Instantaneous phase can be obtained by taking the integral from the instantaneous frequency, 
where 
is the initial phase at time 
and 
is the instantaneous frequency. To compute the integral numerically, cumtrapz can be used.
where is the initial phase at time and is the instantaneous frequency. To compute the integral numerically, cumtrapz can be used. load('sinusoidalSignalExampleData.mat','X','fs')
t = (0:length(X)-1)/fs;
[imf,residual,info] = emd(X,'Interpolation','pchip');
iph = cumtrapz(t,imf);
figure
subplot(211),plot(t,imf(:,3)),xlabel("Time [sec]"),ylabel("Inst. Freq."),grid("minor")
subplot(212),plot(t,iph(:,3)),,xlabel("Time [sec]"),ylabel("Inst. Phase."),grid("minor")
