Backing Out Impulse Response From Signal

I am sure this has been answered somewhere, but I can't seem to locate an answer anywhere. I have a modeled signal and an experimentally obtained signal (taken with a 150 MHz photodiode). It is obvious that there is signal ringing associated with the impulse response. How could I (a) model the impulse response on the modeled signal, or (b) remove the impulse response from the experimentally obtained signal? With my current setup I can't measure the response of the photodiode with a Dirac-delta function input which is making this a little bit more difficult. I assume that I should be able to arrive at a transfer function for the photodiode. I tried convolving the model with a damped oscillator based on the photodiode specs, but that didn't give me the right solution.

[Star Strider]

You most likely need to use the System Identification Toolbox to estimate your transfer function. It might be easiest to do this in the frequency domain, however you need to determine the best approach.

The Signal Processing Toolbox has limited frequency-domain system identification capability (the invfreqz function).

[Rajiv Singh]

Is the signal a response to a measurable input signal, even if not an impulse function? If so, what Strider says is correct. You can pair up the input and response data into an IDDATA object and run an model estimation routine such as SSEST or IMPULSEEST.

If there is no input signal, but yiu believe it is of impulsive nature, try using a numerical impulse signal created explicitly using zeros and ones.

[Anthony LoCurto]

Rajiv,

Would it be correct to treat the model as the "input" and the experimental as the "response data" since the model should assume an ideal situation?

[Rajiv Singh]

No sure what you mean. But let us say you measured a certain signal "y" from a system. Pretend that the signal is in response to a impulsive impact applied to the system. Then your input can be u = [1; zeros(length(y)-1,1)]. Pack this data so:

z = iddata(y,u,Ts); % Ts is sampling interval of y.

model = ssest(z,2); % second order state-space

x = impulse(model); % x is the impulse response that you should compare to y

model can also be obtained using tfest, oe, impulseest etc.