Convolution using fft

1. How do you use FFT for convolution?
2. Why is FFT faster than convolution?
3. What is convolution in Fourier transform?
4. What is the computational complexity using FFT algorithm?

How do you use FFT for convolution?

FFT convolution uses the principle that multiplication in the frequency domain corresponds to convolution in the time domain. The input signal is transformed into the frequency domain using the DFT, multiplied by the frequency response of the filter, and then transformed back into the time domain using the Inverse DFT.

Why is FFT faster than convolution?

The convolution uses your O(n) per output sample. But because the FFT over 2n points coughs up 2n points, and n of those points are 'new', you only do the FFT 1/n as many times as you'd do the convolution.

What is convolution in Fourier transform?

The convolution theorem (together with related theorems) is one of the most important results of Fourier theory which is that the convolution of two functions in real space is the same as the product of their respective Fourier transforms in Fourier space, i.e. f ( r ) ⊗ ⊗ g ( r ) ⇔ F ( k ) G ( k ) .

What is the computational complexity using FFT algorithm?

Radix-2 FFT algorithm reduces the order of computational complexity of Eq. 1 by decimating even and odd indices of input samples. There are two kinds of decimation:[14] decimation in the time domain and decimation in frequency (DIF) domain. Figure 1 shows the flow graph for radix-2 DIF FFT for N = 16.