Digital Signal Processing Reference
In-Depth Information
d.
The output of an LTI discrete-time system is given by:
y
(
n
)
= x
(
n
)
∗
h
(
n
)
where
x
(
n
) is the input,
h
(
n
) is the impulse response of the system,
and
denotes circular convolution.
i. Using the convolution property of the DFT, write down a proce-
dure for obtaining
y
(
n
), given
x
(
n
) and
h
(
n
).
ii. If the convolution were performed using
N
-point DFTs and IDFTs,
determine the number of complex multiplications required.
iii. If the convolution were performed using
radix-
2 FFTs and IFFTs,
determine the number of complex multiplications required.
iv. Compare the results of parts (ii) and (iii) for
N =
32.
∗
3.3
Computer Laboratory
Exercise 2: Simulation of harmonic distortion in signal generators — Use
of the FFT (Fast Fourier Transform)
In this laboratory, the frequency spectra of periodic signals at the output of
signal generator are studied analytically and by experiment. The periodic
signals shown in
Figure 3.7
are considered. There are several useful com-
mands in MATLAB
4
to generate periodic signals, and some examples are
given below.
Periodic square pulse
>> y = A*square(2*pi*f*t); generates a square wave
vector
y
with peak amplitude
A
and frequency
f
Hz.
The elements of
y
are calculated at the time
instances of the vector
t
.
>> y = A*square(2*pi*f*t,duty); generates a square wave
vector, with identical parameters as above, but with
specified duty cycle. The duty cycle,
duty
, is the
percent of the period in which the signal is
positive.
Aperiodic triangular pulse
>> y = A*tripuls(t); generates samples of a continuous,
aperiodic triangle at the points specified in array
