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1. (30 points) Design a high-pass filter that has an wg = 0.17, Wp = 0.57, 81 = 0.05 and 82 = 0.01. The analog equivalent fre

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The analog frequency equivalent of the filter is 2000*2pi/0.5pi = 8000Hz.    

The filter is designed using Matlab:

Fpass = 2000;
Fstop = 2000/5;
Apass = 99;
Astop = 95;
Fs = 8e3;

d = designfilt('highpassfir', ...
'PassbandFrequency',Fpass,'StopbandFrequency',Fstop, ...
'PassbandRipple',Apass,'StopbandAttenuation',Astop, ...
'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d)

Output:

The filter coefficients (and the difference equation coefficients) are as follows:

>> b = d.Coefficients

b =

Columns 1 through 10

-0.0025 -0.0316 0.1355 -0.0868 -0.3065 0.5836 -0.3065 -0.0868 0.1355 -0.0316

Column 11

-0.0025

The filter is a stable filter

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