Table of Contents
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:
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.
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.
Fourier transform references here.
Fourier Transform Pairs
Derivations for (8), (9) and (10) here: Fourier Transform Pairs of Conjugation and Time Reversal
Fourier Transform Properties
Derivation for (11) here: Fourier Transform Convolution Property Derivation
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 .
Derivation for (16) and (17) here: Using Euler’s Formula to Derive Sine and Cosine
Integration by Parts