Integration of data with discrete values

I've amplitude-time data (discrete data) of a signal. I want to find the power of the signal using the algorithm in figure. I'm unable to do the Integration part. Can someone please help me?? (Data file attached)

Answer 1

[Star Strider]

This calculates the power using numerical integration, then integrates it. Either the cumtrapz or trapz call should work for you.

[D,S,R] = xlsread('data.xls');
Amplitude = D(1,:);
Time = D(2,:);

Power = Amplitude.^2;                                       % Data Are Real, ‘abs’ Not Necessary
Cumulative_Integral = cumtrapz(Time, Power);
Total_Power = trapz(Time, Power);

[Athira Surendran]

Can u suggest any smoothing filters for the result obtained above?

[Star Strider]

The ‘Power’ signal doesn’t seem to be noisy. I don’t know what you want to do with a ‘smoothing filter’. Two options I can suggest are the Savitizky-Golay filter (the sgolayfilt function) and the envelope function (also see the hilbert function). A lowpass filter is also an option, however the others are likely easier considering the nature of your signal.