Fourier transforms & the convolution theorem - UGAstro

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Convolution s(t) r(t) s*r • The signal s(t) is convolved with a response function r(t) – Since the response function is broader than some features in the original signal, these are smoothed out in the convolution
Fourier Transforms & FFT • Fourier methods have revolutionized many fields of science & engineering – Radio astronomy, medical imaging, & seismology • The wide application of Fourier methods is due to the existence of the fast Fourier transform (FFT) • The FFT permits rapid computation of the discrete Fourier transform • Among the most direct applications of the FFT are to the convolution, correlation & autocorrelation of data
Page 1 and 2: Convolution, Correlation, & Fourier
Page 3 and 4: Time & Frequency Domains • A phys
Page 5 and 6: Fourier Transforms • The Fourier
Page 7 and 8: FT Symmetries If… h(t) real h(t)
Page 9 and 10: Convolution • With two functions
Page 11 and 12: Correlation • The correlation of
Page 13 and 14: Autocorrelation • The correlation
Page 15: The Response Function • The effec
Page 19 and 20: Discrete Convolution • In the dis
Page 21 and 22: Discrete Convolution s j r k (s*r)
Page 23: Suppose that f and g are functions

Fourier transforms & the convolution theorem - UGAstro

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