Calculating Signal Approximation Error (Theoretical signal - Real hardware signal)?

Question

I've got a FIR filter, which I developed in IC. Now, when I got my results, I ended up with two signals:

1. Theoretical signal calculated through MATLAB as a response to my input.
2. Real response given by the hardware.

What is the best method of calculating the error of the real response with respect to the theroetical one?

I could go

delta = abs(Y) - abs(Yreal);
max_err = max(delta);

but I don't know what to do with the maximum error? Any suggestions?

Answer 1

There are lots of different error statistics you depending on what you want to know. If what you care about is the maximum error then what you suggest is fine.

Probably more common is to use the RMS error i.e. $ \sqrt{\frac{1}{N}\sum(Y-Y_{real})^2} $. This is related to the variance of the system. I'm not sure if this is exactly what you want for your case as I suspect there will be strong spatial correlation across the filter. This is something you should look at.

Another issue is that the error is dependent on the input signal. You may wish to look at the frequency response of both systems to try and remove this issue.