Seonglae ChoCyclic Convolution
special case of periodic convolution
왜 aliasing 생기냐면 convolution 자체가 band를 그만큼 늘여주는 성질을 가지기 때문에 triangular 두개가 겹쳐져서 rectangular 되는 것
주기성 가진다 가졍해주기 때문에 zero padding 더해주고 circular convolution → Linear convolution 그래서 제로패딩 필터 사이즈만큼 해주는 거구나 (일종의 Upsampling )
근데 부족한 만큼만 aliasing되기 때문에 메모리 부족할 경우 그냥 제로패딩 안하고 만큼씩 하고 aliasing 부분 버림. 씩 하는 게 아니라 무한신호에 대해서 DFT하게 된다 computing은 더 많이 생김
- overlap save method
- save non-aliased part and add all
최종적으로 circular convolution은 일종의 필터링하고 컨볼루션하고 샘플링하는 역할
Circular convolution
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution of the DTFTs of the individual sequences. And each DTFT is a periodic summation of a continuous Fourier transform function (see DTFT § Definition). Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation.
https://en.wikipedia.org/wiki/Circular_convolution