Adaptive Filters and Applications - Digital Signal Processing: Fundamentals and Applications - page 491

Audio and periodic interferences

dn ()

en ()

z

Enhanced
audio

yn ()

Adaptive
FIR filter

FIGURE 10.30

Interference cancellation in Problem 10.18.

dn () A cos( 2 fn f / ) nn () s

e ()

z z

1

y ()

Adaptive
FIR filter

Enhanced
output

x ()

FIGURE 10.31

A line enhancement system in Problem 10.26

10.20. In a noisy ECG acquisition environment, the DSP engineer uses an adaptive FIR filter with

20 coefficients to remove 60-Hz interference. The system is set up as shown in Figure 10.19 ,
where the corrupted ECG and enhanced ECG are represented as dðnÞ and eðnÞ , respectively;
xðnÞ is the captured reference signal from the 60-Hz interference; and yðnÞ is the adaptive
filter output. Determine all difference equations to implement the adaptive filter.

10.21. Given an application of the echo cancellation shown in Figure 10.21B , determine all
difference equations to implement the adaptive filter with four adaptive coefficients at the
speaker A site.

10.22. Given an application of the echo cancellation shown in Figure 10.21B ,
a. explain the concepts and benefits using the echo canceller;
b. explain the operations of the adaptive filter at the speaker B site;
c. determine all difference equations to implement the adaptive filter at the speaker A site.
10.7.1 Computer Problems with MATLAB
Use MATLAB to solve Problems 10.23 to 10.26.
10.23. Write a MATLAB program for minimizing the two-weight MSE (mean squared error)
function

2 2

J ¼ 100 þ 100 w

1 þ 4 w 2 100 w 1 8 w 2 þ 10 w 1 w 2