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transforms

Linearity, shifting, scaling, and duality of the Fourier transform

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Local knowledge map

Local knowledge map

Characteristic functions of sums of independent random… Circular convolution and the discrete convolution theorem DTFT properties -- time reversal and frequency shift Magnitude and phase spectra Periodicity of the DTFT Reading a system's frequency response off its difference… Recalling the 1D and multidimensional Fourier transform The Dirac delta, as a limiting generalized function Why a transform beyond the DTFT is needed A gallery of standard Fourier transform pairs Differentiation in time is multiplication in frequency The Fourier convolution theorem The Fourier transform in several dimensions, and separability The discrete-time Fourier transform (DTFT), defined Linearity, shifting, scaling, and duality of the Fourier… Characteristic functions as Fourier transforms of… Convolution — definition and algebraic properties Discrete-time sinusoid periodicity's frequency-domain… The DFT, defined and as a matrix transformation The Nyquist–Shannon sampling theorem The Fourier transform, and its inverse The Fourier transform as an infinite-period limit

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