fdars (version 0.3.3)

instantaneous.period: Estimate Instantaneous Period

Description

For signals with time-varying frequency (drifting period), estimates the instantaneous period at each time point using the Hilbert transform.

Usage

instantaneous.period(fdataobj)

Value

A list with fdata objects:

period

Instantaneous period at each time point

frequency

Instantaneous frequency at each time point

amplitude

Instantaneous amplitude (envelope) at each time point

Arguments

fdataobj

An fdata object.

Details

The Hilbert transform is used to compute the analytic signal, from which the instantaneous phase is extracted. The derivative of the phase gives the instantaneous frequency, and 1/frequency gives the period.

This is particularly useful for signals where the period is not constant, such as circadian rhythms with drift or frequency-modulated signals.

Examples

# Chirp signal with increasing frequency
t <- seq(0, 10, length.out = 500)
freq <- 0.5 + 0.1 * t  # Frequency increases from 0.5 to 1.5
X <- matrix(sin(2 * pi * cumsum(freq) * diff(c(0, t))), nrow = 1)
fd <- fdata(X, argvals = t)

# Estimate instantaneous period
inst <- instantaneous.period(fd)
# plot(inst$period)  # Shows decreasing period over time