# Why do we need circular convolution?

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?

• Your opinion is quite radical because circular convolution is a property of DFT (and DTFT), and not a design requirement. – Juancho Feb 19 '18 at 18:20

• i'll try to add to Jim's answer: Circular convolution is not the end goal we want. Linear convolution (sometimes with a very long impulse response $h[n]$) is the goal. but circular convolution is the only convolution tool that we have when using the FFT (the fast way of doing the DFT) as a means of convolution. so the whole idea of fast convolution (this is that "overlap-add" or "overlap-save" thingie) is how to do linear convolution when your only fast tool is circular convolution. – robert bristow-johnson Feb 19 '18 at 21:23