Advanced Transforms

Topics: Discrete Fourier transform, Fourier analysis, Fourier series Pages: 4 (814 words) Published: August 28, 2013
Queen Mary, University of London|
Lab 1: DFT,FFT and STFT|
ELEM018: Advanced Transform Methods|
|
Arsal Javid|
12/1/2011|

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Section 2:
The following code was used to calculate perform the DFT Function in Matlab: function sw = dft(st)
% DFT - Discrete Fourier Transform

M = length(st);
N = M;
WN = exp(2*pi*j/N);

%Main Loop
for n=0:N-1
temp = 0;
for m=0:M-1
s = st(m+1);
temp = temp + (s* (WN ^ (-n*m))); end
sw(n+1) = temp;
end

The DFT function created was performed on the following signals and a graph was plotted using the function stem4. The function used to display the results was as follows:
function stem4(s)
% STEM4 - View complex signal as real, imag, abs and angle
subplot(4,1,1); stem(real(s)); title('Real');
subplot(4,1,2); stem(imag(s)); title('Imag');
subplot(4,1,3); stem(abs(s)); title('Abs');
subplot(4,1,4); stem(angle(s)); title('Angle');
end

The stem4 function was applied to the DFT function of the following signals.

Uniform Function:
S = ones(1,64)

From the figure above, the Real axis displays a non-zero value at the fundamental frequency; the same is also true when observing the Absolute axis which shows that only a single non-zero value is produced at the fundamental frequency. The Absolute axis displays the result of the Fourier Transform. It is also evident that the angle is changing at a steady rate across the 64 points of the DFT. Delta Function:

S = (1:64) == 1

Only the fundamental frequency, the delta function shown in the above figure provides a non-zero value. The result of the DFT function returns a value of one throughout the whole signal due to the fact that the exponential...
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