GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {aₖ} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {aₖ} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3aₖ} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6π rad/s

For the three statements above, which one of the following is correct?

Two discrete-time signals x[n] and h[n] are both non-zero only for n = 0,1,2, and are zero otherwise. It is given that

x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1

Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is ________.

Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by

$h\left[0\right]=\frac{1}{3};h\left[1\right]=\frac{1}{3};h\left[2\right]=\frac{1}{3};$ h[n] = 0 for n < 0 and n > 2

Let H(ω) be the discrete-time Fourier transform (DTFT) of h[n]. where ω is the normalized angular frequency in radians. Given that H(ω₀) = 0 and 0 < ω₀ < π, the value of ω₀ (in radians) is equal to ________.

The figure shows an RLC circuit excited by the sinusoidal voltage 100 cos(3t) Volts, where t is in seconds. The ratio $\frac{amplitudeof{V}_2}{amplitudeof{V}_1}$ is ________

In the circuit shown, the voltage V${}_{IN}$ (t) is described by:

V_IN≤ft( t ) = ≤ft\{ {*20c 0,&for t < 0\\ 15 Volts,&for t ≥ 0 } .

where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ________.