Digital Signal Processing Reference
In-Depth Information
+
+
+
+
y
[
k
]
(i) Determine and plot the frequency characteristics of the filters.
(ii) If the sequence
x
[
k
] cos(0
.
5
k
)
+
cos(
k
) is applied at the input of
filter
H
1
(
z
), determine the output of the filter from the frequency
characteristics obtained in (i).
(iii) Repeat (ii) for filter
H
2
(
z
). What advantage do you see with the
linear-phase filter?
14.3
Consider a digital filter with impulse response given by
1
/
3
−
1
≤
k
≤
1
h
[
k
]
=
0
otherwise.
(i) Calculate the transfer function of the filter.
(ii) Sketch the amplitude and phase responses of the filter with respect
to frequency.
(iii) How will you classify this filter - lowpass, bandpass, bandstop, or
highpass?
(iv) Does it have a linear phase?
14.4
Consider a digital filter with transfer function given by
H
(
z
)
=
0
.
7
+
0
.
2
z
−
1
+
0
.
8
z
−
2
1
+
0
.
5
z
−
1
−
0
.
24
z
−
2
.
(i) Plot the impulse response and the frequency characteristics of the
filter.
(ii) From the frequency characteristics, determine the maximum magni-
tude of the pass-band and stop-band ripples and the transition band-
width.
14.5
Given the flow graph in Fig. P14.5, calculate the transfer function and the
impulse response of the LTI system of the realization. From the transfer
function, calculate the magnitude and phase spectra for the filter.
14.6
The flow graph of Fig. P14.5 can be implemented by using only three
scalar multipliers. Sketch the flow graph which uses three scalar multipli-
ers without increasing the number of delay elements or two-input adders.
14.7
Repeat Problem 14.5 for the flow graph shown in Fig. P14.7.
14.8
Draw the flow graphs for (i) the direct form and (ii) the cascaded form
for an FIR filter with a transfer function given by
H
(
z
)
=
0
.
4
−
0
.
8
z
−
1
+
0
.
4
z
−
2
.
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