Bilateral ztransform pairs 05 Z where C is

Bilateral z-transform pairs 제 05장 Z 변환

where C is a counterclockwise contour encircling the origin and lying in the ROC 역 변환 방법 (1) 부분분수 전개법 (2) 유수정리(residue theorem) (3) power series 전개법 (4) 순환법 제 05장 Z 변환

p 1 = 0. 5 + j 0. 5 = 0. 7071 ejp/4 , p 2 = p 1* A 1 = 0. 5 - j 1. 5 = 1. 5811 e-j 1. 2490 , A 2 = A 1* h[n]= 1. 5811 e-j 1. 2490 (0. 7071 ejp/4)n u[n] + 1. 5811 ej 1. 2490 (0. 7071 e-jp/4)n u[n] = 2*1. 5811*(0. 7071)n cos(p/4 = 3. 1622 e-0. 3466 n cos(p/4 n - 1. 2490) u[n] where ln|p 1| = ln(0. 7071) = -0. 3466 제 05장 Z 변환

Ex. ) Inverse ZT (1) ROC ; |z|>0. 5 (2) ROC ; |z|<0. 25 (3) ROC ; 0. 25<|z|<0. 5 f[n] = IZT(F(z)) = ? Sol. ) (1) 제 05장 Z 변환

Matlab function ; pzmap -> poles and zeros mapping on the z-plane n=[2 0. 75 0]; d=[1 -0. 75 0. 125]; sys=tf(n, d); [p, z]=pzmap(sys) p= 0. 5000 0. 2500 z= 0 -0. 3750 제 05장 Z 변환

Matlab function ; zplane -> poles and zeros mapping on the z-plane n=[2 0. 75 0]; d=[1 -0. 75 0. 125]; zplane(n, d) 제 05장 Z 변환

Matlab function ; residuez [r, p, c]=residuez(b, a) where b; numerator polynomial a; denominator polynomial r; residues p; pole locations c; direct terms Ex. ) x[n] = ? R. O. C. ; |z|>1 Sol. ) x[n] = 제 05장 Z 변환

Solutions of the Difference Equations 제 05장 Z 변환

One-sided ZT (or unilateral ZT) The sample shifting property or 제 05장 Z 변환

Ex. ) Sol. ) Taking the one-sided z-transform of both sides of the difference equation, Substituting the initial conditions and rearranging, 제 05장 Z 변환

After inverse transformation the solution is Forms of the Solutions 제 05장 Z 변환

Matlab function ; filter, filtic y = filter(b, a, x, xic) xic = filtic(b, a, Y) where b; numerator polynomial a; denominator polynomial x; input Y; initial conditions xic; an equivalent initial-condition input that generates the same output as generated by the initial conditions(zero input response) n=[0: 20]; b=1; a=[1 -3/2 1/2]; Y=[4 10]; %initial conditions x=(1/4). ^n; %input xic=filtic(b, a, Y); y=filter(b, a, x, xic); %output stem(n, y), hold on, plot(n, y, 'r--'), grid on 제 05장 Z 변환

Relationships between System Representations 제 05장 Z 변환