ECE 561 – Digital Communications Systems
MATLAB Tutorial #1
Assignments in this course contain problems that must be completed using MATLAB.
A
minimal knowledge of MATLAB is required to get started.
Advanced MATLAB
features will be introduced in tutorials posted on the homework web page.
Students who
have not used MATLAB before should go to the following web page:
http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
View the “Getting Started” and “MATLAB Examples” videos for an overview.
Then
proceed to the Interactive MATLAB Tutorials and view “Navigating the MATLAB
Desktop” and “MATLAB Fundamentals.”
You may need to return to these tutorials
periodically throughout the semester.
Throughout this course we will need to display waveforms in both the time and the
frequency domain.
This tutorial will introduce some of the tools available to do that with
in MATLAB.
The Discrete Fourier Transform (DFT)
The Discrete Fourier Transform (DFT) takes a discrete signal in the time domain and
transforms that signal into its discrete frequency domain representation.
This transform
is generally the one used in DSP systems.
The theory behind the DFT is covered in the
discrete time linear systems course.
In that course you will find that the DFT of a signal
can be used to approximate the continuous time Fourier transform.
The Fast Fourier Transform
(FFT)
Depending on the length of the sequence being transformed with the DFT the
computation of this transform can be time consuming.
The Fast Fourier Transform (FFT)
is an algorithm for computing the DFT of a sequence in a more efficient manner.
MATLAB provides a built in command for computing the FFT of a sequence.
In this
section we will discuss the use of the FFT to approximate the Fourier transform of
signals.
Recall that the DFT and FFT are discrete frequency domain representations of a
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In our examples, these sequences will be obtained by sampling
continuous time signals.
In general, if a continuous time function, x(t), is sampled every T
s
seconds until N
samples are collected, the DFT/FFT of this sequence is also of length N.
The
components of the resulting transform correspond to frequencies spaced every 1/(N*T
s
)
Hz.
For a 100 Hz sinusoid:
x(t) = cos(200
π
t)
we can produce a sequence of samples of length N = 2048 spaced every T
s
= .001 in
MATLAB using:
>> clear
>> ts=.001;
>> t=0:ts:2047*ts;
>> x=cos(200*pi*t);
>> plot(t,x)
resulting in the following plot (note that the time axis has been reduced):
We can find the amplitude spectrum of this signal using the
fft
command.
The resulting
transform will contain N = 2048 values.
Since the frequency components are spaced
every 1/(N*T
s
) Hz these correspond to frequency values from 0 to (N1)/(N*T
s
) Hz as
shown below.
>> N=length(x);
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 Spring '09
 Digital Signal Processing, Signal Processing, sine wave block

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