List of top Communications Questions on Bandwidth asked in GATE EC

In the context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:
For the Boolean function: \[ F(A, B, C, D) = \Sigma m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15), \] the essential prime implicants are:
A causal and stable LTI system with impulse response \(h(t)\) produces an output \(y(t)\) for an input signal \(x(t)\). A signal \(x(0.5t)\) is applied to another causal and stable LTI system with impulse response \(h(0.5t)\). The resulting output is:

The propagation delay of the \(2 \times 1\) MUX shown in the circuit is \(10 \, {ns}\). Consider the propagation delay of the inverter as \(0 \, {ns}\). If \(S\) is set to 1, then the output \(Y\) is \(\_\_\_\_\). 

Consider two continuous-time signals \(x(t)\) and \(y(t)\) as shown below. If \(X(f)\) denotes the Fourier transform of \(x(t)\), then the Fourier transform of \(y(t)\) is \(\_\_\_\_\).

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 \(\_\_\_\_\).

In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of \(R_1\) and the corresponding frequency of oscillation are \(\_\_\_\_\). 

Consider a system \(S\) represented in state space as: \[ \frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix} x + \begin{bmatrix} 1 \\ 0 \end{bmatrix} r, \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix} x. \] Which of the state space representations given below has/have the same transfer function as that of \(S\)?
In a number system of base r, the equation x2-12x+37=0 has x=8 of its solutions. The value of r is____.
Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X≥Y is_____.
Let \( X(t) = A \cos(2\pi f_o t + \theta) \) be a random process, where amplitude \( A \) and phase \( \theta \) are independent of each other, and are uniformly distributed in the intervals [−2, 2] and [0, 2π], respectively. \( X(t) \) is fed to an 8-bit uniform mid-rise type quantizer.
Given that the autocorrelation of \( X(\tau) \) is \[ R_x(\tau) = \frac{2}{3} \cos(2\pi f_o \tau), \] the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is ___.
In a number system of base \(r\), the equation \(x^2 - 12x + 37 = 0\) has \(x = 8\) as one of its solutions. The value of \(r\) is \(\_\_\_\_\).
Suppose \(X\) and \(Y\) are independent and identically distributed random variables that are distributed uniformly in the interval \([0,1]\). The probability that \(X \geq Y\) is \(\_\_\_\_\).
Let \(X(t) = A \cos(2\pi f_0 t + \theta)\) be a random process, where amplitude \(A\) and phase \(\theta\) are independent of each other, and are uniformly distributed in the intervals \([-2, 2]\) and \([0, 2\pi]\), respectively. \(X(t)\) is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of \(X(t)\) is: \[ R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau), \] the signal-to-quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is \(\_\_\_\_\).

In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).