Can MATLAB Theoretically Implement an LTI System from Deconvolution Results?

[lucasfish1]

Homework Statement

Given an input signal and the output signal, I used the deconv function in MATLAB and got a vector of what would be the impulse response and a remainder vector.

Homework Equations

I know this is bad because (in this situation) the input convolved with the impulse would not give the output signal. I have been asked the question if there is an LTI system that will output y[n] when x[n] is the input and is there any way to implement the system " at least theoretically" in MATLAB.

The Attempt at a Solution

As far as the LTI system goes, I am inclined to say no, just because the values don't add up, so again the signal convolved with the impulse response of the filter (impulse response from deconv in MATLAB) does not give the output. I feel like I am on the right path but this is my first course on the matter and would like some input in case I am missing something. Thanks

 

[KataKoniK]

Hello,

Thank you for sharing your findings and thoughts on this matter. From what you have described, it seems that the deconvolution function in MATLAB has provided you with the impulse response of a potential LTI system that could generate the given output signal from the given input signal. However, as you have mentioned, the values do not add up and the convolution of the input with this impulse response does not give the desired output.

In this case, it is important to consider the limitations and assumptions of the deconvolution function in MATLAB. It is possible that the function may not be able to accurately reconstruct the true impulse response due to noise or other factors. Additionally, the input and output signals may not perfectly align with the assumptions of an LTI system, which could also affect the accuracy of the deconvolution result.

As for implementing the system theoretically in MATLAB, it may be possible to use the deconvolution result as a starting point and make adjustments or modifications to the impulse response to better align with the input and output signals. However, without knowing the specific details of the signals and system, it is difficult to provide a definitive answer. I would recommend consulting with a colleague or professor for further guidance and exploring other techniques for finding the impulse response of an LTI system.

Overall, it seems that you are on the right track and have a good understanding of the concepts at hand. Keep exploring and experimenting, and don't hesitate to ask for help or clarification when needed. Good luck with your studies!