## EE 451

Homework Assignment 10
Due Nov. 1, 2000

1. We wish to design an FIR differentiator which has the ideal frequency response:

1. Take the inverse Fourier transform of to show that:

2. Use the above equation with a Hamming window to find for a differentiator where . Plot and plot the pole-zero diagram for .
3. Plot the gain and phase of the filter.
4. In MATLAB, generate a signal , where . Find 101 terms for :
        wo = pi/16;
n = 0:100;
x = cos(wo*n);


Use the above to filter the signal : y = filter(h,1,x);. Use MATLAB to plot . Over the top of this, plot . (Remember that the output was delayed by samples.) Does look like the derivative of ?

5. Repeat Part (e) for .

2. We wish to design a Hilbert transformer which has the ideal frequency response:

1. Take the inverse Fourier transform of to show that:

2. Use the above equation with a Hamming window to find for a Hilbert transformer where . Plot and plot the pole-zero diagram for .
3. Plot the gain and phase of the filter.
4. In MATLAB, generate a signal , where . Find 101 terms for :
        wo = pi/16;
n = 0:100;
x = cos(wo*n);


Use the above to filter the signal : y = filter(h,1,x);. Use MATLAB to plot . Over the top of this, plot . (Remember that the output was delayed by samples.) Does look like the ouput you would expect for a Hilbert transformer?

5. Repeat Part (e) for .

Bill Rison, <rison@ee.nmt.edu >