The Circular Convolution can be performed using two methods: concentric circle method and matrix multiplication method. Assuming x_{1}(n) and x_{2}(n) as two finite sequences of length N.

Now let us consider X_{1}(K) and X_{2}(K) as the inverse DFTs of sequences x_{1}(n) and x_{2}(n). The DFT for the sequences is

Let x_{3}(n) be one more sequence with DFT X_{3}(K). The relation between the three finite duration sequences is given as

After taking inverse discrete Fourier transform of above sequences we have

The above equation can also be written as

**Methods of Circular Convolution**

The two basic methods normally used for circular convolution are −

- Concentric circle method,
- Matrix multiplication method.

**Concentric Circle Method**

We firstly assume two finite length sequences x_{1}(n) and x_{2}(n). Now using the below steps we can easily circular convolve the two sequences.

- Firstly, we take two concentric circles. Then at the circumference of this circle we plot N samples of x
_{1}(n) with equal distance between each point. This plot is then done in an anticlockwise direction. - In the inner circle we plot N samples of x
_{2}(n) in clockwise direction. Then the starting point is kept the same as in x_{1}(n). - Then we multiply the corresponding samples. The result of multiplication is added to obtain the final value.
- At last the value of the inner circle is to be rotated in an anticlockwise direction with one sample at a time.

**Matrix Multiplication Method**

Here we represent the given sequences x_{1}(n) and x_{2}(n) in matrix form.

- The NXN matrix is formed by repeating one of the sequences. This is then achieved by making a circular shift of one sample.
- Then the Second sequence forms a column matrix.
- Finally the result of circular convolution is calculated by multiplying these two matrices.

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