GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is 10 $\mu$ W. The effective number of bits (rounded off to the nearest integer) of the ADC is ____________

The information bit sequence $\{111010101\}$ is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $G(x)=x^4+x+1$. The encoded sequence of bits is __________

A continuous time signal $x(t)=2\cos (8\pi t+\pi /3)$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response
$h(t)=\left(\frac{\sin (2\pi t)}{\pi t}\right)\cos (38\pi t-\pi /2)$
produces an output $x_0(t)$. The expression for $x_0(t)$ is _______

The opamps in the circuit shown are ideal, but have saturation voltages of $\pm 10$ V.

Assume that the initial inductor current is 0 A. The input voltage ($V_i$) is a triangular signal with peak voltages of $\pm 2$ V and time period of 8 $\mu$ s. Which one of the following statements is true?

In the circuit below, the opamp is ideal.

If the circuit is to show sustained oscillations, the respective values of ${\text{R}}_1$ and the corresponding frequency of oscillation are _____.