Glossary of engineering: A–L

Can you hear colors?

Imagine you're at a concert, and you want to know which instruments are playing, but all you're getting is a mixed-up sound.

Think of a sound wave as a complex dance. Each instrument at the concert has its own unique dance move. The Fourier Transform is like a dance instructor who can break down the mixed-up dance into individual moves.

Example

If the mixed dance moves up and down quickly, it might be a flute. If it moves slowly and smoothly, it could be a cello.

Remember this

The Fourier Transform helps us identify individual instruments in a mixed-up sound by breaking it down into its unique frequency patterns.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

Short-time Fourier transform

STFT divides a signal into shorter segments for analysis

wavelets provide over Fourier: both time and frequency localization

Wavelets provide both time and frequency localization, unlike Fourier transforms which offer only frequency localization

sinusoidal position encoding works: each dimension has a different frequency

Sinusoidal position encoding assigns unique frequencies to each dimension, enabling the model to distinguish positions effectively

Characteristic function (probability theory)

Characteristic function φ(t) = E[e^(itX)] is the Fourier transform of the PDF

a low-pass filter does: removes frequencies above a cutoff, keeps slow-varying signal

Low-pass filter removes frequencies above a cutoff

Discrete Fourier transform

Discrete Fourier Transform (DFT) equation: X[k] = Σ(n=0 to N-1) x[n] * e^(-j*2π*k*n/N)

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