Fast convolution using fft

1. Is FFT faster than convolution?
2. Why is FFT faster than convolution?
3. What is fast in FFT?
4. How much faster is FFT to DFT?

Is FFT faster than convolution?

FFT convolution uses the overlap-add method together with the Fast Fourier Transform, allowing signals to be convolved by multiplying their frequency spectra. For filter kernels longer than about 64 points, FFT convolution is faster than standard convolution, while producing exactly the same result.

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 fast in FFT?

The "Fast Fourier Transform" (FFT) is an important measurement method in the science of audio and acoustics measurement. It converts a signal into individual spectral components and thereby provides frequency information about the signal.

How much faster is FFT to DFT?

Graphical explanation for the speed of the Fast Fourier Transform. For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm.