The Fast Fourier Transform for Experimentalists Part II: Convolutions
D Donnelly, Bert W. Rust
The discrete Fourier transform (DFT) is a widely used tool for the analysis of measured time series data. The Cooley-Tukey fast Fourier transform (FFT) algorithm gives an extremely fast and efficient implementation of the DFT. This is the first of a series of three articles which will describe the use of the FFT for experimental practitioners. This installment gives fundamental definitions and tells how to use the FFT to estimate power and amplitude spectra of a measured time series. It discusses the use of zero padding, the problem of aliasing, the relationship of the inverse DFT to Fourier series expansions, and the use of tapering windows to reduce the sidelobes on the peaks in an estimated spectrum.
and Rust, B.
The Fast Fourier Transform for Experimentalists Part II: Convolutions, Computing in Science & Engineering, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150009
(Accessed June 8, 2023)