Submitted:
22 May 2018
Posted:
23 May 2018
Read the latest preprint version here
Abstract
Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.
Keywords:
Fourier Transform
; Discrete-Time Fourier Transform (DTFT)
; Discrete Fourier Transform (DFT)
; Fourier Series
; Poisson Summation Formula
; discretization
; periodization
; discrete function
; periodic function
; periodization trick
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