GATE EC 2014 Question Paper (15-Feb-2014) (Shift 1)

Five JK flip-flops are cascades to form the circuit shown in Figure. Clock pulses at a frequency of 1 MHz are applied as shown. The frequency (in kHz) of the waveform at Q3 is ______.

A discrete time signal,

x[n] = 2 sin(π²n), n being an integer, is

Consider two real valued signals, x(t) band-limited to [- 500 Hz, 500 Hz] and y(t) band-limited to [-1 kHz, 1 kHz]. For z(t) = x(t)⋅y(t), the Nyquist sampling frequency (in kHz) is ______.

A continuous, linear time-invariant filter has an impulse response h(t) described by

h≤ft( t ) = ≤ft\{ {*20c 3 for 0 ≤ t ≤ 3\\ 0 otherwise } .

When a constant input of value 5 is applied to this filter, the steady-state output is_______.

The forward-path transfer function of a unity negative feedback system is given by:

$G=\frac{K}{\left(s+2\right)\left(s-1\right)}$

The value of K which will place both the poles of the closed-loop system at the same location is.