Fourier Transform

Use case

The Fourier Transform is used to transform a function of time to a function of frequency. With this, it is possible to tell what frequency is present in a particular sound and how strong each frequency is.

Mathematical Definition

$$F(\omega )={\int }_{-\infty }^{\infty }f(t)e^{-i\omega t}dt$$

• $F(\omega )$ is the Fourier Transform of $f(t)$.
• $t$ represents time.
• $\omega$ is the angular frequency (in radians per second).
• $e^{-i\omega t}$ is the complex exponential function.