1
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the system with following input-output relation $$y\left[n\right]=\left(1+\left(-1\right)^n\right)x\left[n\right]$$ where, x[n] is the input and y[n] is the output. The system is
A
invertible and time invariant
B
invertible and time varying
C
non-invertible and time invariant
D
non-invertible and time varying
2
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $$z\left(t\right)=x\left(t\right)\ast y\left(t\right)$$, where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z(ct).
A
$$c.x\left(ct\right)\ast y\left(ct\right)$$
B
$$x\left(ct\right)\ast y\left(ct\right)$$
C
$$c.x\left(t\right)\ast y\left(ct\right)$$
D
$$c.x\left(ct\right)\ast y\left(t\right)$$
3
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is
A
$$\frac1{2e}$$
B
$$\frac2e$$
C
$$\frac1{e^2}$$
D
$$\frac1{2e^2}$$
4
GATE EE 2015 Set 1
Numerical
+1
-0
A moving average function is given by $$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is a sinusoidal signal of frequency $$\frac1{2T}Hz$$, then in steady state, the output y will lag u (in degree) by ________.