Text B. Adaptive Finite Impulse Response Filters (FIR)

Much of the reported literature on adaptive filters has been based on the FIR.filter-based approaches. They are relatively simple to design and construct, and

Well-understood adaption algorithms (e.g., IMS) exist whose performance, with regard to rate of convergence, converged error, and so on, is well documented. Thus this is the approach most widely applied in the telecommunications applications of adaptive filters such as equalization and echo cancellation.

One of the major deficiencies of this approach is that the filter weights are altered according to a single, global error. The weights are therefore interrelated and this is one of the reasons for the relatively slow convergence response of IMS adap­tive filters. One technique for overcoming this is to employ the lattice filter. The adaptive lattice structure, which incorporates recursive calculation of the internal Parcor coefficients, is an adaptive prediction error filter which performs spectral whitening. This property permits it to model the input signal and act as a parametric spectral estimator.

Task 1. Translate the following verbs with the prepositions into English.

Базировать на; быть довольно простым для; в отношении к чему-либо; наиболее широко используемый в; изменяться в соответствии с; способ для продления.

Task 2. Answer the questions to Text B.

1. What is the approach most widely applied in telecommunication applications of adaptive filters?

2. What is one of the major deficiencies of this approach?

3. What is one of the reasons for the relatively slow convergence response of LMA adaptive filters?

4. What is the technique for overcoming this deficiency?

Task 3. Translate the sentences into English.

1. Адаптивные фильтры обычно состоят из двух отдельных частей: фильтра и адаптивного алгоритма.

2. Структура фильтра используется для выполнения искомой функции обработки информации.

3. Адаптивный алгоритм предназначен для построения параметров (коэффициентов) этого фильтра.

4. Большое количество возможных комбинаций структуры фильтра и законов адаптивного управления ими приводят к значительному разнообразию адаптивных фильтров.

Task 4. Put questions (in English) to the statements given above to discover all the details.

UNIT 4. SUPPLEMENTARY TEXTS FOR READING, TRANSLATION AND DISCUSSION

Text 1

Data Transmission. Although data transmission in the form of telegraphy predates telephony, speech communication came to dominate the evolution of telecommunication networks. Developed countries, therefore, have telephony networks that are unrivaled in their ubiquity and offer worldwide communication. When the growth in computer usage created a need for data communications it was not surprising that telephony networks initially offered the best medium for this communication. Unfortunately, transmission systems in telephony networks were optimized for analog speech waveform and introduce various impairments that impede data communications. The most serious of these impairments are linear distortions, and linear filters could be used to equalize or cancel the distortion. However, such distortions vary widely between different network connections, so it became necessary to use adaptive filters.

Today, adaptive filters are widely used to provide equalization in data modems which transmit data at rates of 2400 bits/s up to 16, 000 bits/s over speech-band channels (nominally, 300 to 340O Hz). Although it is theoretically possible to achieve even higher rates, it is practically difficult to obtain a satisfactory error-rate performance without recourse to wider bandwidths. Higher-speed data modems (48, 000 to 72, 000 bits/s) are commercially available for operation over wider-band-width (60 to 108 kHz) channels, and some of these use adaptive equalization.

Recently, there has.been a growing interest, in duplex data transmission over speech-band circuits, which has resulted in adaptive filters being investigated for use as echo cancelers. As yet, very few modems using echo cancelers are commercially available, but that situation may well change in the next few years. Both these applications are described in this section, but first an outline of the types of linear distortion encountered in telephony channels is necessary.

 

Text 2

Linear Distortions In Telephony Networks.Linear distortions arise in many different ways in telephony networks, but three distinct types can be identified: amplitude distortion, group-delay distortion, and echoes. A subscriber is usually connected to his or her local switch by metallic pair cable: within the speech band this introduces amplitude slope. Between the local switch and other switches there may be loaded junction cable which introduces group-delay distortion, at the top end of the speech band. Between switches four-wire circuits are used to enable signal amplification and multichannel transmission systems to be employed. Multichannel transmission systems use band-limiting filters which introduce both group-delay and amplitude distortion. Hybrid transformers are used to separate the go and return paths of the four-wire circuit and should ideally introduce infinite attenuation between the two paths. In practice the attenuation is finite, allowing signals to circulate around the four-wire loop, creating echoes. Those appearing back at the transmitter are referred to as talker echoes, while those arriving at the receiver are called listener echoes. Impedance mismatches in. the network are a further source of echoes. Listener echoes give rise to ripples in the frequency response of the channel, the amplitude of the ripples being proportional to the echo delay.

