ELE315: Random Processes I

Assignment 1: Relating Random Variables to Random Processes

Our first objective is to review what you already know or recall (if anything) about random variables from your previous course.

To begin this review we can develop some simulation results in MATLAB that will allow us to connect familiar concepts such as probability density and distribution functions to some time-varying signals. In addition, some familiar statistical measures like mean and variance can be related to signal properties that are fairly intuitive.

Our primary activity here will be to generate some simulation results and to develop some general observations about how the properties of a random variable affect the appearance of a signal. If we construct a signal model by adding a noise process to a deterministic signal, we can begin to develop some appreciation for the significance of the terms mean and variance in this context.

Procedure

1. Construct the SIMULINK model shown below. Set the Simulation Parameters to a Fixed Step simulation algorithm with a sample time of 0.01 seconds. Leave the start and stop times of the simulation at 0 and 10 seconds respectively. Also, set the sample time for the workspace variable y1 to 0.01 seconds. Once you run the simulation two variables tout and y1 will de automatically defined in the MATLAB workspace.

   

    

2. Code the m-file below and use it to plot the results of the above simulation. Assuming this works, we can now run some simulation exercises and develop a qualitative interpretation of the results.

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   % ELE315: Random Processes I
   %
   %
   % Assignment 1. Due date Sept. 2nd., 1998
   %
   % Relating random variables to random processes
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   clc;close all;
   % Plot the simulation output and the
   % histogram of the data
   figure
   subplot(211);plot(tout,y1)
   subplot(212);hist(y1,50)
   % Compute data statistics
   mean(y1)
   var(y1)

    

3. Experiment with the simulation and generate some representative results. Record the computed mean and variance measures for the results you select. Some typical tests you may wish to observe are (a) Set the signal generator output to zero by setting the amplitude to zero. Run some results with different values for the mean and variance of the random number generator and its seed value. (b) Change the simulation time interval (remember to change y1 also). (c) Add sine-wave and square-wave signals to the random number generator. Vary the magnitude of the deterministic signal component relative to the random number generator output.

4. Repeat some of your results using the other random variable simulation models: the Uniform Random Number generator, and the Band-Limited White Noise generator.

    

   

    

5. Submit a concise report including copies of your simulation results. Annotate your results with the appropriate mean and variance measures calculated with your mfile. Provide some qualitative comments interpreting your results. Explain what looks familiar about the results. What questions do you have? Can you formulate some queries that will provide a focus for our review and discussion for the next few weeks.

6. Due date/time: Wed. Sep. 2^nd, 1996. 6:00 p.m. in KL365C.