Research on circular convolution algorithm in time domain and frequency domain

Circular convolution calculation using the linear convolution is an important means of information processing.In the time domain analysis,the key technology to calculate circular convolution using the linear convolution,which is to add signal elements to the left of the signal,so that the system function elements can be corresponded by the signal elements,is discussed.Three ways to get signal elements from the signal,those are in the index ascending order,in the index descending order,and many times of the signal are given,formula of circular convolution calculation using linear convolution are derived.In the frequency domain analysis,the conditions to transform the circular convolution to the frequency domain are pointed,those are the system function and the signal has the same length,and the signal has to be period.The method of the signal periodic extension and adding zeros to the right of the system function is analyzed,and the circular convolution algorithm by Fourier transform is derived.Circular convolution algorithm flowcharts in the time domain and frequency domain are presented.