List of top Signals and Systems Questions asked in GATE IN

A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a ________.
Given \(x(t) = 4\sin(15\pi t) + 7\cos(4\pi t)\), where \(t\) is in seconds.
The fundamental period of \(x(t)\) is _____ seconds.
A signal \(x(t)\) is shown below.

The plot of \(y(t)=1-x(4-t)\) is shown in ______.
In the table shown below, List-I are the system responses to input \(x(t)\) and List-II are the system properties. The correct matching is ______.
List-IList-II
(M) \(x^2(t)\)(I) Linear and Time-invariant
(N) \(x(-t)\)(II) Non-linear and Time-varying
(O) \(|x(3-t)|\)(III) Linear and Time-varying
(P) \(x(t-3)\)(IV) Non-linear and Time-invariant
Given two signals: \(x(t)=u(t-2)-u(t-3)\), and \(y(t)=e^{-4t}u(t)\).
If \(z(t)=x(t)*y(t)\), then \(Z(s)\) is ______.
An analog speech signal contains signals from \(200\) Hz to \(2400\) Hz. It is sampled at \(6\) kHz and quantized with \(512\) levels for pulse code modulation (PCM). The bit rate will be _____ kbps.
Let \[ f(t)= \begin{cases} 1, & t\in[0,2] \\ -t+3, & t\in[2,3] \\ 0, & \text{otherwise} \end{cases} \] Then \[ \int_{-\infty}^{\infty} f(\tau)\,d\tau = \_\_\_\_\_. \] (rounded off to one decimal place)