Review and study:

Lecture 1

Lecture 2

Lecture 3

Fourier Synthesis

The MATLAB tutorial demonstrations

Results should be completed by Wednesday, February 25th:

Format for CSCI E-129 assignments: Please keep a work disk (some portable storage medium such as a zipdisk, floppy disk or R/W CD) with all of your work on all of the assignments.  Carefully organize your work disk(s) so that all of your efforts on each "Task" are contained within a single, appropriately labeled folder.  To help you in allocating your time, I will give suggested due dates on the assignments, but don't hand them in on those dates!   On one or two occasions, I will, on short notice, ask you to submit a copy of your work disk for evaluation.  Everyone is expected to complete all of the tasks by the end of the semester.  In the midterm (if we have one) and the final exam, I am bound to ask qualitative questions on issues studied in these tasks.

Warm up 1: Fourier synthesis of a square wave -- not required

To help you get started, build and test the following configuration.

Task 1: Fourier synthesis of a pulse.

A periodic pulse of time width t and period T can be represented as the sum of a series of cosine components of the form   .
It is very important that you believe this assertion!   So, I want you to use MATLAB to check it out.  If you like you could write a simple MATLAB program, but it is easier to build a SIMULINK configuration to demonstrate the assertion.  To be specific take t = 3 and T = 15, for example, and add maybe ten of fifteen terms (i.e. n = 0, 1, 2, ··) as "Sine Wave" modules from the SIMULINK "Sources" library.  In SIMULINK, you can directly enter into the dialog for each "Sine Wave" source the amplitudes as "sin(n*pi/5)/n", the frequencies as "2*pi*n/15" and the phases as "pi/2" (for cosines).  (You should note that MATLAB thinks that "sin(0)/0" is undefined, but it is actually "1" so the n = 0 term  should be added to the overall sum as a "constant" from the Simulink "Sources" library.)   After getting things to work, save your best  scope representation of the synthesized pulse as an EPS file.

Task 2: Spectrum of a DSB-AM signal.

In lecture, we discussed amplitude modulation in some detail.  In this assignment I would like you to build and study a model of a DSB-AM modulator.  The linked sketch is annotated with a set of reasonably good starting simulation parameters, but you may be able to enhance system performance by varying a parameter or two.  If no parameter is specified, use the library default value. 

1.  Follow the temporal and spectral evolution of the signals through each phase of the communication process and make sure that you understand each phase.
 
2. Note how the DSB-AM spectrum varies with the amplitude of the modulating signal.


3. Also note the critical role that multiplication (i.e.a nonlinear operation) plays in the modulation (encoding) process.

 

Task 3: Study of the Bandwidth of FM Signals.

As we have seen, the bandwidth of AM signals is simply related to the "information bandwidth" and is independent of the amplitude of the modulation.  However, the bandwidth of FM signals is quite a complicated issue.  For example, the FCC allocates 75 kHz to each broadcast FM channel, but the "information bandwidth" is around 15 kHz.  To gain experience with such spectral ideas, I would like you to build a Simulink configuration to study how FM bandwidth varies with the strength of the modulation (i.e.the modulation index).  You will note that the FM modulator is considerably more complicated than its AM counterpart (This difference in complexity also applies in the decoding processes.).  The linked sketch is annotated with a set of reasonably good starting simulation parameters, but you may be able to enhance system performance by varying a parameter or two.  If no parameter is specified, use the library default value.

1. Build your configuration and make sure you understand what is going on by following the temporal and spectral evolution of the signals.
 
2. From the spectrum analyzer, estimate how the FM signal bandwidth varies with the modulation index (usually denoted as beta) -- start at 0.5 and go to 10 or so.  Record you results on your work disk.

Task 4: Study of the Spectrum of ASK Signals.

1. Build your configuration and make sure you understand what is going on by following the temporal and spectral evolution of the signals.


2. For a given value of the pulse width and repetition rate, make sure that you understand the observed spectra.


3. In particular, for a given pulse width, how does the spectrum change with pulse repetition rate?  Why does it do so?