Classical Digital Design
Given
the limitations of currently available technology, only adaption
algorithms which are relatively
simple in a computational sense
may
be executed in digital
terms
at real-time
bandwidths.
The major computational load is imposed by the need to perform the
linear convolution of the input signal samples with the stored filter
weights (the finite impulse response filter) with a marginal overhead
being provided by the adaption algorithm. To provide updates for the
weight value estimates for the filter the adaption algorithm must be
supplied with
samples
of the
signal
input and the output
error
from the estimation process. This information
permits
implementation of any of
the
algorithms.
Before considering the implementation of the adaption process itself we shall examine one common approach for implementing the FIR filter section. This technique is illustrated in Figure 1. It uses a single digital multiplier with vectors
Figure 1. Block diagram of a fixed response digital filter using a single multiplexed multiplier.
representing the incoming signals and the filter weights stored in digital memory. This implementation with digital memories is a development of the initial versions of this realization, which was based on analog (bulk delay) memories. Each pair of inputs (signal and weight) is presented to the multiplier sequentially and the multiplication product is accumulated. Therefore, for a filter length of N points the multiplier must operate at N times the sampling rate of the filter. This, obviously, provides a fundamental limitation to the available time-bandwidth product, given a target sampling frequency. The time-bandwidth product may be extended by cascading two or more such filter without affecting the sampling frequency. This, however,, results in the use of further multipliers, therefore increasing the cost and power consumption of the system. A number of alternative schemes for filter implementation may be used which have various trade-offs in terms of overall circuit efficiency.
Task 3. Compare your abstract and summary with those presented below.
Аннотация
Представлен
цифровой алгоритм адаптации для
корректировки оценок значений весовых
коэффициентов фильтра. Описан общий
подход к реализации секции фильтра КИХ
- типа на примере одиночного цифрового
умножителя. Кратко отмечены некоторые
трудности использования альтернативных
схем для реализации фильтра.
Abstract
Digital adaption algorithm to provide updates for the weight value estimates is presented. Common approach for implementing the FIR filter with a single digital multiplier is described. A number of alternative schemes for filter implementation are briefly touched upon.