GATE IN 2011 Question Paper (13-Feb-2011) (Shift-2)

A square wave (amplitude $\pm 10mV$, frequency $5kHz$, duty cycle $50\%$) is passed through an ideal low-pass filter with pass-band gain and cut-off frequency of $0dB$ and $10kHz$ respectively. The filtered signal is subsequently "buried" additively into a zero-mean noise process of one-sided power-spectral density (PSD) of $25pWH{z}^{-1}$ up to a frequency of $2MHz$. The PSD of the noise is assumed to be zero beyond $2MHz$. The signal-to-noise ratio of the output is

Consider the difference equation $y[n]-\frac{1}{3}y[n-1]=x[n]$ and suppose that $x[n]=(\frac{1}{2}{)}^{n}u[n]$. Assuming the condition of initial rest, the solution for $y[n]$, $n\ge 0$ is

Consider the circuit shown below.

Consider the circuit shown below.

The open-loop transfer function of a unity negative feedback control system is given by

$G(s)=\frac{K}{(s+5{)}^3}$