Recently, I’m studying Fourier Transform by watching the lectures from Stanford University. I felt that I already forget the math basics that I’ve learnt in college. So, to set up a quick lookup table for myself, I decide to write something to memorize it.
Here I listed some formulas that I’m encountered, And maybe more formulas to come in the future. Hope that will be useful for somebody else too.
Trigonometric Functions and Complex Exponentials:
Fourier Coefficients:
Fourier Series:
Sinc Function:
Duality Properties of FT
Here is the definition of Reversed Signal
Linearity of FT
Shift Theorem of FT
Stretch Theorem of FT
Combine Shift and Stretch of FT
Definition of Convolution:
Convolution Theorem, Which means FT of Convolution is multiplication of FT
Definition of Rapidly decreasing functions
The Delta distribution
The Delta distribution property
Delta with convolution
How a Distribution works on a function
The derivation of How Fourier Transform move from distribution to function
Shift and Stretch of FT
Derivation of FT of delta function
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Different notations for delta function
FT of sine and cosine functions
how Derivation shifts from T to phi.
derivation of FT of H
function g times distribution T means distribution T works on function g times phi
Derivation Theorem for distributions
shift one way in distribution means shift in the other way of function
psi Convolve with f works on phi means f works on reversed psi convolve with phi
Shah function definition
Derivation of the Sampling Theorem
Definition of Discrete Fourier Transform
DFT operation as a matrix multiplication
Reference:
Lecture Notes for EE 261
The Fourier Transform and Its Applications by Prof. Brad Osgood.
Personal reminder (or CheetSheet) about Fourier Transform,布布扣,bubuko.com
Personal reminder (or CheetSheet) about Fourier Transform
原文：http://www.cnblogs.com/mingongdrake/p/3774967.html