Frequentiedomainanalyses

Frequentiedomainanalyses, also known as frequency-domain analysis in English, are methods for examining signals by representing them in the frequency domain rather than the time domain. The approach focuses on the spectral content—what frequencies are present and with what strength—rather than on how the signal varies over time.

Key mathematical tools include the Fourier transform for non-periodic signals, the Fourier series for periodic signals, and, for system analysis, the Laplace transform or Z-transform that express a system's response as a function of complex frequency. In discrete data, the discrete Fourier transform (DFT) and its fast implementation, the FFT, are standard.

Analyses produce spectra, which can be described by magnitude and phase spectra, or by a power spectral density that indicates how signal power is distributed across frequencies. Windowing, sampling rate, and spectral estimation methods (such as Welch's method or periodograms) affect resolution and variance.

Applications span many fields: audio and communications, vibration and structural analysis, radar and imaging, and biomedical signal processing. Frequency-domain insight helps design filters, diagnose resonances, and model dynamic systems via transfer functions in the s- or jω-domain.

Limitations include the assumption of stationarity for many transforms; non-stationary signals require time–frequency methods. Interpretations must consider aliasing, leakage, and window effects. Frequency-domain analyses complement time-domain methods to provide a fuller view of a signal or system.