Text B. Nonrecursive Filters

Essential Vocabulary

all-zero filter   feedforward (feedback) multiplier   finite impulse response (FIR) filter   number of delay stages convolution stored weights a generalized equalizer or filter structure     undefined filter tapped delay line weighted combiner   lattice structure cascade of single tap prediction error filter     residual signal sample backward channel complex conjugate   baseband sampled date (baseband) processors   over successively longer delay

- модель адаптивного фильтра, содержащая только нули - умножитель с прямой (обратной) связью - фильтр с конечным импульсным откликом - число элементов задержки - свертка - накопленные в памяти веса - обобщенная структура выравнивателя или корректирующего фильтра - произвольный фильтр - линия задержки с отводами - взвешивающая комбинирующая цепь - решетчатая структура - каскадное соединение неразветвленных предсказывающих фильтров ошибки - выборка разностных сигналов - обратный канал - комплексносопряженная величина - основной канал - процессоры, которые производят обработку дискретной информации по основному каналу - при последовательно возрастающих задержках

Read and translate Text B using Essential Vocabulary

Text B. Nonrecursive Filters

I.Nonrecursive Filters. One way to overcome the drawback of potential instability in the filter is to design an all-zero filter which uses only feed forward multipliers and is unconditionally stable. This has only a limited memory, which is controlled by the number of delay stages and it results in the finite impulse response (FIR) or transversal filter design. The input signal is delayed by a number of delay elements, which may be continuous but in the present text will be restricted to discrete values. The output of these time-delay elements are subsequently multiplied by a set of stored weights and the products summed to form the output signal. This implies that the output is given by the convolution of the input signal with the stored weights or impulse response values. This filter incorporates only zeros (as there are no recursive feedback elements) and hence a large number of delay elements are required to obtain a sharp cutoff frequency response.

However, the filter is always stable and it can provide a linear-phase response.

An important contribution to the classification of filter designs was made by Chang in 1971 when he attempted to unify all approaches into a generalized equalizer or filter structure. This comprises a set of undefined filters feeding a linear weighting and combining network. The FIR filter can be configured from this generalized structure by replacing the undefined filter structure by a tapped delay line which outputs a series of time-delayed signal samples. The IIR filter structure incorporates further processing, due to the recursive feedback connections, into the time-delayed signal samples which subsequently feed to the weighted combiner.

II.Lattice Structure. An alternative FIB filter realization is the lattice structure which can be considered as a cascade of single tap prediction filters. This structure, which is used extensively in linear predictive coders for speech processing, splits the signal into sets of forward (f) and backward (b) residual signal samples, with delay added into the backward channel. These signals are multiplied by Parcor coefficients, k(n), which are so called because of their correspondence with the reflection coefficients in a discrete lattice. The forward residual Parcor coefficient for any stage is normally equal to the complex conjugate of the backward coefficient, except in sampled data (baseband) processors, where they are equal.

The calculation of these Parcor coefficient values by recursive techniques has been reported by Itakura and Saito in 1970 and refined by both Makhoul and Mead, who have further suggested methods to simplify the algorithm computation. It can be shown that the lattice structure has an equivalent FIR filter realization which bears significant similarities to the Gram-Schmidt preprocessor which is used in adaptive antenna arrays. The 1attice approach provides a very compact hardware realization of this structure.

The key attraction of the lattice structure is that it measures at the backward residual outputs the signal autocorrelation over successively longer delays to output a set of data-dependent orthogonal signal samples, which can then be used to feed the weighted combiner of the generalized Chang structure.

 

Task 1. Describe the work of Nonrecursive Filter using Scheme1. Compress Text B, part I.

Scheme 1.

Task 2. Compose a microtext of your own using the terminology of Scheme 2. Describe the Finite Impulse Response (FIR) Filter Structure.

Scheme 2.

⇐ Предыдущая1234567Следующая ⇒

Поделиться:

Популярное:

1. Text B. Adaptive Finite Impulse Response Filters (FIR)
2. UNIT 1. INTRODUCTION. ADAPTIVE FILTERS