- 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:

Let . Find the impulse response of this discrete-time system by taking the inverse Fourier transform of .

- 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 vs*f*and 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`firt.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`firt`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?
- 7.
- Use an audio CD to detemine the effect this filter has on music. How
different does the filtered music sound?