Text b. Adaptive Filters. The Historical Review

This text examines the theory, design, and application of adaptive filters. The first adaptive or self-training filter is often credited to Lucky for his design of a zero-forcing equalizer (in 1966) which compensated for distortion in data transmission systems. However, prior relevant work on adaptive waveform recognition was reported in 1960 by Jakowatz et al. . Theoretical work in adaptive filters was reported in 1961 in the United States by Glaser and in the same year in the United Kingdom, Gabor et al. used an analog tape transport mechanism to adjust the weights of a nonlinear "learning" filter. We may interpret the title "learning" as a reference to an adaptive processor.

Much of this early work on adaptive filters was arrived at by independent study in different research organizations. Other notable early developments occurred at the Technische Hochschule Karlsruhe in Germany and at Stanford University, where adaptive pattern recognition systems were initiated in 1959. Collaboration in 1964 between these institutions produced a comparative evaluation of their respective techniques /Steinbuch and Widrow/ which subsequently led to the development of the most widely used algorithm for processor weight adjustment. Further relevant work was being conducted simultaneously at the Institute of Automatics and Telemechanics in Moscow. An excellent summary of the status, in the middle 1960s, of adaptive filters and early references for their use in adaptive or automatic equalization is provided by /Rudin/. More recently, simple review articles have been pre­pared on echo cancellation in telephony /Weinstein 1977 and adaptive equalization / Qureshi 1982/.

Many methods exist to adjust the filter weight values to obtain the optimum solution. Random perturbation techniques have been applied /Widrow et al. 1976 /, where the weights are a1tered and the output is examined to ascertain whether the random perturbation moves it toward or away from the desired solution. There are given details on development of the least-mean-squares (LMS) adaptive algorithm, which came from the Stanford Universi­ty pattern recognition work and was first formally reported by Widrow in 1967 in the context of adaptive arrays and in 1971 in the adaptive filter situation. It is now widely applied to the calculation of the adaptive filter weights, as it uses gradient search techniques which converge toward the optimum solution much more efficiently than do other algorithms. It can be shown that this technique is very similar to the technique of maximizing signal-to-noise ratio which was developed concurrently by Applibaum for use when obtaining the optimum weights for an adaptive array. It has also been shown that Lucky's zero-forcing equalizer employs a simplification of the more general LMS gradient search technique.

Text c. Adaptive Filter Operation

Essential Vocabulary

system modeling a spectrally white primary signal optimum impulse response optimum weight vector echo cancellation equalization distorted line output to be trained (by) replica equalized (distortion-free) area (perfect) primary signal noise cancellation spurious signal correlated signal to subtract

– моделирование системы - первичный сигнал с равномерной спектральной плотностью -оптимальная импульсная характеристика - оптимальный весовой вектор - подавление отраженного сигнала - выравнивание - искаженный сигнал с выхода - (зд.) перенастраиваться - точная копия -отфильтрованные (свободные от искажений) данные - неискаженный первичный сигнал - подавление шумов - мешающий сигнал - коррелированный сигнал - вычитать

Task 1. Translate the following word combinations into Russian. Compose sentences with them.

To be performed by the adaptive filter; to be supplied direct to; to be input to a system; to be implemented in the adaptive filter; to be inserted in the input; to be excited by a known signal; to be trained by supplying a replica; to be obtained from another source; to yield an output.