Digital Signal Processing Reference
In-Depth Information
11
Micro-programmed Adaptive
Filtering Applications
11.1 Introduction
Deterministic filters are implemented in linear and time-invariant systems to remove out-of-band
noise or unwanted signals. When the unwanted signals are known in terms of their frequency band,
a systemcan be designed that does not require any adaptation in real time. In contrast, there aremany
scenarios where the system cannot be deterministically determined and is also time-variant. Then
the system is designed as a linear time-invariant (LTI) filter in real time and, to cater for time
variance, the filter has to update the coefficients periodically using an adaptive algorithm. Such an
algorithm uses some error-minimization criterion whereby the output is compared with the desired
result to compute an error signal. The algorithm adapts or modifies the coefficients of the filter such
that the adapted system generates an output signal that converges to the desired signal [1, 2].
There are many techniques for adaptation. The selection of an algorithm for a particular
application is based on many factors, such as complexity, convergence time, robustness to noise,
ability to track rapid variations, and so on. The algorithm structure for effective implementation in
hardware is another major design consideration.
11.2 Adaptive Filter Configurations
Adaptive filters are used in many settings, some of which are outlined in this section.
11.2.1
System Identification
The same input is applied to an unknown system U(z) and to an adaptive filter H(z). If perfectly
identified, the output y[n] of the adaptive filter should be the same as the output d[n] of the unknown
system. The adaptive algorithm first computes the error in the identification as e[n]
ΒΌ
d[n]
y[n].
The algorithm then updates the filter coefficients such that the error is minimized and is zero in the
ideal situation. Figure 11.1 shows an adaptive filter in system identification configuration.
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