Hello Mostafa,
I understand that you want to get the Discrete Time Fourier Series (DTFS) coefficients of a cosine sequence and compute its power.
Given a cosine sequence, which is inherently periodic, we can directly compute its DTFS coefficients. The DTFS coefficients (a_k') of a periodic sequence (x[n]) with period (N) are given by:
for (n = 0, 1, ..., N-1).
Please refer to the below code snippet that illustrates the computation of DTFS coefficients and its power:
% Parameters
N = 100; % Number of samples
f = 1/20; % Frequency
% Generate the cosine sequence for one period
n = 0:N-1; % Time index
x = cos(2*pi*f*n); % Cosine sequence
% Compute DTFS coefficients
ak = zeros(1, N); % Preallocate array for coefficients
for k = 0:N-1
ak(k+1) = (1/N) * sum(x .* exp(-1j * 2 * pi * k * n / N));
end
% For the power, simply square the magnitude of the coefficients
power_ak = abs(ak).^2;
Hope it helps!
