Digital Signal Processing Reference
In-Depth Information
causality, linearity, and time-invariance. Innite Impulse Response (IIR) lters are
also a topic of this chapter. Correlation is covered here as well, which is one appli-
cation of an FIR lter.
3.10
Review Questions
1. What does FIR stand for? What does it mean?
2. What does causal mean?
3. What does linear mean?
4. What does time-invariant mean?
5. Write MATLAB code to compute output (y[n]) for convolution, given any FIR
lter coecients (b[k]) and input (x[n]).
6. Filter input x = [5; 1; 8; 0; 2; 4; 6; 7] with a 2-tap FIR lter of coecientsf1,
1gby hand (do not use a computer).
7. What word describes the operation below?
of x[n] and b[n] produces
y[n].
K
X
y[n] =
b[k]x[nk]
k=0
8. Make up a test signal of at least 10 values, and lter it with the following
coecients. Use MATLAB for this question.
a. b[k] =f:4;:4g
b. b[k] =f:2;:2;:2;:2g
c. b[k] =f:1;:1;:1;:1;:1;:1;:1;:1g
What do you observe? Which set of lter values do the best job of \smoothing
out" the signal?
9. What do we call h[n]? Why is it signicant?
10. What does MAC stand for? What does it mean?
11. For system
1
and system
2
below, are the systems linear? Are they time-
invariant? Are they causal? Explain. Let x[n] be the input and y[n] be the out-
put, where system
1
is y
1
[n] = x[n]x[n1], and system
2
is y
2
[n] = 3x[n]+1.
