LTI Impulse Response Estimation with Point Process Input

In summary, the conversation discusses the estimation of the transfer function of an unknown LTI system using a point process as the input signal. The speaker asks about the best approach for estimating the spectrum of a synthetic point process signal, the theoretical formulation for point process spectrum, and methods for estimating the system's zeros and poles based on output measurements and assumptions about the input. They also mention a helpful resource for this topic.
  • #1
Alexei_Nomazov
3
0
Hello,

I am trying to estimate transfer function of unknown LTI system, given output and assumed input as point process.

I have measurement of output, while input, which is assumed to be point process, could be created synthetically using known times and amplitudes.

My questions:
1. What is the best approach to estimate spectrum of synthetic point process signal (a-parametric/parametric/AR...)?
2. Is there theoretical formulation for point process spectrum, which could be used to create numerical instance for my transfer estimation purpose.
3. Is there a way to estimate zero/poles of system given only output measurement and assumptions on input, without calculation of input and output signals spectrums?
4. Is there methodology to estimate number of zeros/poles based on given input and output?

Thanks,
Alexei Nomazov,
Algorithms Researcher.
 
Mathematics news on Phys.org

1. What is LTI Impulse Response Estimation?

LTI Impulse Response Estimation is a method used in signal processing to estimate the impulse response of a linear, time-invariant (LTI) system. It involves using a known input signal and measuring the output response to determine the system's characteristics.

2. How is Point Process Input used in LTI Impulse Response Estimation?

Point Process Input refers to a type of input signal that consists of discrete events occurring at random times. In LTI Impulse Response Estimation, this type of input is used to stimulate the system and measure the output response, allowing for the estimation of the system's impulse response.

3. What are the advantages of using LTI Impulse Response Estimation with Point Process Input?

One of the main advantages of this method is its ability to accurately estimate the impulse response of a system with minimal prior knowledge of the system. Additionally, the use of point process input allows for the analysis of non-stationary systems, which would be difficult to analyze with traditional input signals.

4. What are some common applications of LTI Impulse Response Estimation with Point Process Input?

This method is commonly used in fields such as neuroscience, where the response of neurons to a stimulus can be modeled as an LTI system. It is also used in the analysis of communication systems, control systems, and audio signal processing.

5. How is LTI Impulse Response Estimation with Point Process Input implemented?

The implementation of this method involves generating a point process input signal, measuring the output response, and then using mathematical techniques such as deconvolution to estimate the impulse response. This process can be carried out using specialized software or programming languages such as MATLAB.

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