Problem 5.17 (a)

Nasser Abbasi

OUTPUT

» nma_ftdemo

nma_ftdemo - Discrete Fourier transform demonstration program

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CODE

% nma_ftdemo - Discrete Fourier transform demonstration program

clear all; help nma_ftdemo; % Clear memory and print header

% modifed by Nasser Abbasi from ftdemo to solve problem 5.17 (a)

%* Initialize the sine wave time series to be transformed.

numberOfPoints = [50 512 4096];

freqs = [0.2 0.2123 0.8];

tau = 1; % Time increment

two_pi = 2*pi;

for(M=1:length(freqs))

freq=freqs(M);

y=[];

t=[];

f=[];

for(i=1:length(numberOfPoints))

N=numberOfPoints(i);

t = (0:(N-1))*tau; % t = [0, tau, 2*tau, ... ]

for(k=1:N)

y(k) = mod(two_pi*t(k)*freq , two_pi);

end

f = (0:(N-1))/(N*tau); % f = [0, 1/(N*tau), ... ]

yt = fft(y);

%* Graph the time series and its transform.

figure;

plot(t,y);

title(sprintf('Original time series, N=%d, fs=%1.4f',N,freq));

ylabel('Amplitude'); xlabel('Time');

figure;

plot(f,real(yt),'-',f,imag(yt),'--');

legend('Real','Imaginary ');

title(sprintf('Fourier transform, N=%d, fs=%1.4f',N,freq));

ylabel('Transform'); xlabel('Frequency');

%* Compute and graph the power spectrum of the time series.

figure;

powspec = abs(yt).^2;

semilogy(f,powspec,'-');

title(sprintf('Power spectrum (unnormalized). N=%d, fs=%1.4f',N,freq));

ylabel('Power'); xlabel('Frequency');

end

end