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N POINT CIRCULAR CONVOLUTION OF VECTORS A AND B

Platform : DSP

IEEE Projects Years : 2006

Version 2.8: Jul 19, 2006 4:36 pm GMT-5 AIM: To Understand circular convolution of vectors ABSTRACT You should be familiar with Discrete-Time Convolution1, which tells us that given two discrete-time signals x [n], the system's input, and h [n], the system's response, we de_ne the output of the system as y [n] = x [n] _ h [n] When we are given two DFTs (_nite-length sequences usually of length N), we cannot just multiply them together as we do in the above convolution formula, often referred to as linear convolution. Because the DFTs are periodic, they have nonzero values for n _ N and thus the multiplication of these two DFTs will be nonzero for n _ N. We need to de_ne a new type of convolution operation that will result in our convolved signal being zero outside of the range n = {0, 1, . . . ,N − 1}. This idea led to the development of circular convolution, also called cyclic or periodic convolution. LEARNING OBJECTIVE : To verification of circular convolution via DFTs INPUT: Two Set of four integer values OUTPUT: Simulated wave form of multiplied version of Two Set of four integer values APPLICATIONS: Signal Processing Software Used: MATLAB2007A

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