# Wave Walker DSP

## DSP Algorithms for RF Systems

DSP for Beginners: Simple Explanations for Complex Numbers! The second edition includes a new chapter on complex sinusoids.

List of Important Math for DSP
November 3, 2021

#### 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.

#### 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

(11) Derivation for (11) here: Fourier Transform Convolution Property Derivation

##### Linearity Property

(12) Derivation for (12) here: Fourier Transform Linearity Property Derivation

##### 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

(15) (16) (17) Derivation for (16) and (17) here: Using Euler’s Formula to Derive Sine and Cosine

#### Calculus

##### Integration by Parts

Reference

(18) ##### Derivatives

(19) (20) ##### L'Hopital's Rule

Reference

(21) 