Why Is Circular Convolution Important in Signal Processing?

[dexterdev]

Hi PF,
What is circular convolution? Why do we need such an operation if we have linear convolution, What is its basic difference of both convolutions. Is circular convolution used only in frequency domain?

-Devanand T

 

[atyy]

http://ocw.mit.edu/resources/res-6-008-digital-signal-processing-spring-2011/study-materials/MITRES_6_008S11_lec10.pdf

According to these notes, we usually want linear convolution. But there's a fast algorithm for circular convolution, so we adapt that to do linear convolution.

 

[rbj]

that's a good pdf.

one note about meaning:

$$((n))_N \ \triangleq \ n\,\bmod\,N \ = \ n - N \left\lfloor \frac{n}{N} \right\rfloor$$

this just makes the index $n$ wrap around so that it is always $0 \le n < N$ . that's what makes it circular.

 

[DSRadin]

I would offer that we don't particularly want circular convolution, but it is a necessary by-product of the finite-length DFT operations.

Circular convolution also drives the need for windowing and filtering to remove all of the translated spectral images. Learning to mitigate the negative effects of circular convolution is important.