Envelope calculation using Matlab...

If I have a digital sampled waveform (for example sampled at 10kHz) and a set of uneven envelope points (say 4 or 5) - how can I use Matlab to work out the following:

Assume the sampled waveform dips into the envelope on several occasions but the majority of the time it should be completely outside of the envelope. I want to calculate what percentage of the overall area of the defined envelope was covered by entries of the sampled waveform into it.

I'm a Matlab beginner so any sample code would be greatly appreciated.

Here is a link to a sketch of a typical waveform: https://picasaweb.google.com/116715492473256943579/Matlab?authuser=0&authkey=Gv1sRgCKqT7Z2PndbYvAE&feat=directlink

Answer 1

[Image Analyst]

Not sure what this means. Do you have a diagram to illustrate what "encroaching" means to you? Do you mean something like

aboveUpperEnvelope = signal > upperEnvelope;
belowLowerEnvelope = signal < lowerEnvelope;

And then just say it's 100% if the signal is within the envelope and it's some fraction if the envelope is within the signal? And the percentage depends on where the zero line is. Is your upper envelope just the negative of your lower envelope, or are they both offset and raised above the x axis?

[Walter Roberson]

And are the envelopes sloped or curved ?

[Walter Roberson]

Is the envelope defined by frequency or by intensity? Because if it is defined by frequency then you will need to convert the signal from intensity to frequency in order to do the matching.

Note: converting a frequency envelope to intensity and trying to match that is unlikely to work. Besides, that would be a back-of-the-envelope calculation.

[S Dodd]

The envelope points would be made up of a set of x-axis time points with corresponding y-axis power points.

[S Dodd]

The envelope is made up of a series of straight lines whereas the actual waveform is a much higher resolution set of data points that is smoothed.