Let us take two finite duration sequences x_{1}(n) and x_{2}(n), having integer length as N. Their DFTs are X_{1}(K) and X_{2}(K) respectively, which is shown below −
Now, we will try to find the DFT of another sequence x_{3}(n), which is given as X_{3}(K)
By taking the IDFT of the above we get
After solving the above equation, finally, we get
Comparison points  Linear Convolution  Circular Convolution 

Shifting  Linear shifting  Circular shifting 
Samples in the convolution result  N_{1}+N_{2}−1  Max(N_{1},N_{2}) 
Finding response of a filter  Possible  Possible with zero padding 
Methods of Circular Convolution
Generally, there are two methods, which are adopted to perform circular convolution and they are −
Concentric Circle Method
Let x_{1}(n) and x_{2}(n) be two given sequences. The steps followed for circular convolution of x_{1}(n) and x_{2}(n) are
Take two concentric circles. Plot N samples of x_{1}(n) on the circumference of the outer circle (maintaining equal distance successive points) in anticlockwise direction.
For plotting x_{2}(n), plot N samples of x_{2}(n) in clockwise direction on the inner circle, starting sample placed at the same point as 0^{th}sample of x_{1}(n)
Multiply corresponding samples on the two circles and add them to get output.
Rotate the inner circle anticlockwise with one sample at a time.
Matrix Multiplication Method
Matrix method represents the two given sequence x_{1}(n) and x_{2}(n) in matrix form.
One of the given sequences is repeated via circular shift of one sample at a time to form a N X N matrix.
The other sequence is represented as column matrix.
The multiplication of two matrices give the result of circular convolution.
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