fourier series

Concept

Isolating frequencies

• inner product with the signal

Strength

• need to use both sine and cosine
• representing sine and cosine within a frequency as a complex number

use to represent the imaginary number, physics convention

Magnitude

• represents the actual amplitude of the frequency

Phase

• represents the phase shift

Simplify with euler’s formula

Fourier series

• the expansion of a periodic function into a discrete sum of sine and cosine
• periodic signal -> discrete frequencies

assuming the signal is periodic, this can be used to extract discrete frequencies