Digital Signal Processing Reference
In-Depth Information
kind of symmetry do you expect (for the magnitudes), and why?
3. An input sequence, x[n], has the Fourier transform performed on it. The result
is:
X[m] =f3, 2+j4, 1, 5-j3, 0, 0, 0, 5+j3, 1, 2-j4g:
Given that x[n] was sampled at f
s
= 100 samples per second,
a. What is the DC component for this signal?
b. What frequencies are present in the input? Rank them in order according
to amplitude.
c. Using MATLAB, nd x[n].
4. Given x
2
= [0:4786;1:0821;0:5214;0:5821;0:2286; 1:3321; 0:7714; 0:8321];
nd (using MATLAB) the FFT values X
magnitude
[m] and X
phase
[m] for m =
0::7. Show all of your work. Also, graph your results.
5. Try a 5-tap FIR lter using the following random data. Note that this com-
mand will return dierent values every time.
x = round(rand(1, 20)*100)
Use h
1
[k] =f0:5; 0:5; 0:5; 0:5; 0:5g, and compare it to h
2
[k] =f0:1; 0.3, 0.5,
0.3, 0:1g, and h
3
[k] =f0:9; 0:7; 0:5; 0:7; 0:9g. Graph the lter's output, and
its frequency magnitude response. Be sure to use the same x values. Make
one graph with the lters' outputs, and another graph with the frequency
responses. Judging each set of lter coecients as a lowpass lter, which is
best? Which is worst? Why?
6. Try an 8-tap FIR lter using the following random data.
Note that this
command will return dierent values every time.
x = round(rand(1, 20)*100)
Use h
1
[k] =f0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5g, and compare it to h
2
[k] =
f0.1, 0.2, 0.3, 0.5, 0.5, 0.3, 0.2, 0.1g, and h
3
[k] =f0.9, 0.7, 0.6, 0.5, 0.5, 0.6,
0.7, 0.1g. Graph the lter's output and its frequency magnitude response.
Be sure to use the same x values. Make one graph with the lters' outputs,
and another graph with the frequency responses. Judging each set of lter
coecients as a lowpass lter, which is best? Which is worst? Why?
