Adaptive Filters and Applications - Digital Signal Processing: Fundamentals and Applications - page 489

using the LMS algorithm for i ¼ 0 ; 1 ; 2 ; 3 ; 4; that is, write the equations for all adaptive
coefficients:

wð 0 Þ¼
wð 1 Þ¼
wð 2 Þ¼
wð 3 Þ¼
wð 4 Þ¼

10.13. Consider the DSP system set up for noise cancellation applications with a sampling rate of
8,000 Hz shown in Figure 10.27 . The desired 1,000 Hz tone is generated internally via
a tone generator, and the generated tone is corrupted by the noise captured from a micro-
phone. An FIR adaptive filter with 25 taps is applied to reduce the noise in the corrupted
tone.
a. Determine the DSP equation for the channel noise nðnÞ .
b. Determine the DSP equation for signal tone yyðnÞ .
c. Determine the DSP equation for the corrupted tone dðnÞ .
d. Set up the LMS algorithm for the adaptive FIR filter.

10.14. Consider the DSP system for noise cancellation applications with two taps in Figure 10.28 .
a. Set up the LMS algorithm for the adaptive filter.

yy ()

d ()

xx n () 5000 () n

Sine wave generator
1000 Hz

Noise channe l

n ()

Gain Clean

signal

0.

Delay for 5 samples

e ( )

y ()

x ()

Adaptive
filter

Noise from line in

FIGURE 10.27

Noise cancellation in Problem 10.13.

Signal and noise

dn ()

Output

e ()

Adaptive filter

Noise

x () yn () w (0)() xn w (1)( xn 1)

y ()

FIGURE 10.28
Noise cancellation in Problem 10.14.