Signal and systems miscellaneous Easy Questions and Answers | Page - 36

Signal and systems miscellaneous

Let h(t) be the response of a linear system to a unit impulse δ(t). Consider the following statements in this regard—
(i) If the system is causal, h(t) = 0 for t < 0.
(ii) If the system is time-variable, then the response of the system to an input of δ(t – T) is h(t – T) for all values of the constant T.
(iii) If the system is non-dynamic then h(t) is of the form Aδ(t), where the constant A depends on the system of these the correct statements.

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

View Hint View Answer Discuss in Forum

NA

Correct Option: B

NA

The system described by the difference equation y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1) has y(n) = 0 and n < 0. If x(n) = δ(n) then y(2) will be—

1. 2
1. 1
1. 0
1. – 1

View Hint View Answer Discuss in Forum

Given equation is
y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1)
Taking z-transform on both side
Y(z) – 2Y(z).z^–1 + Y(z).z^–2 = X(z) – X(z).z^–1
or
Y(z) = 1 – z^–1 = 1 – z^–1
X(z) 1 – 2z^–1 + z^–2 (1 – z – 1)²

or
H(z) = 1
1 – z^–1

or
h(n) = 1.u(n)
Now, y(n) = h(n).x(n)
y(n) = 1.u(n).δ(n)
y(2) = 0
Hence, alternative (C) is the correct choice.

Correct Option: C

Given equation is
y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1)
Taking z-transform on both side
Y(z) – 2Y(z).z^–1 + Y(z).z^–2 = X(z) – X(z).z^–1
or
Y(z) = 1 – z^–1 = 1 – z^–1
X(z) 1 – 2z^–1 + z^–2 (1 – z – 1)²

or
H(z) = 1
1 – z^–1

or
h(n) = 1.u(n)
Now, y(n) = h(n).x(n)
y(n) = 1.u(n).δ(n)
y(2) = 0
Hence, alternative (C) is the correct choice.

The group delay function τ(ω) is related to phase function φ(ω) as—

1. τ(ω) = dφ(ω)
  dω
1. τ(ω) = – d²φ(ω)
  dω²
1. τ(ω) = – d²φ(ω)
  dω²
1. τ(ω) = d²φ(ω)
  dω²

View Hint View Answer Discuss in Forum

NA

Correct Option: B

NA

The theoretical spectral density of white noise is—

1. zero
1. finite
1. infinite
1. depends on frequency of the signal

View Hint View Answer Discuss in Forum

Spectral density of a white noise is given below:

From figure given above it is clear that spectral density of a white noise is constant throughout the whole frequency range.

Correct Option: C

Spectral density of a white noise is given below:

From figure given above it is clear that spectral density of a white noise is constant throughout the whole frequency range.

A rectangular pulse is passed through an LPF: The response is a—

1. triangular pulse
1. trapezoidal function
1. sampling function
1. None of these

View Hint View Answer Discuss in Forum

We know that a LPF acts as an integrator.

When rectangular pulse is applied at the input, we get triangular pulse.

Correct Option: A

We know that a LPF acts as an integrator.

When rectangular pulse is applied at the input, we get triangular pulse.