Fourier Transform Pairs

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This section gives a list of Fourier Transform pairs. That is, we present several functions and there corresponding Fourier Transforms. The derivation is provided if it isn't too difficult.

Table of Fourier Transforms

g(t)
 fourier transform symbol
G(f)
box or rectangle function
Square Pulse (Box Function)
sinc function
triangle function
Triangle Function
sinc squared
gaussian or normal function
The Gaussian
fourier transform of gaussian
constant function
fourier transform of constant
dirac delta functional
The Dirac-Delta Impulse
fourier transform of delta
cosine function
Cosine
fourier transform of cosine
sine function
Sine
fourier transform of sine
step function
Step Function
fourier transform of step function
signum function
fourier transform of the signum function
left sided exponential
Right-Sided Decaying Exponential
fourier transform of the left sided decaying exponential
left sided exponential
Left-Sided Decaying Exponential
fourier transform of the left sided decaying exponential
two sided decaying exponential
Two-Sided Decaying Exponential
fourier transform of the two sided decaying exponential
shah function
Shah Function (Bed of Nails)
fourier transform of the bed of nails function

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