Micro-programmed Adaptive Filtering Applications - Digital Design of Signal Processing Systems: A Practical Approach - page 454

x[n]

d[n]

U(z)

y[n]

H(z)

-

e[n]

Adaptive Algorithm

Figure 11.1 Adaptive filter in system identification configuration

11.2.2 Inverse System Modeling
The adaptive filter H(z) is placed in cascade with the unknown system U(z). A known signal d[n]is
periodically input to U(z) and the output of the unknown system is fed as input to the adaptive filter.
The adaptive filter generates y[n] as output. The filter, in the ideal situation, should cancel the effect
of U(z) such that H(z)U(z) 1. In this case the output perfectlymatches with a delayed version of the

input signal. Any mismatch between the two signals is considered as error e[n]. An adaptive
algorithm computes the coefficients such that this error is minimized. This configuration of an
adaptive filter is shown in Figure 11.2.
This configuration is also used to provide equalization in a digital communication receiver.
For example, inmobile communication the signal transmitted froman antenna undergoes fading and
multi-path effects on its way to a receiver. This is compensated by placing an equalizer at the
receiver. A know input is periodically sent by the transmitter. The receiver implements an adaptive
algorithm that updates the coefficients of the adaptive filter to cancel the channel effects.

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11.2.3 Acoustic Noise Cancellation
An acoustic noise canceller removes noise from a speech signal. A reference microphone also picks
up the same noisewhich is correlated with the noise that gets added in the speech signal. An adaptive
filter cancels the effects of the noise from noisy speech. The signal v 0 [n] captures the noise from the
noise source. The noise in the signal v 1 [n] is correlated with v 0 [n], and the filter H(z) is adapted to

Data
x[n]

Training
t[n]

y[n]

^

U(z)
Channel

H(z)

Data

-

x[n]

Training

d[n]

Adaptive Algorithm

e[n]

Figure 11.2 Adaptive filter in inverse system modeling