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So, I'm evaluating the Discrete Sine transform Basis functions and I found on the internet the following picture:

DST Basis Functions

So, I may be getting the point wrong, but, if the 2D DCT equation is:

DCT equation

Then the Discrete Sine transform shall be: DCT equation

Then, it is clear that for the lower frequency (u=0,v=0) all cosines will be 1, but in the case of the sines all will be 0 (for frequency=0), therefore, the basis function for the lower frequency, in the sine case, will be zero, right?

Is the upper left image (u=0,v=0) correct? It should be constant, right? (btw: It shall also be zero, right?)

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I think I got it:

While in the DCT there are definitions of the DCT that make cos(0) when u and v are zero, this does not apply to DST (see: https://en.wikipedia.org/wiki/Discrete_sine_transform).

In the DST definition, there is always a +1 or a +1/2 adding to the frequency.

This explains why it is not zero and also the graph above. It varies (for u=0 and v=0) because the content of the sine is not zero.

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No, an all-zero function cannot be a base function; therefore, the DST can not be constructed the way you recommend.

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  • $\begingroup$ I was not recommending doing it that way, based on the wikipedia page: en.wikipedia.org/wiki/Discrete_sine_transform It seems like in the case of the DST a +1 or +1/2 is added to the frequency (u or v) in order to avoid making 0 the sine when u=0 or v=0 for all the DST types. Indeed, that also explains why it is not constant for u=0 and v=0 $\endgroup$
    – f.gallardo
    Dec 3 '17 at 17:40

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