Write a function FIR_freq_resp_single that computes the frequency response hfd for a given impulse response h[n] and a given frequency fd.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Part 1:

Write a function FIR_freq_resp_single that computes the frequency response hfd for a given impulse response h[n] and a given frequency fd. Start your function implementation as follows function H — FIR_freresp_single(h, f d)  % FIR_freqresp_single - compute frequency response from impulse  response at single frequency  

% H — FIR_freq_resp_single(h, fd)

% Input Variables:

% h - vector, samples of the impulse response of the filter

% fd — scalar, normalized frequency to compute frequency

response at (0 <= fd < 0.5)

% Output Variable:

% H - complex scalar, frequency response at frequency fd

Verify that your function works correctly using the following test script. The total error you observe must be very, very close to zero.

%% Test case: 3-pt averager

% expected values at four frequencies

f = [0, 1, 2, 3)16;

expected — [1, 2/3*exp(—lj*pi/3), 0, 1/3];

% coefficients for 3-py averager

M — 3;

b = ones(1, 3)13;

$ compute sum of absolute errors — should be very close to zero

sum_errors — 0;

for n = 1:4

sum_errors += abs(expected(n) - FIR_freq_resp_single(b, f(n)));

end

printf (“Total absolute error: %g”, sum_errors)

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