I'd really appreciate some help. So, I have a black box which we will assume is linear and time invariant. The inputs to the system can either be +.5V or -.5V. The output of the system is continuous, varying from +.5V to -.5V. I can sample the output of the signal at a frequency that matches the input signal rate. So, the input waveform is a square wave, and the output is continuous.

How do I take my sampled output and determine the impulse response of the system? The impulse response seems to be 63 samples long (that is how long it takes for the decaying waveform to settle back at the midpoint.)

Once I have that impulse response (in any usable form) how can I use it to determine the ideal input signal to generate an optimal output signal based on a defined target signal. I hope I said that right.

In short, I have a black box, I can only send 1's or 0's to it, but it outputs a continuous signal from 0 to 1 and I want to create the series of 1's and 0's to recreate the best approximation of a target signal at the output.

Thoughts?

 

Attached to this message is a graph of the input signal and the resulting output signal. What I'd like to do is to determine the optimal input signal to match a desired output signal.

Any ideas?

 

In general, the following holds:

\(y(t)=\int_0^t x(\tau) h(t-\tau) t\tau\)
where x is your input and
h is the impulse response.

But I don't think a simple derivation would cut it. Maybe someone else can shed some light.