GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

The system function of an LTI system is given by

$H(z)=\frac{1-\frac{1}{3}{Z}^{-1}}{1-\frac{1}{4}{Z}^{-1}}$

The above system can have stable inverse if the region of convergence of H(z) is defined as

The figure is a logic circuit with inputs A and B and output Y. Vₛₛ = + 5 V. The circuit is of type

The impulse response of an LTI system is given as :

$\mathrm{h}[\mathrm{n}]=\{\begin{array}{cc}\frac{{\omega }_c}{\pi }& n=0\\ \frac{\sin {\omega }_{c}n}{\pi n}& n\ne 0\end{array}$

It represents an ideal

A discrete-time signal 𝑥[𝑛] is obtained by sampling an analog signal at 10 kHz. The signal 𝑥[𝑛] is filtered by a system with impulse response ℎ[𝑛] = 0.5{𝛿[𝑛] + 𝛿[𝑛 − 1]}. The 3dB cutoff frequency of the filter is:

A full-duplex binary FSK transmission is made through a channel of bandwidth 10 kHz. In each direction of transmission, the two carriers used for the two states are separated by 2 kHz. The maximum baud rate for this transmission is: