Description

1 Definitions
1) 0 n < 0
u(n) =1 n ≥ 0 (1.1)
2) The Z transform of X is defined as
MX(z) = E z−kpX(k) (1.2)
2 Problems
1. If
pY(n) ←→Z MY(z), (2.1.1)
show that
pY(n − k) ←→Z PY(z)z−k, (2.1.2)
2. Show that
u(n) ←→Z, |z| > 1 (2.2.1)
3. Show that
nu(n) ←→Z (1 −z−z1−1)2, |z| > 1 (2.3.1)
4. Let
MY(z) = z6−1((1 − z−−16))2 , |z| > 1 (2.4.1)
1 − z
Show that pY(n) = − 1)u(n − 1) − 2(n − 7)u(n − 7)+(n − 13)u(n − 13) (2.4.2)
(n
36
2
5. The vertices of a △ABC are
A= (38),B= (−21),C= (−66), (2.5.1)
Find the equation of a line perpendicular to BC and passing through A.