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# Computer Assignment 3

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Objective:   To experiment with aliasing and discrete-time single side band modulation.

You may do this experiment in Matlab or in Simulink.  I think Matlab is much easier.

Aliasing
1. Obtain a wav file of a speech signal that was originally sampled at 20k samples per second or more.
3. Cause aliasing by down sampling without filtering.
4. Write the down sampled signal out to a file and listen to it.  Try different down sampling factors.  What does aliasing sound like?
5. Here's some example code.  You can use this file if you wish:  accessutah44.wav
M = 20;
xd = x(1:M:end);
wavwrite(xd,fs/M,16,'accessutahdown.wav');

Single Side Band Modulation
1. Design a Hilbert transformer and a matching delay filter.  Here's some example code for an equiripple Hilbert transformer.
L = 61;
delay = zeros(L,1); delay((L+1)/2) = 1;
bhilb = remez(L-1,[0.025 0.975],[1 1],'Hilbert');

1. Plot the magnitude and phase response of the Hilbert transformer.  You should see something like this.

1. Load the signal in " holly.wav " using the "wavread" command.  We want to modulate this signal using single sideband modulation.  To accomplish this task, we will use a Hilbert transformer to supress negative frequencies.  Then we will frequency translate the signal by cosine modulation.
2. Using the Hilbert transform filter and the delay filter, create a complex signal that contains only positive frequencies.  The Fourier transform of the signal should look like this.

1. We want to up sample this signal by 8, but note that the signal has frequency content all the way out to 0.5 cycles/sample.  Therefore, the filter applied to remove images that arise in the up sampling process will have to have very sharp transition bands.  The requirements on this filter can be eased by frequency shifting down by 0.25 cycles per sample, inserting 7 zeros between each good sample, filtering, and then frequency translating back up by 0.25/8 cycles per sample.
2. Modulating by a complex exponential with a frequency of -0.25 cycles per sample leads to a signal with spectrum that looks like this.

1. This centers the positive frequency portion of the signal around zero so that we can apply a low pass filter to remove the images after up sampling.
2. After up sampling by 8, the signal spectrum should look like this.  This figure also shows the low pass filter response in red.  This filter was designed by:
[b,a] = butter(8,1/(2*M))

1. After applying the filter, the signal spectrum looks like this.

1. After complex exponential modulation to shift the frequencies up, the signal spectrum looks like this.

1. Now, this signal may be modulated to some carrier frequency by complex exponential modulation and taking the real part.  The resulting signal spectrum looks like this.

1. This is a single side band/upper side band (SSB-USB) modulated signal.  Experiment with different carrier frequencies.  Write the SSB-USB signal out to a wave file and listen to it.  To sound inteligible, you may have to keep the carrier frequency fairly low (1/30 to 1/60 cycles/sample range).  Even these small frequency shifts produce a pronounced effect upon the sound of the speech.
2. Determine a system for recovering the original signal sampled at the original sample rate.  Draw a block diagram of the system and carry out the steps in the recovery.  Does the recovered signal sound like the original?  How does the spectrum of the recovered signal compare with the original?

1. To complete this lab, do the following.
• Write a description of the effects of aliasing upon the sound of a signal.
• Show spectral plots demonstrating that you have created a single side band signal.
• Show spectral plots comparing the original signal spectrum with the recovered signal spectrum.  Describe the difference between these two.
• Draw a block diagram of the SSB-USB modulation system.
• Draw a block diagram of the SSB-USB demodulation system.
• E-mail your report and code examples to the TA.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 28). Computer Assignment 3. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Communication_Systems_I/lab3.html. This work is licensed under a Creative Commons License