Sorry if this sounds like a stupid question, I'm new to DCT.
I've implemented various types of DCT (like IV and II) and they all give vastly different coefficients. From what I've read, the DCT expresses a signal as a sum of cosine waves with various oscillating frequencies. How can different formulas that give different coefficients express the same signal? I created 7 cosine waves (With one DC coefficient) on a graph with proportional periods according to N, and summed them but end up with a function that doesn't represent the signal at all. I'm probably doing this wrong, but here's what I did:
Calculated the 1D-DCT-II of this array:
[1 2 3 4 5 6 7 8]
[12.727922061358 -6.4423230227051 -1.3322676295502E-15 -0.67345480090394 0 -0.200902903736 -1.5765166949677E-14 -0.050702322759621]
Now I don't know if this is how to do it but I tried this (with a window of length 8):
12.72 + -6.44cos((pi/7)x)+ 0cos((pi/3.5)x)...
I can use the inverse DCT (DCT-III) and get the input values back, but I want to see the signal that represents the original input values. I tried summing the frequencies but I don't know if I'm doing it right so can someone guide me? Btw the formula I used was