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Hilbert transform: analytic signal, instantaneous amplitude and frequency, Hilbert spectrum.
Conventions and sources: docs/time-frequency.md.
Structs§
Enums§
- Padding
- How the signal is extended before the FFT, which treats it as periodic.
- Weight
- What each sample contributes to its frequency bin.
Functions§
- analytic_
signal - Analytic signal
x + i·H{x}by the FFT method: keep DC (and Nyquist for even lengths), double positive frequencies, zero negative ones. - hilbert_
spectrum - Hilbert spectrum, channel × frequency × sample: each sample’s weight is added to the bin holding its instantaneous frequency, summed over modes (Huang et al. 1998).
- instantaneous
- Instantaneous amplitude and frequency of every mode and channel.
- instantaneous_
frequency - Instantaneous frequency in Hz from an analytic signal: centred difference of the unwrapped
phase,
(φ[n+1] − φ[n−1]) · fs / 4π; at each end, the slope of a line through 3 points (the same estimator as a 3-point Savitzky-Golay derivative). Phase steps are taken one sample at a time, so frequencies up to Nyquist are estimated without wrapping.