Digital Signal Processing Reference
In-Depth Information
x(t)
t,
sec
T
1
0
T
2
FIGURE 3.5
Nonperiodic signal
x
(
t
)
.
FFT evaluation of nonperiodic signals
Step 1.
Sample the signal
x
(
t
), shown in Figure 3.5,
over the complete range
of
the signal in the interval
T
1
≤
t
≤
T
2
.. The sampling interval is:
∆
t
= (
T
2
-T
1
)/
N
where
N
is the number of points in the FFT.
Step 2.
Generate the sampled signal
x
(
n
)
, n =
0, 1
… N -
1. The input signal
is stored as a vector
x
=
[
x
(0)
, x
(1)
, … x
(
N -
1)].
Step 3.
The frequency interval is:
∆ω
=
2
π
/
(
Ν ∆
t
)
The MATLAB program for FFT computation is identical to the one given
in the previous section, for periodic signals.
3.2
Problem Solving
Exercise 1: Solve the following problems, briefly outlining the important
steps.
a.
Suppose that we are given an ideal low-pass discrete-time filter with
frequency response:
()
=
He
j
ω
1
,
0
≤
ωπ
<
4
=
0
,
πωπ
4
<
≤
