EE 451

Lab 5: FIR Filters and the 56002

1.
The Fourier transform of a low-pass filter will have a value of 1 for low frequencies and a value of 0 for high frequencies:


\begin{displaymath}H(^{j\omega}) = \left\{ \begin{array}{ll}1 & \vert\omega\vert... ...\ 0 & \omega_0 < \vert\omega\vert < \pi \end{array} \right. \end{displaymath}

Let $\omega_0 = \pi/4$. Find the impulse response of this discrete-time system by taking the inverse Fourier transform of $H(e^{j\omega})$.

2.
h[n] has an infinite number of terms, so cannot be implemented. We can get an approximation of h[n] by taking a limited number of terms. Take 101 terms of h[n], n = -50 ... +50. Print out a stem plot of this truncated impulse response, h[n].

3.
Take the Fourier transform of h[n]. Plot the frequency response $\vert H(e^{j\omega})\vert$ vs f and $\angle H(e^{j\omega})$ vs f.

4.
Implement the FIR filter on the 56002. The program fir.asm is a macro to implement an FIR filter on the 56002, and the program fir_test.asm shows how to use the macro. Note that when you call the fir macro, it expects the new input data x(n) to be in the x0 register, and when it exits, the new output data y(n) will be in the a accumulator. You need to reserve storage in x data space for the input data (states in the fir_test program), and need to put the filter coefficients in the y data space (coef in the firt program). Before you call the fir macro the first time, you need to set up r0 to point at the input data array, r4 to point at the filter coefficients, and m0 and m4 to be modulo the number of coefficients in the filter.

5.
Measure the frequency response of the filter. Compare the frequency response to the plots of Part 1.

6.
This it a 100th order filter. What is the maximum order filter you could implement on the 56002, keeping the 48 kHz sampling rate?


Bill Rison
1999-10-01