DFT of a cosine/sine wave? I'm seeing everywhere that the DFT of a sinusoid (i.e. a sine that has been windowed with a rectangular window) are just two deltas. What I don't understand is why the DFT is not the convolution of the transform of the infinite sinusoid (two deltas) and the transform of the rectangular window (a sinc). Wouldn't this be the right thing to do?
If a pure sinusoid is exactly integer periodic in the DFT's aperture, then the Sinc function, resulting from the rectangular window, will pass exactly thru zero at all but two points of the DFT results, thus appear to be invisible except for the two deltas.  If you vary the DFT window size by fractions of a period of the sinusoid, then it will show up, as you expect, since the DFT will no longer sample the Sinc when it crosses zero.