FFTanalys

FFTanalys, or FFT analysis, is the process of using the Fast Fourier Transform to decompose a time-domain signal into its frequency components. The FFT is an efficient algorithm for computing the discrete Fourier transform, enabling rapid estimation of a signal's spectrum. The result typically includes a magnitude spectrum, showing the strength of each frequency component, and a phase spectrum, indicating the phase shift relative to a reference. The analysis is constrained by the sampling rate, with the highest resolvable frequency (the Nyquist frequency) equal to half the sampling rate.

Procedure: collect samples of the signal at a chosen sampling rate, select a window length N, and apply a window function to reduce spectral leakage. Compute the FFT to obtain complex frequency coefficients, then derive the magnitude and phase for each frequency bin. Often the power spectrum (magnitude squared) or a spectrogram (short-time Fourier transform) is used to study how frequency content evolves over time. Zero-padding and different window choices (Hanning, Hamming, Blackman) affect resolution and leakage.

Applications: FFTanalys is used in audio and music analysis, vibration analysis of machinery, speech processing, telecommunications, radar and sonar signal processing, and image processing when extended to two dimensions. It is also used in scientific measurements to identify dominant frequencies and harmonics.

Limitations: the time–frequency resolution trade-off means that improving resolution in frequency reduces temporal precision. Noise, windowing effects, and aliasing can distort results. The method relies on adequate sampling and, for non-stationary signals, may be complemented by short-time or multi-resolution approaches. Many software packages implement FFT with libraries such as FFTW or NumPy's FFT.