EE 3512 – Signals
Dr. Obeid Computer Assignment 3
Fall 2012
Due Wednesday 3/27/2013
The purpose of this assignment is to learn about how the duration of a signal affects the properties
of its Fourier Transform.
Part 1: In Matlab, create the following signal x(t) with a duration of 50 seconds.
x(t) = cos(2π · 1 · t) + cos(2π · 2 · t)
Use myFFT to generate the Fourier Transform of x(t). Plot the absolute value of the Fourier
Transform and zoom in to the range 0 to 10Hz. Can you see the two peaks corresponding to the
cosines at frequencies f = 1Hz and f = 2Hz?
Now repeat the above steps but reduce the signal duration first to 5 seconds, then to 1 second. How
does the Fourier Transform change as a result of shortening the signal duration? Can you think of
why this might be happening (you might want to look back at Computer Assignment 1 for some
insight)? If you are supposed to analyze the frequency content of a signal, would you prefer that
the signal be long or short? Why?
Part 2: For signals where the frequencies vary with time, we typically use a tool called a spectrogram to analyze the signal. The spectrogram basically takes the signal, splits it down into windows,
and takes the Fourier Transform of the signal in each window. In this part, you will be taking the
spectrogram of a signal and evaluating how the window duration affects the frequency analysis.
Use your results from Part 1 to inform your observations.
From the Blackboard page, download mySpectrogram.m as well as the audio files piano.wav and
sax.wav. Use the wavread command to load the piano signal into Matlab. Recall that you can use
the soundsc function to listen to the imported sound. Use mySpectrogram to look at the frequency
content. That command can be called by entering
mySpectrogram(s,win,fs)
where s is the imported signal, win is the window length (in seconds) and fs is the sampling rate
of the signal. Create the spectrogram using window durations of 0.01, 0.1, and 0.25 seconds. How
do the spectrograms differ? Why? What are the tradeoffs that an engineer should consider when
selecting a spectrogram window duration? Although the piano sound is a bit easier to interpret,
you might also consider loading and analyzing the sax sound since it has lots of short notes instead
of a handful of long ones.
One more helpful hint: you can zoom in on your spectrogram plots by either using the magnifying
glass icon in the plot window, or by using the xlim and ylim commands.
You do this assignment with a partner. Turn in a report of any duration you see fit (using the
two-column IEEE format) describing what you’ve observed and explaining why that makes sense
and/or fits with the intuition we’ve been learning. You should submit your paper (either MSWord
or PDF format) along with any code you’ve written in a single zip file via email to this address:
iobeid+3512ca3@temple.edu. The name of the zip file should be the last names of your team
members. Papers should arrive by Wednesday 3/27/2013 at 5pm.
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