Digital Signal Processing Reference
In-Depth Information
ylabel(
'
ADF output
'
)
subplot(4,1,4),plot(e);grid; axis([0 length(e) -1.5 1.5]);
ylabel(
'
Error
'
); xlabel(
'
Number of samples
'
)
figure
subplot(3,1,1),plot(f,X(1:length(f)));grid; ylabel(
'
Syst. input spect.
'
)
subplot(3,1,2),plot(f,D(1:length(f)));grid; ylabel(
'
Syst. output spect.
'
)
subplot(3,1,3),plot(f,Y(1:length(f)));grid
ylabel(
ADF output spect.
); xlabel(
Frequency (Hz)
);
'
'
'
'
10.3.3
Line Enhancement Using Linear Prediction
We study adaptive filtering via another application example: line enhancement. If the signal frequency
content is very narrow compared with the bandwidth and changes with time, then the signal can
efficiently be enhanced by the adaptive filter, which is line enhancement.
Figure 10.15
shows line
enhancement using the adaptive filter where the LMS algorithm is used. As illustrated in the figure,
the signal
dðnÞ
is the sine wave signal corrupted by the white Gaussian noise
nðnÞ
. The enhanced line
consists of the delay element to delay the corrupted signal by
D
samples to produce an input to
the adaptive filter. The adaptive filter is actually a linear predictor of the desired narrow band signal.
A two-tap FIR adaptive filter can predict one sinusoid (proof is beyond the scope of this text). The
value of
D
is usually determined by experiments or experience in practice to achieve the best enhanced
signal.
Our simulation example has the following specifications:
• Sampling rate
¼
8,000 Hz
• Corrupted signal
¼
500 Hz tone with white Gaussian noise added to the unit amplitude
• Adaptive filter
¼
FIR type, 21 taps
• Convergence factor
¼
0.001
• Delay value
D ¼
7
• LMS algorithm is applied
Figure 10.16
shows the time domain results. The first plot is the noisy signal, while the second plot
clearly demonstrates the enhanced signal.
Figure 10.17
describes the frequency domain point of view.
The spectrum of the noisy signal is shown in the top plot, where we can see the white noise is populated
() cos( / ) ()
2
s
e
()
z
y
()
Adaptive
FIR filter
Enhanced
output
x
()
FIGURE 10.15
Line enhancement using an adaptive filter.
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