Why does fft energy leakage was solved

Question

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

Answer 1

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.

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

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

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

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

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

Which is pretty darn close to a whole number.