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I am going through DFT basics. I found somwhere it is represented by the equation $$ x[n] \ \triangleq \ \sum_{k=0}^{N-1} \ X[k] \ e^{j 2 \pi nk/N} $$

$$ X[k] \ = \ \frac{1}{N} \sum_{n=0}^{N-1} \ x[n] \ e^{-j 2 \pi nk/N} $$

While in other literature $$ x[n] \ \triangleq \frac{1}{N} \sum_{k=0}^{N-1} \ X[k] \ e^{j 2 \pi nk/N} $$

$$ X[k] \ = \ \sum_{n=0}^{N-1} \ x[n] \ e^{-j 2 \pi nk/N} $$

When is the scaling factor needs to be reversed? Which equation is to be used for 2-d Fourier Transform (Image TransforM - where to include $\frac{1}{MN} $)?

avi1987
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  • this is a question so often asked here... wait, I'll find you a duplicate. – Marcus Müller Mar 31 '17 at 15:28
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    http://dsp.stackexchange.com/questions/31984/matlab-tt-fft-and-tt-ifft-scaling || http://dsp.stackexchange.com/questions/32187/what-should-be-the-correct-scaling-for-psd-calculation-using-tt-fft || http://dsp.stackexchange.com/questions/17864/please-give-the-reason-why-every-notation-for-dft-is-valid and many more – Marcus Müller Mar 31 '17 at 15:31
  • Which one depends on whether you want energy preserving or magnitude preserving... – hotpaw2 Mar 31 '17 at 16:15

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