Spectral analysis

Spectral analysis describes how a signal’s power or energy is distributed across frequencies. It uses transforms, estimators, and visualizations to reveal periodic components and frequency-dependent structure.

Fourier transform: A mathematical transform that represents a signal as a combination of frequency components. It is the central operation for expressing a signal in the frequency domain.
Sampling theorem: A theorem stating conditions under which a band-limited continuous signal can be reconstructed from its samples. It sets the sampling conditions needed to avoid losing or misrepresenting spectral content.
Harmonic analysis: The study of representing functions and signals through oscillatory components such as sines and cosines. It provides the broader mathematical framework behind frequency-based signal descriptions.
Fourier series: A representation of a periodic function as a sum of harmonically related sinusoidal components. It describes periodic functions, while spectral analysis also handles finite and nonperiodic data.
Power spectral density: A function describing how a signal’s average power is distributed over frequency. It gives the standard quantitative description of power versus frequency.
Nyquist frequency: Half the sampling rate, the highest frequency representable without aliasing in a sampled signal. It marks the upper limit of an unaliased spectrum.
Audio signal processing: The analysis and transformation of sound signals using digital or analog methods. Audio spectra expose pitch, harmonics, timbre, and noise.
Wavelet transform: A transform that represents a signal using localized waveforms at multiple scales and positions. It offers adaptive time-scale detail where fixed-window spectral methods face resolution limits.
Periodogram: An estimate of a signal’s power spectral density formed from the squared magnitude of its finite-record Fourier transform. It is the simplest direct estimate, though its variance does not vanish with longer records.
Aliasing: The misidentification of signal components caused when sampling cannot distinguish frequencies above the Nyquist frequency. It can make high-frequency energy appear at incorrect lower frequencies.

Linked from 5 pages