Bandmaxima

Bandmaxima is a term used in signal processing and spectral analysis to denote the peak magnitude values within predefined frequency bands of a signal’s spectrum. In discrete-time analysis, the signal s[n] is transformed to a spectrum S[k] using an FFT; the frequency axis is partitioned into contiguous bands B_i, each defined by a range of frequencies. The band maximum M_i is defined as M_i = max_{f in B_i} |S(f)|, or in discrete indices M_i = max_{k in B_i} |S[k]|. The collection of M_i across bands forms the bandmaxima sequence, describing how energy concentrates across bands.

Applications include characterizing spectral content, guiding equalization, and performing feature extraction in music information retrieval. Band maxima can assist in adaptive compression by identifying dominant bands, and may be used in audio onset detection or as part of dynamic range control that emphasizes bands with higher energy.

Computation considerations involve spectral resolution, windowing, and leakage. In practice, a filter bank or band-pass analysis is used, and local maxima within each band can be detected via peak-picking after smoothing. Some implementations define band maxima with thresholds or relative to band averages.

Variants and related concepts: Some definitions replace the maximum with band energy or average magnitude within a band. The idea is related to, but distinct from, spectral peaks, spectral centroid, and the use of mel-frequency bands in MFCCs. History and context: the term appears in engineering literature as a descriptive label for band-limited spectral peaks and is not universally standardized across domains.