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Determine the Fourier series coefficients for each of the following discrete-time peri- odic signals. Plot the magnitude and phase of each set of coefficients ak using MATLAB.

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Answer:

As there are no specific signals given in the question, I will provide the general approach to find the Fourier series coefficients for a discrete-time periodic signal.

Suppose we have a discrete-time periodic signal x[n] with period N. Its Fourier series coefficients can be calculated using the following formula:

ak = (1/N) * sum(x[n] * exp(-j2pikn/N)), for k = 0,1,2,...,N-1

where j is the imaginary unit, and * denotes complex conjugation.

To plot the magnitude and phase of each set of coefficients using MATLAB, we can use the following commands:

Ak = abs(ak); % magnitude of coefficients

theta_k = angle(ak); % phase of coefficients

figure; % create new figure

stem(Ak); % plot magnitude

xlabel('k'); ylabel('|Ak|');

figure; % create new figure

stem(theta_k); % plot phase

xlabel('k'); ylabel('theta_k (radians)');

These commands will generate two separate plots, one for the magnitude and one for the phase, with k on the x-axis and |Ak| or theta_k on the y-axis.

User Rajan Chauhan
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