Signal and systems miscellaneous Easy Questions and Answers | Page - 26

Signal and systems miscellaneous

If y[n] = nx[n], then its inverse system is—

1. n²
1. 1
1. 1
  n
1. n

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For the system to be invertible final output must be equal to applied input.

H^{– 1} (z) = y₁(n)
y(n)

= x(n)
nx(n)

= 1
n

Hence, alternative (C) is the correct choice.

Correct Option: C

For the system to be invertible final output must be equal to applied input.

H^{– 1} (z) = y₁(n)
y(n)

= x(n)
nx(n)

= 1
n

Hence, alternative (C) is the correct choice.

For n < 0, there is no overlap between the non-zero postions of x[k] and h[n – k] and consequently, y[n] has a value equal to—

1. 1
1. – 1
1. 0
1. ± 1

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_∞
y(n) = x(k) x[n – k]
^{k = – ∞}

i.e., convolution of two sequence x[ n] and x[ n] then loss if there is no overlap between the non-zero portion of x[ k] and x[n – 1] then y (1) will be zero.

Correct Option: C

_∞
y(n) = x(k) x[n – k]
^{k = – ∞}

i.e., convolution of two sequence x[ n] and x[ n] then loss if there is no overlap between the non-zero portion of x[ k] and x[n – 1] then y (1) will be zero.

The z-transform of discrete time signal x[n] is defined as—

1. _∞
  x(z) = x[n].z^{– n}
  ^{n = – ∞}
1. ₀
  x(z) = x[n].z^{– n}
  ^{n = – ∞}
1. _∞
  x(z) = x[n].z^{– n}
  ^{n = – 0}
1. ₁
  x(z) = x[n].z^{– n}
  ^{n = 0}

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NA

Correct Option: A

NA

System represented by equation y′′(t) – 2t y′(t) = x(t) is—
(i) Causal
(ii) Dynamic
(iii) Non-linear
(iv) Time invariant
The correct statements are—

1. (ii) and (iii) only
1. (i) and (ii) only
1. (i), (ii) and (iii) only
1. (i), (ii) and (iv) only

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The given system equation
y′′(t) – 2t y′(t) = x(t)
● is causal since output depends only on present and past value of the input.
● is dynamic since the I/O relation of system is an integrate-differential equation.
● is linear since there is no constant and square terms in the equation.
● is time variant since there is time factor t in the given system equation.
Hence, alternative (B) is the correct choice.

Correct Option: B

The given system equation
y′′(t) – 2t y′(t) = x(t)
● is causal since output depends only on present and past value of the input.
● is dynamic since the I/O relation of system is an integrate-differential equation.
● is linear since there is no constant and square terms in the equation.
● is time variant since there is time factor t in the given system equation.
Hence, alternative (B) is the correct choice.

System represented by equation y(t) = x(t) + 3 is—
(i) Causal
(ii) Linear
(iii) Static
(iv) Time variant
The correct statements is/are—

1. (i) only
1. (i) and (ii) only
1. (i) and (iii) only
1. (i), (ii) and (iv) only

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The given system equation
y(t) = x(t) + 3
● is causal output depends only on present and past value of the input.
● is non-linear since is constant term.
● is static since there is no integrate-differential equation.
● is time invariant since there is no time factor in the given equation.
Hence, alternative (C) is the correct choice.

Correct Option: C

The given system equation
y(t) = x(t) + 3
● is causal output depends only on present and past value of the input.
● is non-linear since is constant term.
● is static since there is no integrate-differential equation.
● is time invariant since there is no time factor in the given equation.
Hence, alternative (C) is the correct choice.