Hartogs - Hughes algorithm

Hey Everyone,

Considering the following impulse response:

h(t) = a1δ(t − D1) + a2δ(t − D2) + a3δ(t − D3) + a4δ(t − D4)

with a and D known, how do I impute this impulse response in MATLAB and do I calculate H(f). There is also a random phase uniformly distributed between 0 and 2π.

The purpose of this is to compute the attenuation values Ai = 1/|H^|2 and plotting the attenuation profile in dB.

I have this code but it's not plotting properly, what might be the problem:

% Set parameters

D = [1, 1.01, 1.015, 1.02];

a = [1, 0.5, 0.9, 0.3];

h = zeros(1, 128); % Initialize h as an array of size 1x1

N=128;

% Generate impulse response

for i = 1:4

% Generate a random phase between 0 and 2pi

phase = rand * 2*pi;

% Convert the phase to a complex number

a_complex = cos(phase) + 1i*sin(phase);

h = h + a(i) * a_complex * delta(t - D(i));

end

% Compute H and Hi

H = fft(h);

f = (0:1:127);

% Compute Ai

Ai = 1./abs(H).^2;

% Compute attenuation in dB

attenuation_db = 10*log10(Ai);

% Plot attenuation profile

figure(1);

scatter(f, attenuation_db, 'bo')

title('Attenuation')

xlabel('f')

ylabel('Att(dB)')

Answer 1

[Sulaymon Eshkabilov]

As given in your formulation, is this Dirac delta fcn with a few different time delays t1, t2, t3. If so, you can consider using dirac() and heaviside() - see DOC1 and DOC2.