How can a DCT help identify the obvious frequency of a discrete wave?

[yetar]

Hello,

Suppose I have a discrete function of a perfect cosine wave.
So if I will do a DCT on this function I will get one non zero coefficient which corresponds to the perfect cosine wave, and the rest will be zero.
Now I have a pass filter, which filters out anything with a frequency which is different from the original cosine wave.
If I will do this filter on the DCT I did to the cosine wave, then no coefficient should change.
Now, suppose I have a second function which is also a perfect cosine wave of the same frequency as the cosine wave in the first function, but with a different phase.
So the DCT of the second function will give me many non zero coefficients.
If will pass the same filter I did on the first function DCT, then I will loose many coefficient and the result will be some wave which is weaker then the second function original cosine wave.
Is that true?

Basicaly I am trying to find the "obvious" frequency of a discrete wave.
Lets say I have a pure triangle wave. Doing DCT on it will produce a lot of coefficients of different frequencies, but how do I discover the obvious frequency of the triangle wave from these coefficients?

Thanks in advance.

 

[DrClaude]

The problem is that you are confining yourself to a DCT. Do a full Fourier Transform instead.