Time-Frequency Analysis
Moving window analysis
One way to analyse the time-varying frequency content of a signal is to
apply windows in the time domain to the signal and to calculate a Fourier spectrum
of the windowed part. The window marches along the signal with defined overlap creating
a series of Fourier spectra associated with the center times of the windows. The resulting amplitude
spectra are then plotted versus window center time. In more detail:
- Choose windowing functions:
w(t,t_m) with t_m the center of the window.
- Multiply windowing function with time series:
f_m(t) = f(t)w(t,t_m)
- Detrend the windowed signal.
- Perform a DFT:
F_{km} = \Delta t\sum_{n=0}^N f_m(t)\exp(-2\pi i \frac{kn}{N})
and calculate the absolute value, |F_{km}|.
- Plot the resulting matrix:
|F_{km}| in the time-frequency plane.
