Question

Compute The Z-Transform Of The Following Sequences And Determine The Corresponding Region Of Convergence:

A. X(n)=(0.25)nu(n)+4nu(n)
B. X(n)=(0.25)nu(n)-4nu(n)
C. X(n)= - (0.25)nu(-n-1) -4nu(-n-1)

Answer 1

To compute the Z-transform of the given sequences and determine the corresponding region of convergence, apply the definition of the Z-transform, use its properties to simplify the expression, and analyze the values of Z for convergence.

Step-by-step explanation:

To compute the Z-transform of the given sequences and determine the corresponding region of convergence:

a) X(n) = (0.25) * n*u(n) + 4*u(n)

b) X(n) = (0.25) * n*u(n) - 4*u(n)

c) X(n) = - (0.25) * n*u(-n-1) -4*u(-n-1)

Here's the step-by-step process:

• Apply the definition of the Z-transform to each term in the sequence
• Use the properties of the Z-transform to simplify the expression
• Determine the region of convergence by analyzing the values of Z where the Z-transform converges