>> help zplane ZPLANE Z-plane zero-pole plot. ZPLANE(B,A) where B and A are row vectors containing transfer function polynomial coefficients plots the poles and zeros of B(z)/A(z). Note that if B and A are both scalars they will be interpreted as Z and P.*Both B(z) and A(z) are polynomials of z-1

>> b=[1,0]; a=[1,-0.9];>> zplane(b,a)

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imag

inar

y P

art

>> b=[3,-4]; a=[1,-3.5,1.5];>> zplane(b,a)

-1 -0.5 0 0.5 1 1.5 2 2.5 3

-1.5

-1

-0.5

0

0.5

1

1.5

Real Part

Imag

inar

y P

art

>> b=[1];a=poly([-1,1,1]);>> n=0:7;x=impseq(0,0,7);>> format long; y1=filter(b,a,x)

y1 =

1 1 2 2 3 3 4 4>> y2=(1/4)*(-1).^n+3/4+n/2 %Analytical solution

y2 =

1 1 2 2 3 3 4 4

Numerical solution of Z-Transform

>> help filtic FILTIC Make initial conditions for 'filter' function. Z = filtic( B, A, Y, X ) converts past input X and output Y into initial conditions for the state variables Z needed in the TRANSPOSED DIRECT FORM II filter structure. The vectors of past inputs & outputs are stored with more recent values first, i.e. X = [ x[-1] x[-2] x[-3] ... x[-nb] ... ] Y = [ y[-1] y[-2] y[-3] ... y[-na] ... ] where nb = length(B)-1 and na = length(A)-1. Short input vectors X and Y are zeropadded to length nb and na respectively. If X or Y are longer than nb or na, the values beyond those lengths are irrelevant to the filter's initial conditions and are ignored. Z = filtic( B, A, Y ) assumes that X = 0 in the past.

>> b=[1];a=[1,-1.5,0.5];Y=[4,10];>> xic=filtic(b,a,Y)

xic =

1 -2

y = filter(b, a, x, xic)

>> n=[0:7];x=(1/4).^n;xic=[1,-2];>> b=[1];a=[1,-1.5,0.5];>> format long; y1=filter(b,a,x,xic)

y1 =

Columns 1 through 4

2.00000000000000 1.25000000000000 0.93750000000000 0.79687500000000

Columns 5 through 8

0.73046875000000 0.69824218750000 0.68237304687500 0.67449951171875

>> y2=(1/2).^n+2/3+(1/3)*(1/4).^n %Analytical solution

y2 =

Columns 1 through 4

2.00000000000000 1.25000000000000 0.93750000000000 0.79687500000000

Columns 5 through 8

0.73046875000000 0.69824218750000 0.68237304687500 0.67449951171875