#### Table of Contents

#### Introduction

The is a list of math for DSP I have found to be useful over my career in DSP. This post will be updated periodically.

More posts on DSP Math:

#### Cross-Correlation

##### Discrete-Time Cross-Correlation

(1)

##### Discrete-Time Autocorrelation

(2)

#### Fourier Transform and Inverse Fourier Transform

##### Transforms in frequency f (Hertz)

The Fourier transform relates the impulse response which is continuous in time and the frequency response X(f) which is continuous in frequency f.

(3)

(4)

##### Transforms in frequency omega (radians per second)

The Fourier transform and inverse Fourier transform can be written with the frequency f in Hertz, or by using which is in radians per second.

(5)

(6)

Fourier transform references here.

##### Fourier Transform Pairs

(7)

(8)

(9)

(10)

Derivations for (8), (9) and (10) here: Fourier Transform Pairs of Conjugation and Time Reversal

#### Fourier Transform Properties

##### Convolution Property

##### Linearity Property

##### Discrete-Time Fourier Transform and Inverse Transform

The discrete-time Fourier transform relates the impulse response x[n] which is discrete in time n and the frequency response which is continuous in frequency .

(13)

(14)

#### Trigonometric Identities

#### Calculus

##### Integration by Parts

(18)

##### Derivatives

(19)

(20)