Fast Fourier Transform
Fast Fourier Transform — A family of algorithms that computes the Discrete Fourier Transform by exploiting structure to reduce typical complexity from O(N²) to O(N log N).
DFT Is the Transform, FFT Is the Algorithm
The DFT defines the mathematical transform. An FFT is a family of algorithms for computing that result more efficiently. Cooley-Tukey-style methods recursively decompose the problem into smaller transforms.
For suitable sizes, this reduces the typical operation count from O(N²) toward O(N log N).
Signal Analysis
In audio and vibration analysis, FFT output exposes frequency-domain structure from time-domain samples. Interpretation still depends on windowing, sample rate and frame length.
An FFT bin is not automatically the exact physical frequency of a component; frequency resolution follows from sample rate and transform size.
Real-Time Cost
A longer transform can improve frequency resolution while increasing compute and the amount of signal that must be accumulated before processing.