spectrumplots

Spectrum plots are graphical representations of a signal’s frequency-domain content, showing how energy or amplitude is distributed across frequencies. They are derived from time-domain samples using a Fourier transform or from other spectral estimation techniques. The most common forms are the magnitude spectrum, the power spectrum, and the phase spectrum. The magnitude spectrum plots the magnitude of the spectrum, |X(f)| for continuous signals or |X[k]| for discrete signals; the power spectrum plots |X(f)|^2 or P(f); the phase spectrum shows the phase angle ∠X(f), indicating how each frequency component is shifted in time.

To compute a spectrum plot, the fast Fourier transform (FFT) is typically used for efficiency. Finite-length data require windowing to reduce spectral leakage; common windows include Hann, Hamming, and Blackman. The frequency axis is determined by the sampling rate Fs and the data length N, with frequency resolution Δf = Fs/N and a Nyquist limit of Fs/2 for real-valued signals.

Spectrum plots can be presented on linear or logarithmic scales; decibel units are common, such as 20 log10|X(f)| or 10 log10 P(f). For noisy data or to improve reliability, spectral estimates like Welch’s method or multitapering are employed to reduce variance. When a signal’s frequency content evolves over time, a spectrogram provides a time-frequency representation that complements static spectrum plots.

Applications include audio analysis, vibration monitoring, communications, seismology, and physics, where identifying dominant frequencies, harmonics, and spectral patterns is essential.