List of top Signals and Systems Questions asked in GATE IE

Consider the transfer function \[ H_c(s) = \frac{1}{(s + 1)(s + 3)} \] Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function \( H_d(z) \). Then \( H_d(z) \) is _________

The output of a system \( y(t) \) is related to its input \( x(t) \) according to the relation \( y(t) = x(t) \sin(2\pi t) \). This system is _________

A signal \( x(t) \) is band-limited between 100 Hz and 200 Hz. A signal \( y(t) \) is related to \( x(t) \) as follows:
y(t) = x(2t - 5)
The statement that is always true is_________

The input \( x(t) \) to a system is related to its output \( y(t) \) as
\[ \frac{d y(t)}{dt} + y(t) = 3x(t - 3)u(t - 3) \] \text{Here \( u(t) \) represents a unit-step function.}
\text{The transfer function of this system is _________}

The sinusoidal T.F. Corresponding to the polar plot for T>0.