Open AccessRevised fast convolution
Author(s) -
Rimantas Pupeikis
Publication year - 2016
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.a.2016.18
Subject(s) - convolution (computer science) , fast fourier transform , overlap–add method , computation , convolution theorem , sample (material) , discrete time fourier transform , circular convolution , algorithm , fourier transform , computer science , split radix fft algorithm , mathematics , short time fourier transform , fourier analysis , mathematical analysis , artificial intelligence , physics , fractional fourier transform , thermodynamics , artificial neural network
It is assumed that linear time-invariant (LTI) system input signal samples are updated by a sensor in real time. It is urgent for every new input sample or for small part of new samples to update a convolution as well. The idea is that fast Fourier transform (FFT) algorithm, used to calculate output frequency samples (f.s.), should not be recalculated with every new input sample. It is needed just to modify the convolution algorithm, when the new input sample replaces the old one. An example of computation of the convolution with ordinary and modified 8-point Fourier code matrix is presented.