z-Transform

ECGR4124 Project 7, z-Transform

Form the same groups of 3 as before. Members of any group must be all graduate or all undergrad.

Do NOT use "zoom" feature on any plots unless specifically requested.

Preliminary tasks

Run NetBeans 5.5, or a later version (Start>AllPrograms>MosaicXp>Programming>Netbeans>NetBeans55)
Make a copy of your previous project from within NetBeans, and name this new project p5DSPsoundv55a.

Create a function to plot the frequency response |H(w)| of H(z)=N(z)/D(z),
from 0 to 2pi, using the DSPsoundv55a "freq response" button.
N(z) is a numerator polynomial (i.e., 2 + z^2 + 3z^3)
D(z) is the denominator polynomial of the z-transform.
Use 2048 points in the plots.
Use: H(w) = H(z)|z=e^(jw)
Hint: prevent divide by zero by adding 1e-8.
Hint: create a Myclass function
freqresp(a3,a2,a1,a0,b3,b2,b1,b0) :
where a3,a2... are numerator coefficients, b3,b2,... are denominator coefficients of :
H(z) = [a3z^3+a2z^2+a1z+a0]/[b3z^3+b2z^2+b1z+b0].

Then your code calling the function should perhaps be (for case 1):
    float a3=0, a2=1, a1=1, a0=1;
    float b3=0, b2=1, b1=0, b0=0;
    x.freqresp(a3,a2,a1,a0, b3,b2,b1,b0);
    dispData.equals(x);
and edit the above variables and recompile for each case below.

Using the above function plot the frequency responses |H(w)| of the following H(z)'s:
1. ( P1 ) N(z) = z^2 +z^1 + 1
  D(z) = z^2
2. ( P2 ) N(z) = z^3 +z^2 +z^1 + 1
  D(z) = z^3
3. ( P3 ) N(z) = z
  D(z) = z - 1/2
4. ( P4 ) N(z) = z
  D(z) = z - 2
5. ( P5 ) N(z) = z^2
  D(z) = z^2 - z + 1/2
On a separate sheet of paper, find the poles and zeroes of the above H(z)'s and plot them in the z-plane.
Use Matlab if you wish. On these plots, show the ROC for causal h[n]. (Handwritten plots are OK) ( Q1-Q5 )
What are the frequencies in rad/sample at the two locations of zero-crossings of |H(w)| in plot P1.( Q6 )
Do the locations of the zeroes of H(z) in the pole-zero plot correspond the locations of minima or maxima of |H(w)| in plot P1.( Q7 )

On a separate sheet of paper, state which of the 5 systems above are stable. ( Q8 )
What did Lofti Zadeh and John Ragazzini develop in 1952? ( Q9 )

Report

Use the Project Report Template (also shown as pdf file)

Include the plot numbers P1, P2, etc in captions, along with a short description!
Write a cover sheet + 1 page executive summary ONLY!!! Describe any unresolved issues.
Place answers to all questions on one or more consequitive sheets of paper at the front of the report!
Do NOT scatter the question answer sheets throughout the report, keep them together
Do NOT use "zoom" feature on any plots unless specifically requested.
Make sure that you include question numbers and plot numbers on all sheets!
I will only look on the question answer-sheets for any discussion.
All extraneous material WILL BE IGNORED!
Do not write any discussion, except directly on the question answer-sheets or 1 page summary.
Do not add extraneous pages.
Do not put explanations on plots unless specifically directed to do so.
Include any problems or unresolved issues in the summary.

ECGR4124 Project 7, z-Transform

Copyright 2009 T.P. Weldon