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Why does fft energy leakage was solved

Signal Processing Asked on October 24, 2021

if we take a sinus with Fd=100KHz with fs=1000KHz sampling rate We do an FFT with 256 members we get energy leakage.
Why choosing Fd=113.28Khz solves this problem?
Thanks

One Answer

See my answer here on how to work with the units in question:

DFT exercise in the book Understanding digital signal processing 3 Ed

Then apply the fact that leakage does not occur when the DFT frame covers a whole number of cycles of your tone signal.


$$ Fs = 1000000 frac{Samples}{Second} $$

$$ Fd = 113280 frac{Cycles}{Second} $$

$$ N = 256 frac{Samples}{Frame} $$

$$ frac{Fd}{Fs} cdot N = frac{frac{Cycles}{Second}}{frac{Samples}{Second}} cdot frac{Samples}{Frame} = frac{Cycles}{Frame} $$

$$ frac{113280}{1000000} cdot 256 = 28.99968 $$

Which is pretty darn close to a whole number.

Answered by Cedron Dawg on October 24, 2021

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