Digital Signal Processing Reference
In-Depth Information
8.12
Review Questions
1. What is the z-transform of x =f3, 2, 4g?
2. A FIR lter has the following lter coecients:f1,1g. What is the frequency
response? Where are the zeros located? Use MATLAB to calculate the output
with an input of cos(2100t), sampled at f
s
= 200 samples/second.
3. A FIR lter has the following lter coecients:f1, 1g. What is the frequency
response? Where are the zeros located? Use MATLAB to calculate the output
with an input of cos(2100t), sampled at f
s
= 200 samples/second.
4. A lter has the following transfer function:
1
4z
2
)=(1z
1
6z
2
):
H(z) = (1 + 3z
a. Determine where the zeros and poles are.
b. Plot these (by hand) on the z-plane, with an x for a pole and an o for
a zero. Is this lter stable?
c. Draw the lter in terms of multipliers, adders, and delay units.
5. What is the z-transform of the transfer function, H(z), for the following lters?
a. FIR lter with coecients b[k] =f-17, 29, 107, 62g
b. IIR lter with feed-forward coecients b[k] =f17; 29; 107; 62gand feed-
back coecients a[k] =f4;7;26;15g
6. Where are the zeros and poles located for the following transfer functions?
Are these lters stable?
a.
1
p
2
1
p
1
H(z) =
2
z
b.
1
p
1
p
1
2
z
2
H(z) =
1z
1
c.
2
)=(14z
1
+ 3z
2
)
H(z) = (1 + 4z
