Time response of an LTI system using transfer function and equivalent difference equation.

1. I have estimated a discrete Transfer function H(z) using tfest command in Matlab for my data set. Then I used it to calculate the time response of my LTI system by using the matlab command LSIM for a unit impulse as an input. It worked as expected. However, when I calculated the equivalent difference equation from the transfer function H(z) and used it iteratively to calculate the time response for the exact same input, it does not give me the same results, In fact in this case the response just blows up midway. Am I missing out on any information during the conversion from transfer function domain to difference equation domain?
2. So, I want to replace one dimensional convolution performed on my LTI system with matrix multiplication to fit into into a convex optimization framework. I have the transfer function H(z) representing my system. Is there a way to find the equivalent Toeplitz matrix A in matlab, such that

conv(h,x) = Ax

for an input vector x ( a unit impulse funtion in this case) and h is the time domain representation of the transfer function H(z).

[Fiona]

Hello. Have you found a solution to your number 1? I am having the same issue.

[Hafsa Farooqi]

Hi Fiona,

I realized the estimated TF values are very sensitive to rounding off and a slight variation like rounding off the estimated values can give unexpected results. Once I sorted that, it worked perfectly.

[Fiona]

Hafsa,

I appreciate your response. Changing to using the full value instead of rounded values stopped the output from blowing up and I got the expected output. (Note: I accidentally used rounded values because I forgot that the variable viewer in MATLAB shows a rounded value unless you double click to see the full value.)

Thanks,

Fiona

[Paul]

Why did you have to use the variable viewer? Can't the relevant values be obtained directly from the object in the workspace?

[Fiona]

Paul,

I was originally using the variable viewer to get the coefficient values and put them in a new array manually. Yes you can obtaining them directly from the workspace, I previously changed to using this method.