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Suppose we have a system which we want to know the exact transient times. In ideal case, we can extract the transient times, but in practice it will be affected by another system with a known transfer function. We know the system with a transfer function changes the transient times and also the shape of output. How can we obviate its effects on the (main) system?

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That is pretty broad question, as it depends on the system.

However, your problem is extremely common: Every communication system works because a receiver is able to estimate the original events (symbols sent by the transmitter) after the signal has gone through a system with transfer function (the channel).

So, receivers need to do exactly that: reverse the effect of the channel as good as possible. The thing that does that is usually called an equalizer; the equalizer you pick, and how much info about the system you need to make that equalizer work, depends on your "main system".

So, if you need to solve that: go ahead; define your main system as well as possible. Find stochastic descriptions for the parts of the system that you don't know with certainty. Then, find a channel model that fits that model, and look for equalizers used with such a channel.

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  • $\begingroup$ Specifcally, I have a pulse (rectangular pulse) which is the output of a detector (light detector). In ideal case, if detector is ideal we have no delay and changes in pulse (then we can extract transient times). But, detector is not ideal, and we can model that by a a 1st order transfer function. Can we use equalizer like a communication channel? $\endgroup$ – Reza Mahjoob Dec 16 '17 at 10:13
  • $\begingroup$ yes! That very much sounds like a simple channel model. $\endgroup$ – Marcus Müller Dec 16 '17 at 10:15
  • $\begingroup$ Thanks, can you refer me to some good references to do that? $\endgroup$ – Reza Mahjoob Dec 16 '17 at 10:17
  • $\begingroup$ I really don't know your background – but equalizers should be part of any digital communications textbook that takes readers from the basics to working single-carrier systems, so: one of the classics? Proakis? Sklar? $\endgroup$ – Marcus Müller Dec 16 '17 at 10:20
  • $\begingroup$ ok, maybe we're not on the same page: how do you define "transient times"? For me, this sounds very much like the question at which point to sample a signal in order to get the transmitted symbol, and your system exhibits ISI, so yes, you need an equalizer, to do exactly that. $\endgroup$ – Marcus Müller Dec 16 '17 at 22:05

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