Question: 21 -

The z-transform of the signal a^nx(n) is:

X(z/a)

X(z + a/a)

None of these

X(za)

Answer:

X(z/a)

Solution:

The above property is defined as the scaling property of the signal.

Question: 22 -

The Z-transform of the function y(n) = x(n) + y(n - 1) is:

z/ z - 1

z/ z + 1

z - 1/z

z/ 2z

Answer:

z/ z - 1

Solution:

 y(n) = x(n) + y(n - 1)

Applying Z-transform on both the sides,

Z [y(n)] = Z [x(n)] + Z y[(n - 1)]

Y(z) = X(z) + z^(-1) Y(z)

Y(z) - z^(-1) Y(z) = X(z)

Y(z) (1 - 1/z) = X(z)

Y(z) (1 - 1/z) = X(z)

Y(z)/X(z) = 1/ (1 - 1/z)

H(z) = z / z-1

Thus, the Z-transform of the function y(n) = x(n) + y(n - 1) is z / z-1

Question: 23 -

The addition of zeroes at the end of the sequence when it is represented as the power of integer is refer as:

Region of Convergence

None of the above

Zero padding

Bilateral transform

Answer:

Zero padding

Solution not available.

Question: 24 -

The z-transform of the impulse response y(n) = x(n) + 2x(n - 1) is:

1 + 2z^-1

1 - 2z

1 + 2z²

1/2z

Answer:

1 + 2z^-1

Solution:

Z [y(n)] = Z [x(n)] + Z [2x(n - 1)]

Y(z) = X(z) + 2z^-1X(z)

Y(z) = X(z) (1 + 2z^-1)

Y(z)/X(z) = 1 + 2z^-1

H(z) = 1 + 2z^-1