Question about an LTI System and its Frequency Response

[ntran26]

Hello All,
I am trying to learn about lti systems and what not for my research work but before I can apply my research I have to understand the fundamentals, which is what this question is kind of about!

I want to find h(t), the impulse response of an LTI system where my input and output are sinusoids. So I have made two functions.
Input(t)=4*SIN(3*t+PI/8)+9*SIN(4*t-PI()/6)
Output(t)=2*SIN(8*t+PI/3)+5*SIN(2*t-PI()/7)
I did use matlab's fast Fourier transform to bring results of n^10 data points to the frequency domain.
I then do output(w)/input(w) ,output and input in frequency domain, to get H(w), the frequency response. I then use MATLAB to apply the inverse fast Fourier transform to H(w) to obtain h(t).

I use matlabs convolution function which should result in I(t)*h(t)=o(t)

The problem is that this is not matching up.

Am i doing something wrong with my thought process? Thanks!

 

[marcusl]

Your system is nonlinear, so it is not LTI. In particular, the output frequencies of a linear system must match those of the input (another way of saying that sines and cosines are the eigenfunctions of an LTI system).

It is invalid to arbitrarily make up an output function. I suggest you read and understand LTI systems, then you can generate an appropriate impulse response and watch what it does to your input signal. (Alternately, work the exercises in your textbook...)

 

[ntran26]

Your system is nonlinear, so it is not LTI. In particular, the output frequencies of a linear system must match those of the input (another way of saying that sines and cosines are the eigenfunctions of an LTI system).

It is invalid to arbitrarily make up an output function. I suggest you read and understand LTI systems, then you can generate an appropriate impulse response and watch what it does to your input signal. (Alternately, work the exercises in your textbook...)

I see, thank you! Unfortunately, I do not have any textbooks on this subject and have just been using online resources. I am using a reservoir simulator, where I apply a pressure pulse that is sinusoidal and observing pressures at another location. The reservoir is supposed to be an LTI system, but I cannot seem to get the convolution correctly. Thank you for your help!