EE 451
Lab 3: Frequency Response of Difference Equations

A linear constant-coefficient difference equation is of the form

                   M              N 
                   --             --
            y[n] = \  b  x[n-k] - \  a  y[n-k]
                   /   k          /   k
                   --             --
                  k=0            k=1

The frequency response of such a system can be determined by finding its impulse response h(n), and taking the Fourier transform of h(n). In this week's lab, you will implement a second-order difference equation in real time, measure its frequency response, and compare it to the theoretical response.

Consider the difference equation

             y(n) = x(n) - x(n-4)

1. Find the impulse response h(n) of the system.

2. Find the Fourier transform H(w) of the impulse response.

3. Plot the magnitude of H(w) vs. w and the phase of H(w) vs. w.

4. Plot the magnitude of H(f) vs. f and the phase of H(f) vs. f, where f is the continous-time frequency of the sampled signal.

5. Implement the difference equation on the 56002 using the attached code . Use the program from Lab 2 which reads data from the A/D and writes it to the D/A at 48 kHz. Between reading and writing the data, process it with the difference equation. On one channel of the D/A put out the processed data. On the other channel put out the unprocessed data.

6. Use a 0.5 V P-P sine wave from your function generator. Measure and plot the amplitude and phase of the output from 100 Hz to 20 kHz. Compare to the plots of Part 3.