Freqüencials

Freqüencials is a concept used in signal analysis to describe the sequence or set of instantaneous frequencies that a signal exhibits as it evolves over time. In this sense, a freqüencial trajectory f(t) captures how frequency content changes, providing a time-resolved view of the signal’s spectral components. For multi-component signals, freqüencials can consist of several trajectories, one per constituent component, enabling a per-component view of frequency variation.

Computation typically starts from the analytic signal x_a(t) = A(t) e^{jφ(t)} obtained via the Hilbert transform. The instantaneous frequency is defined as ω(t) = dφ(t)/dt. In discrete data, f[n] approximates ω(n) after phase unwrapping. For complex signals, methods such as ridge extraction on the spectrogram, empirical mode decomposition, or synchrosqueezing can yield per-component freqüencials, isolating distinct frequency tracks.

Applications of freqüencials appear in speech and music processing, where they provide pitch contours, vibrato analysis, and modulation tracking. They support tasks such as pitch estimation, voice separation, and time-varying audio modeling, contributing to synthesis and expressive analysis by representing how frequency content changes over time.

Key properties and challenges include sensitivity to noise, choice of window or frame length, and the problem of phase unwrapping. Ambiguities can arise when multiple components share similar instantaneous frequencies, necessitating component separation or regularization. Variants include discrete freqüencial sequences across frames, multi-channel freqüencial representations, and probabilistic models that describe frequency evolution over time.

See also: time-frequency analysis, instantaneous frequency, Hilbert transform, ridge extraction, synchrosqueezing, pitch tracking. The term freqüencials is used in some non-English literature to denote frequency-related sequences and is not universally standardized.