Spectrum analysis refers to the distribution of frequencies present in a signal, system, or phenomenon under study. In signal processing and engineering contexts, spectrum analysis involves decomposing a signal into its constituent frequency components. This process helps in understanding the frequency content, amplitude and phase characteristics of the signal.

Spectrum analysis can also refer to the range or variety of elements, attributes, or factors examined within a specific analytical framework, as in the spectral analysis of signals, systems, or data.

In statistics, spectrum refers to the frequency distribution or range of variation in a set of data. Spectral analysis in statistics involves techniques for decomposing time series data into its frequency components to understand patterns, cycles, and trends.

Methods like Fourier analysis are commonly used in statistical spectrum analysis to extract and analyze spectral features from data, providing insight into periodic behavior or underlying structures in the data set.

Spectrum analysis theory encompasses the mathematical and conceptual frameworks used to analyze signals and data in the frequency domain. It draws heavily on the principles of Fourier analysis, digital signal processing and spectral estimation techniques.

The theory explains how signals are decomposed into frequency components, the algorithms and methods used for spectral analysis, and the interpretation of spectral data to extract meaningful information about signal characteristics. Spectrum analysis theory finds applications in various disciplines, including telecommunications, audio engineering, geophysics, astronomy, and biomedical signal processing