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|

[Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.]|

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;

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');

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...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Pygmalion: Transform and Eliza Essay
  • Fast Fourier Transform Essay
  • Fourier Transform Assignment Essay
  • Fast Fourier Transforms lecture notes Essay
  • Essay on Computation of the Fractional Fourier Transform
  • Discrete Wavelet Transform Based Digital Image Processing Essay
  • Laplace Transforms Essay
  • My Transformation Transforms Nation Essay

Become a StudyMode Member

Sign Up - It's Free