MODULE 5

Question 1

Z TRANSFORM

Answer 1

• Refers to a signal processing operation that transforms a discrete-time signal into a complex frequency signal.

Question 2

MATHEMATICAL FORMULA

Answer 2

X(z)=∑_(n=-∞)^∞▒〖x(n) 〖 z〗^(-n) 〗

Question 3

2. TIME SHIFTING

Answer 3

x(n-k)↔z^(-k) X(z)
x(n+k)↔z^k X(z)

Question 4

3. Z SCALING

Answer 4

a^n x(n)↔X(z/a)
a^(-n) x(n)↔X(az)

Question 5

4. TIME FOLDING

Answer 5

x(-n)↔ x(1/z)

Question 6

5. DIFFERENTIATION IN Z

Answer 6

nx(n)↔-z d/dz [X(z)]

Question 7

6. CONVOLUTION

Answer 7

〖x_1 (n)*x〗_2 (n)↔X_1 (z)∙X_2 (z)

Question 8

δ(n)

Answer 8

1

Question 9

δ(n-k)

Answer 9

〖 z〗^(-k)

Question 10

a^n u(n)

Answer 10

z/(z-a)

Question 11

a^n u(-n-1)

Answer 11

(-1)/(1-a/z)

Question 12

〖-a〗^n u(-n-1)

Answer 12

z/(z-a)

Question 13

na^n u(n)

Answer 13

az/(z-a)^2

Question 14

REGION OF CONVERGENCE

Answer 14

• This refers to the region in the z-plane where the z-transform converges.