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transforms

The Fourier transform, and its inverse

taught

Taught in

The Fourier transform, defined
Fourier Analysis
The inverse Fourier transform
Fourier Analysis
Existence conditions — L¹ functions
Fourier Analysis
Beyond the bound: transforms decay at high frequency
Fourier Analysis
The frequency spectrum, continuous case
Fourier Analysis
Reading a magnitude/phase plot
Fourier Analysis
A first gallery: the transform of a simple pulse
Fourier Analysis
Constant-coefficient differential equations become algebra in frequency space
Fourier Analysis

Requires

fourier-transform-as-a-limit-of-fourier-series required

Required by

Characteristic functions as Fourier transforms of densities required
Convolution — definition and algebraic properties required
Linearity, shifting, scaling, and duality of the Fourier transform required
The Nyquist–Shannon sampling theorem required

Local knowledge map

Local knowledge map

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.