EE313 Linear Systems and Signals - Homework #1 Hints

• 1.1(a). Please simplify the expression in polar form. For example, with z1 = r1 exp(j theta1), z1* = r1 exp(-j theta1). Appendix H in the Signals and Systems textbook by Roberts might be helpful.
• 1.1(b). Compare the calculation using built-in Matlab functions with the calculation using your simplification. In Matlab, z1 = 3 - j*4. For the first part, compare

  conj(z1)
  

  with

  r1 = abs(z1);
  theta1 = angle(z1);
  r1*exp(-j*theta1)
  

  If you leave off the semicolon at the end of the command, then the output will be displayed in the window. If you include the semicolon at the end of the command, then the output will not be displayed in the window.
• 1.2. Once you have generated a plot in Matlab or LabVIEW Mathscript, you can export the plot to another program for editing, such as to shrink the plot to save paper. In the Matlab plot window, first select the Edit menu, then select the "Copy Figure" option, and finally paste the plot into a word processing program for editing.
• 1.3(c). Recall from class lecture that

  ramp(t) = t u(t)
  

• 1.5(a). The problem involves plotting

  g[n] = u[n] + u[-n]
  

  The Matlab/Mathscript implementation of the unit step function, stepfun(t,0), requires the vector t to be in ascending order. So, simplying writing the Matlab code

  n = -10:10;
  g = stepfun(n,0) + stepfun(-n,0);
  

  will produce an incorrect result due to the -n term.

  As an alternative, we can use the fliplr function in Matlab/Mathscript to implement -n.

  n = -10:10;
  g = stepfun(n,0) + fliplr(stepfun(n,0));
  

• 1.5(c). The notation comb₃[n] means a discrete-time impulse train in which impulses occur every three samples. Here is Matlab/Mathscript code to generate a discrete-time comb₃[n] signal for sample indices n = 1 to n = 15:

  n = 1:15;
  comb3 = zeros(1,15);
  comb3(1:3:end) = 1;
  

bevans@ece.utexas.edu