ELEC 310  Signal Analysis II
Assignment 3
 For the 3 filters of Assignment 1,
find the transfer function H(z).
Write H(z) as a ratio of polynomials
and identify the poles and zeros. Choose a = 0.9.
 For the 3 filters of Assignment 1,
find the impulse response h(n) in two ways:
 work out algebraically using the inverse ztransform,
and evaluate the first few terms numerically.

Use the POI software
to place the poles and zeros in the complex
plane, and let the program calculate
the impulse response. in POI, drag zeros on the
zplane from the top left, and drag poles from the top right.
Under the tab "analysis",
choose "analysis graph", and then in the new window
under the tab "graph" choose "impulse response".
Under the tab "file" choose "save values" which will
save the impulse response values in a file.
Compare the results of algebra with POI.
The sampling rate fs is not
defined in Assignment 1, the POI software
lets you choose the sampling rate.
Choose fs = 44,100 Hz used for music CDs.
 POI also calculates the
frequency response H(z) with z along the unit
circle z = exp(jw_hat) = exp(j2pif/fs)
for f less thanl fs/2.
The sampling rate fs is not
defined in Assignment 1, the POI software
lets you choose the sampling rate.
For fs = 44,100 Hz,
calculate the frequency response for each of the
3 filters of Assignment 1. Do this two ways:

Use the POI software
to place the poles and zeros in the complex
plane, and let the program calculate the
frequency response.
 work out the algebraic expression for the
frequency response and plot using Matlab.
Compare the results from POI and Matlab.
 Example Matlab code for plotting frequency response
filtdemo.m

A linear time invariant filter is described by the difference
equation y[n]=0.8y[n1]0.8x[n]+x[n1].

Find H(z) and identify the poles and zeros.

Find an expression for the frequency response, assuming fs=44,100 Hz.
 Show that the magnitude of the frequency response is 1 for all
values of f.