Digital Signal Processing Reference
In-Depth Information
by applying the steepest descent algorithm for 500 iterations. The derivatives are
dJ
dw
1
¼
200
w
1
100
þ
10
w
2
dJ
dw
2
¼
8
w
2
8
þ
10
w
1
and
and the initial weights are assumed as
w
1
ð
0
Þ¼
0,
w
2
ð
0
Þ¼
0,
m ¼
0
:
001. Plot
w
1
ðkÞ
,
w
2
ðkÞ
,
and
JðkÞ
versus the number of iterations, respectively. Summarize your results.
10.24.
In Problem 10.10, the unknown system is assumed to be a fourth-order Butterworth
bandpass filter with a lower cutoff frequency of 700 Hz and an upper cutoff frequency of
900 Hz. Design a bandpass filter by the bilinear transformation method for simulating the
unknown system with a sampling rate of 8,000 Hz.
a. Generate the input signal for 0.1 second using a sum of three sinusoids with 100 Hz, 800
Hz, and 1,500 Hz and a sampling rate of 8,000 Hz.
b. Use the generated input as the unknown system input to produce the system output.
The adaptive FIR filter is then applied to model the designed bandpass filter. The following
parameters are assumed:
Adaptive FIR filter
Number of taps: 15 coefficients
Algorithm: LMS algorithm
Convergence factor: 0.01
c. Implement the adaptive FIR filter, and plot the system input, system output, adaptive
filter output, and error signal, respectively.
d. Plot the input spectrum, system output spectrum, and adaptive filter output spectrum,
respectively.
10.25. Use the following MATLAB code to generate reference noise and a signal of 300 Hz
corrupted by the noise with a sampling rate of 8,000 Hz.
fs
¼
8000; T
¼
1/fs;
% Sampling rate and sampling period
t
¼
0:T:1;
% Create time instants
x
¼
randn(1,length(t));
% Generate reference noise
n
¼
filter([0000000000.8],1,x); % Generate the corruption noise
d
¼
sin(2*pi*300*t)+n;
% Generate the corrupted signal
a.
Implement an adaptive FIR filter to remove the noise. The adaptive filter specifications
are as follows:
Sample rate
¼
8,000 Hz
Signal corrupted by Gaussian noise delayed by nine samples from the reference noise
Reference noise: Gaussian noise with a power of 1
Number of FIR filter taps: 16
Convergence factor for the LMS algorithm: 0.01
Search WWH ::
Custom Search