DET: Module 7

Question 1

Z-Transform

Answer 1

Z[u(n)] = ∑ u(n) z^-n

Question 2

Z[a^n]

Answer 2

z/z-a

Question 3

z[1]

Answer 3

z/z-1

Question 4

z[n]

Answer 4

z/(z-1)^2

Question 5

z[n^2]

Answer 5

z^2+z/(z-1)^3

Question 6

z[cosnθ]

Answer 6

z(z-cosθ)/(z^2-2zcosθ+1)

Question 7

z[sinnθ]

Answer 7

zsinθ/(z^2-2zcosθ+1)

Question 8

Damping Rule

Answer 8

1) Divide by a^n ==> z –> az
2) Multiply by a^n ==> z –> z/a

Question 9

Multiplication by a^n

Answer 9

(-z)^m d^m/dz^m [u[z]]

Question 10

Convolution Theorem

Answer 10

F[z]*G[z] = ∑ f(m).g(n-m)

Question 11

Sum of GP series

Answer 11

S = a(r^n -1)/r-1

Question 12

sin(A±B)

Answer 12

sinAcosB ± cosAsinB

Question 13

cos(A±B)

Answer 13

cosAcosB ∓ sinAcosB

Question 14

Shifting Property: Forward Shift

Answer 14

z[yn+2] = z^2 [ y(z) - y0 - y1/z]
z[yn+1] = z [ y(z) - y0]

Question 15

(1-x)^-1 expansion

Answer 15

1+x + x^2 + x^3 + ….