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Applications of Circular Convolution

Circular convolution is a special case of periodic convolution. It is therefore useful in case of discrete time Fourier transform (DTFT). We require Fast Fourier transform to efficiently calculate the DFT(Discrete Fourier transform) and IDFT(Inverse DFT). This algorithm consists of Overlap–add method and Overlap–save method which require circular convolution in the process of calculating linear convolution in an efficient manner, using FIR filter. By being used in other methods, circular convolution can be used in a wide variety of options.

More Applications

• A circular convolution can be used to detect repeating waveforms such as GPS, as it is prone to aliasing.
• For two vectors, x and y, the circular convolution is equal to the inverse discrete Fourier transform (DFT) of the product of the vectors' DFTs. Hence it is faster to use circular convolution in this case
• Due to Overlap add and overlap save , it is used to compute fft in a more efficient manner
• Periodic data analysis, audio and image processing
• Cryptographic algorithms, radar,etc.

Disadvantages of using Circular convolution

While circular convolution has its uses, there are a challenges to using it as well. They are as follows:

• It can’t be used for non-periodic signals.
• Signal wrapping needs to be properly dealt with
• Linear convolution, compared to circular convolution, has a wider range of application areas.
• Difficulties in understanding and execution.