Electrical Engineering - Poles and zero`s in matlab?

Question

Anyone know the command to sketch the pole and zero locations in the z-plane for α = 0.8 and Δ = 6 for the equation y[n] = x[n] + α x[n - Δ] I have learnt how to do it with normal equations like 1-2j but have no idea about the above equation of the code.

Answer 1

its very simple, first take the inverse z-transform of the system. You can do it by hand very easily and determine the transfer function.

in this case you have Y(z) = X(z)*(1 + 0.8z^-0.6)

and hence your transfer function is T(z) = Y(z)/X(z) = 1/1 + 0.8z^-0.6)

then in matlab, you can enter in the transfer function for some sampling time Ts, and the simply use the command pzmap(T(z))

remember the pole locations of a discrete time system especially L.T.I systems depend on the sampling time. ie they move when Ts changes

Answer 2

Your question yesterday asking about echo & FIR filters that had as part of the question Matlab routines to look at.

"Hint use the Matlab functions fvtool or zplane and freqz."

I'm a little lost about your question today.

Can you make the expression into a polynomial in z?

Seems Delta is a fixed delay.  There are no terms in n-1, n-2, n-3 except the n-delta term.  Sounds like a FIR with not many taps.

From memory freqz & such take polynomials (well coefficients) in z.

I guess if you can't find a routine to do ti (& I suspect there is one) you could always solve for the roots & plot them yourself?

Maybe, again if you can't find it,  you can get the poles by finding the roots of a related polynomial?