I am undergoing a course on DSP and we were recently introduced to the amazing concept of DFT.
But I have some apprehensions against it. DFT is supposed to be the methodology of fourier transform, as implemented in hardware or software. Now, if I want to convolve two signals' DFT, I could simply linearly convolve them. There would be no wraparound error, because all that I have to do to implement linear convolution is tell my computer that the array now flips and then multiplies and slides - i.e., linearly convolves.
Circular convolution was developed to avoid wraparound error; however, the computer does not know that DTFT is a periodic function, and, thus, shifting the DFT array will render me with a circular shift.
I know my opinion is rather radical, but I am sure that this is because I have a very abstract level acquaintance to this concept. Can someone enlighten me more, herein?