Adaptive Filters and Applications - Digital Signal Processing: Fundamentals and Applications - page 454

Noise spectum

Spectrum

Desired signal spectrum

f

FIGURE 10.1

Spectrum illustration for using adaptive filters.

only introduce some fundaments of the subject, that is, adaptive finite impulse response (FIR) filters
with a simple and popular least mean square (LMS) algorithm. Further exploration into adaptive
infinite impulse response (IIR) filters, adaptive lattice filters, their associated algorithms and appli-
cations, and so on, can be found in comprehensive texts by Haykin (1991), Stearns (2003), and Widrow
and Stearns (1985).
To understand the concept of adaptive filtering, we will first look at an illustrative example of the
simplest noise canceller to see how it works before diving into detail. The block diagram for such
a noise canceller is shown in Figure 10.2 .
As shown in Figure 10.2 , first, the DSP system consists of two analog-to-digital conversion (ADC)
channels. The first microphone with ADC is used to capture the desired speech sðnÞ . However, due to
a noisy environment, the signal is contaminated and the ADC channel produces a signal with the noise;
that is, dðnÞ¼sðnÞþnðnÞ . The second microphone is placed where only noise is picked up and the
second ADC channel captured noise xðnÞ , which is fed to the adaptive filter.
Note that the corrupting noise nðnÞ in the first channel is uncorrelated to the desired signal sðnÞ ,so
that separation between them is possible. The noise signal xðnÞ from the second channel is correlated

S i g n a l a n d n o i s e E r r o r s i g n a l

() () () ~ ()

dn sn nn () () ()

en dn yn sn

ADC

DAC

y ()

x ()

yn wxn () ()

n

ADC

Adaptive filter

Noise

ww e n x n
n

00. ()()

1 n

LMS algorithm

FIGURE 10.2
Simplest noise canceller using a one-tap adaptive filter.