I have a measured eye diagram of data. I want generate a model that takes a random bit sequence and through impairments generate an eye diagram close to what was measured. Any ideas on the best way to do this? I had thought of using a cosine filter but have not seen much info to go from a measured waveform to a generalized model
Thank you

Just an eye diagram won't be sufficient if you have significant intersymbol interference. Do you have the underlying time-domain data? 

Yes I have the time domain data

I forgot to ask if you have the original data stream.

I'm assuming that your channel acts like

\[r = h\left(s\right) + n\]

where \(s\) is the transmitted signal, \(r\) is the received signal, \(h\) is a linear time invariant system, and \(n\) is white noise (this may work if \(n\) is colored noise, but I'd have to, like, think about that answer).

If you do have the original data stream, and if the SNR is high enough, then you should be able to use an ARMAX algorithm to come up with a model of the channel distortion (\(h\)), and then once you have that, come up with an estimate of \(n\) by subtracting a distorted but noise-free version of the signal from \(r\).

If you don't have the original data stream, but if you can reconstruct it somehow, then you can do the same thing -- but doing this sort of thing blind is harder.

I don't know if this is the usual way to do this -- if it isn't, hopefully someone will pipe up with something useful.