Fast Fourier Transform: Difference between revisions

Revision as of 13:01, 22 March 2022

Fast Fourier transform (FFT) is an efficient algorithm for calculating the discrete Fourier transform (DFT). The FFT produces the same results as a DFT but it reduces the execution time by hundreds in some cases. Whereas DFT takes an order of $O(n^{2})\,$ computations, FFT takes an order of $O(n\,\log \,n)$ , and is definitely the preferred algorithm to be used in all applications in terms of computational complexity. The FFT in most implementations consistent of samples that are exactly a power of 2, this is commonly known as a FFT Radix 2 algorithm where $n=64,128,256,512,1024,2048$ etc.

Unlike the DFT, the frequency spacing nor window size per-bin can't be adjusted because FFT bins aren't calculated individually.

External links

Fast Fourier transform on Wikipedia

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-'''Fast Fourier transform''' ('''FFT''') is an efficient algorithm for calculating the [[DFT|discrete fourier transform]] (DFT). The FFT produces the same results as a DFT but it reduces the execution time by hundreds in some cases. Whereas DFT takes an order of <math>O(n^2)\,</math> computations, FFT takes an order of <math>O(n\,\log\,n)</math>, and is definitely the preferred algorithm to be used in all applications in terms of computational complexity. The FFT in most implementations consistent of samples that are exactly a power of 2, this is commonly known as a ''FFT Radix 2'' algorithm where <math> n = 64,128,256,512,1024,2048</math> etc.
+'''Fast Fourier transform''' ('''FFT''') is an efficient algorithm for calculating the [[DFT|discrete Fourier transform]] (DFT). The FFT produces the same results as a DFT but it reduces the execution time by hundreds in some cases. Whereas DFT takes an order of <math>O(n^2)\,</math> computations, FFT takes an order of <math>O(n\,\log\,n)</math>, and is definitely the preferred algorithm to be used in all applications in terms of computational complexity. The FFT in most implementations consistent of samples that are exactly a power of 2, this is commonly known as a ''FFT Radix 2'' algorithm where <math> n = 64,128,256,512,1024,2048</math> etc.
+Unlike the DFT, the frequency spacing nor window size per-bin can't be adjusted because FFT bins aren't calculated individually.
 ==External links==