down sampling" is a process of removing some samples, without the low pass filtering. Block diagram of a decimator "Up sampling" is the process of inserting zero valued samples between original samples to increase the sampling rate.

This is called "zero-stuffing".

The result is a signal sampled at a higher rate. The interpolation factor L is the ratio of the output rate to the input rate. This leads to a whitening of the input signals and therefore an improved convergence behavior of the adaptive filter system is expected. The subband decomposition is aimed to reduce the update rate, and the length of the adaptive filters, hopefully, resulting in a much lower computational complexity [4]. The conventional noise cancellation model is extended to a subband configuration by the insertion of sets of analysis and synthesis filters in signal paths.

Here, P z represents the acoustic noise path, n being correlated with and uncorrelated with s. The update equation of the adaptive filter using the LMS algorithm is given by the following set of equation. Depending on the decimation rate used for analysis and synthesis filter bank the subband structure is divide as, www.

Critically Sampled In critically sampled the decimation factor is equal to the number of subband. Oversampled Structures In Oversampled structure the decimation factor is greater than the number of subbands.

Filter Banks A. Direct Implementation In the Analysis filter bank a signal is being separated into its low frequencies and high frequencies. The sub-band signals V0 n and V n are then down-sampled by a factor of 2.

Adaptive processing is done in both subband separately.

The perfect reconstruction process requires four filters, two lowpass filters H0 and G0 and two highpass filters H1 and G1 [7]. In addition, it requires a downsampler and upsampler between the two lowpass and between the two highpass filters.

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The combination of Decimation filter and low pass filter makes together analysis filter bank similarly the synthesis filter bank consist of interpolation and filters.

The distortion transfer function T z is expressible in terms of the lowpass filter H0 z.

Direct implementation for Subband adaptive filtering B. Proposed Implementation In direct implementation the filtering is applied to all original signal samples, even though only every Mth filtering output is retained finally. Even if H z operates only for time instants multiple of M and idle www.

This additional Computational burden can be reduced by the use of noble identities of the decimation and filter.

Performance Parameter A. We will then broaden the discussion to estimation when we have a observation of another random variable X, together with the joint probability density function of X and Y.The designing of such filter which removes or suppress noise required the signal and the noise be stationary that the statistics of both signals be known a priori.

Several problems are included at the end of chapters and some of these problems address applications.

## [PDF] Subband Adaptive Filtering: Theory and Implementation Popular Collection

PDF Excerpt 3: Although a higher PSNR generally indicates that the reconstruction is of higher quality, in some cases it may not. Most noise sources tend to be broadband in nature and while a large portion of the energy is concentrated in the lower frequencies, they also tend to have significant high frequency components.

Subband Adaptive Filtering is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students.