How to plot time-frequency evolution based on zero crossings?

Question

In a paper that analyzes the data from GW150914, a time-frequency plot was shown.

The paper proposes that, quote:

An approximate version of the time-frequency evolution can also be obtained directly by measuring the time differences $t$ between successive zero-crossings and estimating $f_{GW} = 1/(2\Delta t)$, without assuming a waveform model

I would like to create this alternative version. So far I have already obtained data from successive zero crossings and used $f_{GW} = 1/(2\Delta t)$ to generate a list of frequencies. However I am a bit confused on how to plot it vs. time as the two arrays have different dimensions. Also because frequency at a single time doesn't make sense to me.

I looked up some time-frequency analysis technique, but they all use some form of Fourier Transform. Can anyone shed some light on how might I proceed?

Link to the paper

Answer 1

Here is an example:

1. First we create some data with increasing frequency.
2. Then we calculate the zero crossings.
3. Finally we plot the differences of the crossings and its inverse

fun[t_] := Sin[t^2/100];
Plot[fun[t], {t, 0, 100}]
zeros = t /. 
    Solve[fun[t] == 0, t, Assumptions -> {0 <= t <= 100}, 
     WorkingPrecision -> 64] // N;
ListPlot[Differences[zeros]]
ListPlot[1/Differences[zeros]]