Thread: How are the DFT and DCT related?

1. How are the DFT and DCT related?

Essentially the question's in the header... I need to write something about the Discrete Cosine Transform, and I'd rather I was able to derive it somehow using the DFT, but I've looked all over and I can't see how I might do this... Any ideas? Please?

2. Originally Posted by malibupete
Essentially the question's in the header... I need to write something about the Discrete Cosine Transform, and I'd rather I was able to derive it somehow using the DFT, but I've looked all over and I can't see how I might do this... Any ideas? Please?
This does depend on how your DCT has been defined. The essential
connection is if you assume that the real signal is symmetric about 0, and
extend it to include the negative time components (at large positive
times as the signal is assumed periodic) then the imaginary components
of the DFT will be zero, and the real components will contain the DCT.

The Wikipedia article on the DCT discusses this WikiDCT

RonL