For a 2nd order IIR filter, can I use Matlab to find difference equation and impulse response?

For a 2nd order IIR filter, can I use Matlab to find difference equation and impulse response?

x(n)=u(n) with 5 output values y(n), for n=0,1....,4 with the following values: y(0)=0.2, y(1)=0.59, y(2)=0.8030, y(3)=0.8951, and y(4)=0.9527

I am new to Matlab and was unable to find a method in the various help menus? Is it possible? If so, how?

Thanks,

Josh

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you have to find the difference equation first.

you will have to solve a system of equations (5 in this case).

y(n) = b0x(n) + b1x(n-1) +b2x(n-2) -a1(n-1) -a2(n-2)

sub in the known values and obtain 5 equations:

y(0) = b0*1 + 0+ 0+ 0+ 0, y(1) = b0*1 + b1*1 + 0 -a1y(0) + 0, etc, etc, etc

then use a matrix to solve for the constants b0,b1,b2,a1,a2

once you obtained the difference equation you should be able to use filter() or similar functions