ASN11 - Leakage demonstration in Octave

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Leakage occurs when the Discrete Fourier Transform (DFT) is applied to a signal whose range is not a multiple of the total period. The DFT function assumes that the signal is periodic it when it repeats the function should be periodic. If the sample range is not a multiple of the period them when the DFT repeat the function will have disctonuity at the restarting point.

Example octave script no leakage

fs=1500

t=[1:20]/fs; %is multiple of the period 1/fs

y=sin(2*pi*t);

x= dft(y,t); %function x is continous

Example octave script with leakage

fs=1500

t=[1:20]/500; %does not include whole periods

y=sin(2*pi*t);

x= dft(y,t); %function x is not continuous and demonstrates leakage