Write your OWN Matlab algorithm without using any builtin Fo

Write your OWN Matlab algorithm (without using any built-in Fourier Transform algorithm of any software) to determine and plot the DFT, specifically the amplitude spectrum in the range 0 lessthanorequalto omega lessthanorequalto 2pi for the following cases: (a) 1 cycle of x(n) = 10cos (2pi5/4n) + cos (2pi17/16n) with 10 zeros padded;

Solution

x = [0 2*3.14];

N = length(x);

X = zeros(4,1)

for k = 0:N-1

    for n = 0:N-1

        X(n) = 10*cos(2*3.14*5/4*n) + cos(2*3.14*17/16*n)

    end

end

t = 0:N-1

subplot(311)

stem(t,x);

xlabel(\'Time (s)\');

ylabel(\'Amplitude\');

title(\'Time domain - Input sequence\')

subplot(312)

stem(t,X)

xlabel(\'Frequency\');

ylabel(\'|X(k)|\');

title(\'Frequency domain - Magnitude response\')

subplot(313)

stem(t,angle(X))

xlabel(\'Frequency\');

ylabel(\'Phase\');

title(\'Frequency domain - Phase response\')

X         % to check |X(k)|

angle(X) % to check phase