Real network connections are often more complicated, than this simple model and are becoming more so as modern pulse-code modulation (PCM) transmission systems and digital switches are introduced. However, the three basic impairments remain and identifying them separately helps us to understand what the adaptive filters used to combat linear distortion are required to do and how they behave.

Text 3

Types of Filters. To facilitate discussion of the various types of filters, three basic terms must first be defined. These terms are illustrated in the context of the normalized low-pass filter. In general, the filter passband is defined as the frequency range over which the spectral power of the input signal is passed to the filter output with approximately unity gain. The input spectral power that lies within the filter stopband is attenuated to a level that effectively eliminates it from the output signal. The transition band is the range of requencies between the passband and the stopband. In this region, the filter magnitude response typically makes a smooth transition from the passband gain level to that of the stopband. This band has zero width only for the ideal rectangular filter that is not realizable in either the analog or the discrete time domain.

Four basic types of filters can now be defined in terms of their frequency response characteristics. The low-pass filter passes low-frequency components to the output while attenuating high-frequency components. Conversely, the high-pass filter permits high-frequency components to appear at the output while effectively eliminating low-frequency components. The bandpass filter rejects both high- and low-frequency components while passing an intermediate range. Note that this filter could, in some cases, be realized as a cascade of a low-pass filter and a high-pass filter whose passbands overlap. The bandstop filter rejects an intermediate band of frequencies while passing high- and low-frequency components. This filter could be implemented using low-frequency components. This filter could be implemented using low-pass and high-pass filters with nonoverlapping passbands in the parallel configuration.

The filter response may be specified in terms of the squared magnitude /H(e^jw)/². Alternatively, the power gain is often defined in decibels. Thus, the filter passband with unity magnitude gain corresponds to a power gain of 0 dB. A filter may equivalently be described, as in the following figures, in terms of its amplitude gain or, magnitude response characteristic, /H(e^jw)/.

The filters are normalized examples in the sense that the passbands are specified to have approximately unity gain. In general, this need not be the case. It is, however, a simple matter to adjust the gain of a filter by using a single multiplicative coefficient, for example, A H(z), where A denotes the amplitude gain. Unless otherwise specified, the digital filter-design routines provided in this book produce normalized transfer functions.

Digital filters are further categorized in terms of their responses. In this context, there are infinite impulse response (IIR) and finite impulse response (FIR) digital filters. For each task, the digital filter category is typically determined by weighing the specific requirements of the application against the digital processing capacity available. The primary advantage of IIR filters is that sharp frequency cutoff characteristics are attainable with a relatively low-order structure. This translates to a large.savings in processing time and/or hardware complexity. In addition several familiar analog filters are easily converted to IIR digital structures. On the other hand one of the most important features of FIR filters is that they can he designed to, have exactly linear phase characteristics. Whereas FIR filters typically require many coefficients, implementation via fast convolution will reduce the number of computations required, thus making this filter category more widely applicable. Routines for fast convolution are to be cisucessed.

Each of the four types of filters (that is, low-pass, high-pass, bandpass, bandstop) described can, in general, be realized by either an IIR or an FIR filter. The remainder of this chapter is devoted to the description of algorithms that enable time-domain realization of IIR and FIR filters.

 

Text 4

Adaptive algorithms for finite impulse response filters. Adaptive filters generally consist of two distinct parts: a filter, whose structure is designed to perform a desired pro­cessing function, and an adaptive algorithm for adjusting the parameters (coefficients) of that filter. The many possible combi­nations of filter structures and the adaptive laws /governing them/ lead to a sometimes bewildering variety of adaptive filters.

