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

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?

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.