Why do we use complex exponentials in the Fourier transform, why do we want the phase part? As opposed to in DCT where there is no phase and only magnitude?
Moreover, what does this phase concretely mean for the signal reconstruction/decomposition? (I know it is related to a shift of a signal, i.e. i know that sin and cos are phase shifted by pi/2 rad u.e. 90 degrees but i can t really make sense of it in Fourier?
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