We focus on what is, perhaps, the simplest class of filter structure: linear filters with a finite impulse response (FIR). Note that the filter output is a linear combination of a finite number of past inputs. The filter is not recursive (i.e., conta­ins no feedback). This property leads to particularly simple adap­tive algorithms.

Having specified the filter structure it is next required to design an adaptive algorithm for adjusting its coefficients. We are to consider adaptive laws whose objective is to minimize the energy of the filter output (i.e., the output variance or the output sum of squares). The need to minimize this particular cost function arises in many applications involving least-squares es­timation, such as adaptive noise canceling, adaptive line enhan­cement, and adaptive spectral estimation.

We are to present two adaptive algorithms for FIR fillers: the recursive least-squares (RLS) algorithm and the Widrow-Hoff least-mean-squares (LMS) algorithm. The LMS algorithm has gained considerable popularity since the early 1960s. Its simplicity makes it attractive for many applications in which computational requirements need to be minimized. The RLS algorithm has been used extensively for system identification and time-series analysis. In spite of its potentially superior performance, its use in signal processing applications has been relatively limited, due to its higher computational requirements. In recent years there has been renewed interest in the RLS algorithm, especially in its " fast" (computationally efficient) versions. The RLS algorithm has been applied to adaptive channel equalization adaptive array processing and other problems.

Text 5

Adaptive algorithms for infinite impulse response filters. General Scope. The concept of adaptation in digital filtering has proven to be a powerful and versatile means of signal proces­sing in applications where precise a priori filter design is im­practical. For the most part, such signal processing applications have relied on the well-known adaptive finite impulse response (FIR) filter configuration. Yet, in practice, situations commonly arise wherein the nonrecursive nature of this adaptive filter results in a heavy computational load. Consequently, in recent years acti­ve research has attempted to extend the adaptive FIR filter into the more general feedback or infinite impulse response (IIR) con­figuration. The immediate reward lies in the substantial decrease in computation that a feedback filter can offer over an FIR filter. This computational improvement comes at certain costs, however. In particular, the presence of feedback makes filter stability an issue and can impact adversely on the algorithm's convergence time and the general numerical sensitivity of the filter. Even so, the largest obstacle to the wide use of adaptive IIR filters is the lack of robust and well-understood algorithms, for adjusting the required filter gains. The classes of algorithms to be currently under development are to be explored those based on minimum mean-square-error concepts, and another which has its roots in nonlinear stability theory. The basic derivation of each will be pre­sented and certain aspects of performance examined. Other key de­sign concerns, such as the fact chat certain algorithms require the use of specific filter structures, will also be to be illumi­nated.

 

СПИСОК ЛИТЕРАТУРЫ

Большой англо-русский политехнический словарь: В 2 т. / Сост.: С.М.Баринов, А.Б.Борковский, В.А.Владимиров и др. М.: РУССО, 2006.

Cowan C.F.N. and Grant P.M. Adaptive Filters. Prentice-Hall Canada, Incorporated, 1985.

Monson H. Hayes. Statistical Digital Signal Processing and Modeling, Wiley, 1996.

Simon H.aykin. Adaptive Filter Theory, Prentice Hall, 2002.

ИНТЕРНЕТ-ИСТОЧНИКИ

 

http: //www.springerlink.com/content/978-1-4020-8011-1/contents/

CONTENTS

UNIT 1. INTRODUCTION. ADAPTIVE FILTERS. 3

Text A. Adaptive Processing. 3

Text B. Adaptive Filters. The Historical Review.. 11

Text C. Adaptive Filter Operation. 12

UNIT 2. PROGRAMMABLE FILTER DESINGS. 20

Text A. Recursive Filters. 20

Text B. Nonrecursive Filters. 26

Text C. Transformed-Based Filters. 35

UNIT 3. ADAPTIVE FILTERS. 38

Text A. Adaptive Infinitive Impulse Response Filters (IIF) 38

Text B. Adaptive Finite Impulse Response Filters (FIR) 41

UNIT 4. SUPPLEMENTARY TEXTS FOR READING, TRANSLATION AND DISCUSSION.. 44

Text 1. 44

Text 2. 45

Text 3. 45

Text 4. 47

Text 5. 48

Литература……………………………………………………………………………………………………………………………………………51

 

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