Re: Computing DFT of a signal from its DCT coefficients?
- From: glen herrmannsfeldt <gah@xxxxxxxxxxxxxxxx>
- Date: Sat, 22 Jul 2006 12:51:32 -0700
crazydspguy wrote:
I have the following question regarding obtaining the DFT of a signal
directly from its DCT representation:
Say we are given the N-point DCT coefficients Xdct(k) of some real-valued
signal x(n), but what we really want is the N-point DFT of x(n), Xdft(k).
There might be. I would read the description in Numerical Recipes, which describes the differences, especially in boundary conditions,
between DFT and DCT.
I need to obtain the power spectrum of the signal x(n) in the DFT domain,
but I only have the DCT domain information.
For real source data and 2N input values, DFT gives you N sine (imaginary) terms and N (real) cosine terms. DCT gives you 2N cosine terms. I haven't gone through the math, but there might be some trig. identities between those terms.
Note, though, that there are some that don't exist in one or the other,
that is, they are fundamentally different. The DCT boundary condition is that the derivative is zero at the ends, the DST has the function going to zero at the ends, where the DFT is a compromise between the two, with periodic boundary conditions.
You can go from a 2N point DCT to a 4N point DFT, where half the terms are zero, and consider that a DFT domain power spectrum. The terms
that are zero are those that are not allowed by the DCT boundary conditions. If they were supposed to be in the power spectrum, were lost by the DCT operation.
-- glen
.
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- Computing DFT of a signal from its DCT coefficients?
- From: crazydspguy
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