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I'm reading the following PDF about the DFT:

http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch8.pdf

Please see pages 152-153.

So the inverse DFT (frequency to space, x= ...) is given on page 152. Then it is claimed that the amplitudes for the space-domain synthesis (inverse DFT) are different than the frequency domain of a signal (page 153).

In short, the amplitude for the space-domain synthesis is the corresponding frequency domain multiplied by 2/N, except for the zero frequency term and the last frequency term, which are multiplied by 1/N.

A short digression on 'spectral densities' are made, and I really don't see the connection. Why are the different frequency components weighted differently in the space-domain synthesis?

Any help would be great.

Thanks.

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# Discrete Fourier Transform and Hand-waving

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