Suppose we are given a finite-length sequence h[n](it could be part of an infinite-length impulse response from
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H(z) A(z) = B(z)
Letting
for some choice of M and N, equations from H(z) A(z) = B(z) should allow us to find the M + N 1 coefficients {ak bk}.
(a) Find a matrix equation that would allow us to find the coefficients of B(z) and A(z).
(b) Let h[n] = 0.5n (u[n] u[n 101]) be the sequence we wish to obtain a rational approximation and let B(z) = b0 while A(z) = a0 + a1z1 , find the equations to solve for the coefficients {b0, a0, a1}.
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