hello
you have to compute the angle increment vs time then take the sine of that angle (or, in other words, do the integral of the time varying frequency and then take the sine of that angle )
NPTS=500000;
t_final = 450;
A=(log(50)-log(7))/t_final;
time = linspace(0,t_final,NPTS)';
dt = mean(diff(time));
fs = 1/dt
freq = 7*exp(A*time); % The frequency varies from 7 to 50 Hz
freq(1)
freq(end)
ang = cumsum(2*pi*freq)*dt; % integral of the time varying frequency
Y = sin(ang);
% spectrogram plot
nfft = 1000;
overlap = 0.75; % 75% overlap
spectrogram(Y,hanning(nfft),round(overlap*nfft),nfft,fs,'yaxis')
ylim([0 100])
