1
GATE ECE 2023
Numerical
+2
-0.67

Let X(t) be a white Gaussian noise with power spectral density $$\frac{1}{2}$$W/Hz. If X(t) is input to an LTI system with impulse response $$e^{-t}u(t)$$. The average power of the system output is ____________ W (rounded off to two decimal places).

Your input ____
2
GATE ECE 2023
Numerical
+2
-0.67

The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _____________ (rounded off to two decimal places).

Symbols a b c d e f g h
Frequency of occurrence $$\frac{1}{2}$$ $${1 \over 4}$$ $${1 \over 8}$$ $${1 \over {16}}$$ $${1 \over {32}}$$ $${1 \over {64}}$$ $${1 \over {128}}$$ $${1 \over {128}}$$

Your input ____
3
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The phase cross-over frequency, in rad/s, is

A
$${1 \over {\sqrt {{T_1}{T_2}} }}$$
B
$${1 \over {{T_1}{T_2}}}$$
C
$${1 \over {{T_1}\sqrt {{T_2}} }}$$
D
$${1 \over {{T_2}\sqrt {{T_1}} }}$$
4
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67

A closed loop system is shown in the figure where $$k>0$$ and $$\alpha > 0$$. The steady state error due to a ramp input $$(R(s) = \alpha /{s^2})$$ is given by

GATE ECE 2023 Control Systems - Time Response Analysis Question 3 English

A
$${{2\alpha } \over k}$$
B
$${{\alpha } \over k}$$
C
$${{\alpha } \over 2k}$$
D
$${{\alpha } \over 4k}$$
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