Signals and systems electrical engineering miscellaneous Difficult Questions and Answers | Page - 26

Signals and systems electrical engineering miscellaneous

Let X(z) = 1
1 - z^-3

be the Z-transform of a causal signal x[n]. Then, the values of x[2] and x[3] are

1. 0 and 0
1. 0 and 1
1. 1 and 0
1. 1 and 1

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Given x(z) = 1
1 - z^–3

x(z) can be written as = 1 + z^–3 + z^–6 + 2^–9
Now x[2] correspond to coefficient z^–2 = 0
and x [3] correspond to coefficient of z^–3 = 1

Correct Option: B

Given x(z) = 1
1 - z^–3

x(z) can be written as = 1 + z^–3 + z^–6 + 2^–9
Now x[2] correspond to coefficient z^–2 = 0
and x [3] correspond to coefficient of z^–3 = 1

The functi on shown in the figure can be represented as

1. u(t) - u(t - T) + (t - T) u(t - T) - (t - 2T) u(t - 2T)
  T T
1. u(t) + t u(t - T) - t u(t - 2T)
  T T
1. u(t) - u(t - T) + (t - T) u(t) - (t - 2T) u(t - 2T)
  T T
1. u(t) + (t - T) u(t - T) - 2 (t - 2T) u(t - 2T)
  T T

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NA

Correct Option: A

NA

For a periodic square wave, which one of the following statements is TRUE?

1. The Fourier series coefficients do not exist
1. The Fourier series coefficients exist but the reconstruction converges at no point
1. The Fourier series coefficients exist and the reconstruction converges at most points.
1. The Fourier series coefficients exist and the reconstruction converges at every point

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For a Periodic square wave, the fourier series coefficients exist and reconstruction converges at most points.

Correct Option: C

For a Periodic square wave, the fourier series coefficients exist and reconstruction converges at most points.

x(t) is nonzero only for T_x < t < T'_x, and similarly, y(t) is nonzero only for T_y < t < T'_y. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?

1. z(t) can be nonzero over an unbonded interval
1. z(t) is nonzero for t < T_x + T_y
1. z(t) is zero outside of T_x + T_y < t < T'_x + T'_y
1. z(t) is nonzero for t > T'_x + T'_y

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Given that z(t) is x(t)* y(t)
Range of z(t) is [sum of lower limits of x(t) and y(t) to sum of upper limit of x(t) and y(t)].
T_x + T_y < t < T_x + T_y

Correct Option: C

Given that z(t) is x(t)* y(t)
Range of z(t) is [sum of lower limits of x(t) and y(t) to sum of upper limit of x(t) and y(t)].
T_x + T_y < t < T_x + T_y

Let S be the set of points in the complex plane corresponding to the unit circle. (That i s, S = {z: | z| = 1}. Consider the function f(z) = zz* where z* denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

1. Unit circle
1. Horizontal axis line segment from origin to (1, 0)
1. The point (1, 0)
1. The entire horizontal axis

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ƒ(Z) = Z.Z*
where Z* is conjugate of Z
∴ ƒ(Z) = | Z|²
= 1 + i.0
∴ ƒ(Z) maps S to the point (1, 0) in the complex plane

Correct Option: C

ƒ(Z) = Z.Z*
where Z* is conjugate of Z
∴ ƒ(Z) = | Z|²
= 1 + i.0
∴ ƒ(Z) maps S to the point (1, 0) in the complex plane