List of top Signals and Systems Questions asked in GATE IN

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 input-output relationship of an LTI system is given below.

\( \text{For an input } x[n] \text{ shown below,} \)

\( \text{the peak value of the output when } x[n] \text{ passes through } h \text{ is:} \)

Given \( y(t) = e^{-3t}u(t) u(t + 3) \), where denotes convolution operation. The value of \( y(t) \) as \( t \to \infty \) is \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).

The input signal shown below

is passed through the filter with the following taps

The number of non-zero output samples is \(\underline{\hspace{2cm}}\).

Let \( u(t) \) denote the unit step function. The bilateral Laplace transform of the function \( f(t) = e^t u(-t) \) is \(\underline{\hspace{2cm}}\) .

The signal \( \sin(\sqrt{2\pi t}) \) is

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