Prof. Rich Kozick
ELEC 320, Fall 1997

Homework 11

Date Assigned: Monday, September 22, 1997
Date Due: Wednesday, September 24, 1997

Revision in class on September 22: Items 4 and 5 below will be due on Friday, September 26.

  1. Please continue reading Chapter 3, Sections 3.3 and 3.4. Also review Section 1.2 on signals, with particular attention to the impulse function delta(t), step function u(t), and time-shifted signals.

  2. Please show me a draft you your lab report this week. The final report will be due on Monday, September 29.

  3. Problem 3.1 in the text. Note that the term "unit-pulse response" in the text means the same thing as "impulse response", which I have used in class. Also, the impulse response h[n] is computed with all initial conditions equal to zero. This is because h[n] is used via convolution to compute the zero-state response (ZSR) of a system, and the ZSR has all initial condtions equal to zero.

  4. Consider a linear, time-invariant, discrete-time system with impulse response h[n] plotted below. Plot the system output y[n] when the input is the sequence x[n] shown below.
    Hint: y[n] = x[n] * h[n] where * denotes convolution!


    Check your result using MATLAB and the conv command as follows:

    >> h = [1, 1, 1];
    >> x = [1, 1, 1, 1, 1];
    >> y = conv(x, h);
    >> n = 0:length(y)-1;
    >> stem(n, y)

    A note about MATLAB help:

    Remember that MATLAB has on-line help available. For example, typing help conv will describe the convolution command and how to use it. Also, if you type hthelp on the Suns, then a hypertext version of help will be opened in a new window. This might be useful to view the available commands and follow links to related commands.

  5. Problem 3.4 in the text, for the signals x[n] and v[n] in Figure P3.4(b) only. Show all of the steps when you compute your answer on paper, and use the MATLAB conv command to check your results.

Thank you.