Figure 8.2 Block diagram of adaptive filter
Figure 8.3 Block diagram of FIR filter for adaptive filtering
minimize the mean-square value of e(n). Therefore the filter weights are updated so that
the error is progressivelyminimized on a sample-by-sample basis.
In general, there are two types of digital filters that can be used for adaptive filtering:
FIR and IIR filters. The choice of an FIR or an IIR filter is determined bypractical
considerations. The FIR filter is always stable and can provide a linear phase response.
On the other hand, the IIR filter involves both zeros and poles. Unless theyare properly
controlled, the poles in the filter maymove outside the unit circle and make the filter
unstable. Because the filter is required to be adaptive, the stabilityproblems are much
difficult to handle. Thus the FIR adaptive filter is widelyused for real-time applications.
The discussions in the following sections will be restricted to the class of adaptive FIR
The most widelyused adaptive FIR filter is depicted in Figure 8.3. Given a set
of L coefficients, w
n, l 0, 1, . . . , L À 1, and a data sequence, fxn xn À 1
. . . xn À L 1g, the filter output signal is computed as
nxn À l,
where the filter coefficients w
n are time varying and updated by the adaptive algo-
rithms that will be discussed next.
We define the input vector at time n as
xn xn xn À 1 . . . xn À L 1