Howtosignalprocessing
- Why the result of circular and linear convolution is not same?
- Why linear convolution is important in digital signal processing?
- Why do we need circular convolution?
- How circular and linear convolutions are performed using DFT?
Why the result of circular and linear convolution is not same?
Linear convolution may or may not result in a periodic output signal. The output of a circular convolution is always periodic, and its period is specified by the periods of one of its inputs.
Why linear convolution is important in digital signal processing?
Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response. This chapter presents convolution from two different viewpoints, called the input side algorithm and the output side algorithm.
Why do we need circular convolution?
Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation.
How circular and linear convolutions are performed using DFT?
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. Knowing the conditions under which linear and circular convolution are equivalent allows you to use the DFT to efficiently compute linear convolutions.
