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There is a whole lot easier a way to understand what the DFT does which doesn't involve complex things. If you really believe this, try to generate a discrete
by lutusp 13y ago
There is a whole lot easier a way to understand what the DFT does which doesn't involve complex things.
If you really believe this, try to generate a discrete Fourier transform without using complex numbers of one kind or another. It can't be done. Typically, scalars are (and must be) placed in s complex context (i.e. each term with a zero imaginary part) for the process to succeed.
> The second table is the same as the first except that sampled cosinusiods (the quaduratures) are used instead of sinusoids.
Ah. I see you proved my point. I should have read ahead. Your cosines are the imaginary terms, each 90 degrees away from their partners.
- DonGateley 13y agoSorry, but the real and imaginary designation is imaginary. The Fourier transform is just a functional decomposition using the sine and cosine as basis functions (the Fourier basis.) They have some special and useful properties such as being the eigenfunctions of a linear system which make them the preferred basis for most work. Many other functions could be used in those tables which have the properties of orthogonality and completeness and the decomposition would still be one to one and self invertible. The wavelet transform, for example, which doesn't even pretend to be complex. It was the understanding of wavelet theory that made me realize that sin and cosine decomposition (the Fourier basis) is just one of many.