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UNIT 1. INTRODUCTION. ADAPTIVE FILTERSСтр 1 из 7Следующая ⇒
UNIT 1. INTRODUCTION. ADAPTIVE FILTERS
Text A. Adaptive Processing Text B. Adaptive Filters. The Historical Review Text C. Adaptive Filter Operation Text A. Adaptive Processing
Essential Vocabulary
Read and translate Text A using Essential Vocabulary Text A. Adaptive Processing
Conventional signal processing systems for the extraction of information from an incoming signal such as a matched filter operate in an open-loop fashion. That is, the same processing function is carried out in the present time interval regardless of whether that function produced the correct result in the preceding time interval. In other words, conventional signal processing techniques make the basic assumption that the signal degradation is a known and time-invariant quantity. Adaptive processors on the other hand, operate with a closed-loop (feedback) arrangement. The incoming signal s(n) is filtered or weighted in a programmable filter to yield an output y(n) which is then compared against a desired, conditioning or training signal, y(n), to yield an error signal, e(n). This error is then used to update the processor weighting parameters (usually in an iterative way) such that the error is progressively minimized (i.e., the processor output more closely approximates to the training signal). Such processors fall into the two broad classes of adaptive filters (Figure 1.) and adaptive antennas. Adaptive filters, which are the subject of this text, are concerned with the use of a programmable filter whose frequency response or transfer function is altered, or adapted, to pass the desired components of the signal without degradation and to attenuate the undesired or interfering signals, or to reduce any distortion on the input signal. Adaptive antennas employ the spatial processing in an antenna array to steer the main-lobe toward the signal and generate nulls in the beam pattern in the direction of the interfering sources. Thus they use spatial processing techniques for interference reduction.
Fig.1. Schematic of adaptive filter In an adaptive system an absolute minimum of a priori information about the incoming signal is necessary. The adaptive filter operates by estimating the statistics of the incoming signal and adjusting its own-response in such a way as to minimize some cost function. This cost function may be derived in a number of ways depending on the intended application but normally it is derived by the use of the secondary signal source or conditioning input shown in Figure 1. This secondary signal input y(n) may be defined as the desired output of the filter, in which case the task of the adaptive algorithm is to adjust the weights in the programmable filter device in such a way as to minimize the difference or error e(n) between the filter output y(n) and the y(n) input. These adaptive filters are frequently used to recover signals from channels whose characteristic is time varying. All the systems considered in this text are sampled-data (discrete-time) systems. For convenience the explicit time index has thus been omitted from all mathematical expressions. Task 1. Translate and learn the following word combinations from Text A. Compose sentences with them. Conventional signal processing systems; extraction of information; incoming signal; matched filter; open-loop fashion; preceding time interval; basic assumption; time-invariant quantity; closed-loop arrangement; conditioning signal; processor weighting parameters; antenna array; spatial processing; interference reduction; sampled-data system. Task 2. Compose microtexts to the logical Scheme 1 and Scheme 2 (A, B). Try to reproduce them both: orally and in written form. Task 3. Home assignment. Compose a microtext to the logical Scheme 3. Present it in written form. Scheme 1. *quantity – величина Scheme 2A.
Scheme 2B. Scheme 3. Essential Vocabulary
Text A. Recursive Filters
Essential Vocabulary
Text A. Recursive Filters There are several types of programmable filters /Hamming/ that can be used in the design of the adaptive filters. Here we summarize initially the two basic filter designs and then expand them into the processors. The most generalized digital filter structure is the recursive filter design. This comprises both feed-forward multipliers, whose weights are controlled by the «a» coefficients, and feedback multipliers, which are controlled by the «b» coefficients. The response of this n-stage filter is governed by the nth-order difference equation which shows that the value of present filter output sample is given by a linear combination of the weighted present and past input samples as well as the previous output samples. This structure results in a pole-zero filter design where the pole locations are controlled by the «b» coefficients and the zero locations by the «a» coefficients. The number of poles and zeros, or order of the filter, is given by the number of delay stages. Second-order integrated filters are commercially available for input sample rates (64 kilobaud), which are compatible with digital telephony systems. This recursive structure has theoretically an infinite memory and hence it is referred to as an infinite impulse response (IIR) filter design. It is not unconditionally stable unless restrictions are placed on the values of the «b» coefficients. However, the inclusion of poles as well as zeros makes it possible to realize sharp cutoff filter characteristics incorporating a low transition bandwidth with only a modest number of delay stages (i.e., low filter complexity). One drawback of the IIR design is that no control is offered on the phase (group delay) response of the filter. However, the major problem, with adaptive IIR filter design is the possible instability of the filter due to poles straying outside the stable region. Scheme 1
What are the types of the programmable filters that can be used in the design of the adaptive filters? Scheme 2.
What is the Recursive filter design? Essential Vocabulary
Scheme 2. UNIT 3. ADAPTIVE FILTERS
Text A. Adaptive Infinitive Impulse Response Filters (IIF) Text B. Adaptive Finite Impulse Response Filters (FIF) Essential Vocabulary
Scheme 1.
Essential Vocabulary
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(ejw)/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(ejw)/. 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
UNIT 1. INTRODUCTION. ADAPTIVE FILTERS
Text A. Adaptive Processing Text B. Adaptive Filters. The Historical Review Text C. Adaptive Filter Operation Text A. Adaptive Processing
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