Micro-programmed Adaptive Filtering Applications - Digital Design of Signal Processing Systems: A Practical Approach - page 455

Signal + Noise
s[n] + v [n] 1

H(z)

Noise
v [n]
0

Adaptive Algorithm

Figure 11.3 Acoustic noise canceller

produce an estimate of v 1 [n], which is then cancelled from the signal x[n], where x[n] ¼ s[n] þ v 1 [n]
and s[n] is the signal of interest [3, 4]. This arrangement is shown in Figure 11.3.

11.2.4 Linear Prediction

Here an adaptive filter is used to predict the next input sample. The adaptive algorithmminimizes the
error between the predicted and the next sample values by adapting the filter to the process that
produces the input samples.
An adaptive filter in linear prediction configuration is shown in Figure 11.4. Based on N previous
values of the input samples, x[n 1], x[n 2], ... , x[n N], the filter predicts the value of the next
sample x[n]as x½n

. The error in prediction e[n] ¼ x[n] x½n is fed to an adaptive algorithm to

modify the coefficients such that this error is minimized.

11.3 Adaptive Algorithms
11.3.1 Basics
An ideal adaptive algorithm computes coefficients of the filter by minimizing an error criterion (h).

The criterion used in many applications is the expectation of the square of the error or mean squared
error:

x

2

xðhÞ¼ E ½e½n

x[n]

^

x[n]

Linear Predictor

e[n]

Adaptive Algorithm

Figure 11.4 Adaptive filter as linear predictor