1
GATE EE 2014 Set 2
+1
-0.3
Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system is cos(3t) and the steady state output is $$A\sin\left(3t+\alpha\right)$$, then the value of A is
A
1/30
B
1/15
C
3/4
D
4/3
2
GATE EE 2014 Set 2
+2
-0.6
A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is
A
a highly attenuated square wave at 10 kHz
B
nearly zero.
C
a nearly perfect cosine wave at 30 kHz.
D
a nearly perfect sine wave at 30 kHz.
3
GATE EE 2014 Set 2
+2
-0.6
An input signal x(t) = 2 + 5sin(100$$\mathrm\pi$$t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by $$\frac{Y\left(z\right)}{X\left(z\right)}=\frac1N\left[\frac{1-z^{-N}}{1-z^{-1}}\right]$$$where, N represents the number of samples per cycle. The output y(n) of the system under steady state is A 0 B 1 C 2 D 5 4 GATE EE 2014 Set 2 MCQ (Single Correct Answer) +2 -0.6 A discrete system is represented by the difference equation $$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a-1\\a+1&a\end{bmatrix}\begin{bmatrix}X_1\left(k\right)\\X_2\left(k\right)\end{bmatrix}$$$ It has initial condition $$X_1\left(0\right)=1;\;X_2\left(0\right)=0$$. The pole location of the system for a = 1, are
A
$$1\pm j0$$
B
$$-1\pm j0$$
C
$$\pm1+j0$$
D
$$0\pm j1$$
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