The function tfridge can be found helpful here. Below is an example showing how to extract the ridge from the spectrogram.
%% Signal model
fs = 3.6e3; % sampling rate in Hz
t0 = 2; % signal duration in seconds
t = (0:1/fs:t0)'; % time samples
x = vco(sawtooth(2*pi*t,0.5),[0.1 0.4]*fs,fs);
%% Spectrogram
NFFT = 256; % number of FFT points
[S,F,T] = spectrogram(x,NFFT,NFFT/2,NFFT,fs,'yaxis');
spectrogram(x,NFFT,NFFT/2,NFFT,fs,'yaxis')
%% Extract ridge (highest power)
[fridge,~,lridge] = tfridge(S,F);
ridge = S(lridge);
%% Figure
figure
spectrogram(x,NFFT,NFFT/2,NFFT,fs,'yaxis')
hold on
plot3(T,fridge/1e3,abs(ridge),'k','LineWidth',2)
For more complicated time-frequency maps, the input penalty in the tfridge should be tuned. Further information can be found in the documentation page (link to Documentation page). Another useful function/GUI is rpmtrack (link) where points on the ridge with the highest power can be inserted manually to further help ridge extraction.
In addition, it would be great if the audio file could be shared.
