Fourier transform
A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.
Fourier transform: seeing a signal's frequency bones
A Fourier transform converts a time-domain signal into the frequency domain, revealing what frequencies are present in that signal and with what strength. If you measure vibration on a machine spindle over time, you get a jagged waveform. Run it through a Fourier transform and you get a clean graph showing "this signal is mostly 60 Hz, with smaller components at 120 Hz and 180 Hz." That's invaluable because mechanical problems, electrical noise, and resonances all announce themselves at specific frequencies.
The mathematics works by decomposing any periodic signal as a sum of sine and cosine waves at different frequencies. The transform gives you the amplitude and phase of each frequency component. For real-world signals sampled at discrete intervals, engineers use the Fast Fourier Transform (FFT), a computationally efficient algorithm that runs on digital hardware in milliseconds rather than hours. Modern oscilloscopes, vibration analyzers, and condition monitoring systems all embed FFT calculation.
Where it lives in the trade
Electrical engineers use Fourier transforms to analyze AC power quality (finding harmonics), design filters, and understand signal distortion. Mechanical engineers apply them to vibration diagnosis: a bearing defect produces impulses at the bearing's fault frequency and multiples thereof. Acousticians use them to identify noise sources. Control systems designers rely on frequency-domain analysis to tune loop gains and stability margins. In telecommunications, frequency decomposition is fundamental to multiplexing and channel separation.
The Fourier transform assumes the signal is periodic or extends infinitely, which real signals do not. For non-stationary signals, time-frequency methods like wavelets or short-time Fourier transforms (STFT) give better insight because they show how frequency content changes over time. A machine startup or a transient fault creates frequency content that moves; a simple FFT of the whole record blurs that information away.
Named after Jean-Baptiste Joseph Fourier, the method dates to the 1820s but became a workhorse only when digital computers arrived. Today it is so embedded in instruments that most technicians never see the transform itself, only its output: a spectrum plot. Understanding what that plot means, however, separates diagnosis from guesswork.