Recent activity in Signals and Systems

Let $f(t)=\left\{\begin{array}{cc}1, & t \in[0,2] \\ -t+3, & t \in[2,3] \\ 0, & \text { otherwise }\end{array}\right.$Then$\int_{-\infty}^{\infty} f(\tau) d \tau=$ $\_\_\...

Given two signals: $x(t)=u(t-2)-u(t-3)$, and $y(t)=e^{-4 t} u(t)$. If $z(t)=x(t) * y(t)$, then $Z(s)$ is $\_\_\_\_$.$\dfrac{e^{-3 s}\left[e^{s}-1\right]}{s(s+4)}$$\dfrac{...

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 $\_\_\_\_\_\_$.$$\begin{array}{|l...

A signal $x(t)$ is shown below.The plot of $y(t)=1-x(4-t)$ is shown in $\_\_\_\_\_\_$.  

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.$15$$60$$30$$2$

A square wave signal of frequency $20$ $\mathrm{kHz}$ is passed through an ideal low-pass filter with cut-off frequency of $21$ $\mathrm{kHz}$. The output signal is a $\_...

​​​​​Laplace transform of a signal $x(t)$ is$$X(s)=\frac{1}{s^{2}+13 s+42}$$Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if t...

​​​​Consider a discrete-time sequence$x[n]=\begin{cases} (0.2)^{n}, & 0 \leq n \leq 7 \\ 0, & \text { otherwise } \end{cases}$The region of convergence of $X(z)$, the $z$...

The current $i(t)$ drawn by a circuit is given as$$i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A}$$The root-mean-square value of $i(t)$ is $\_\_\_\...

The Nyquist sampling frequency for $x(t)=10 \sin ^{2}(200 \pi t)$ is $\_\_\_\_\_\_\_ \mathrm{~Hz}$ (rounded off to nearest integer).

The number of complex multiplications required for computing a $16$-point DFT using the decimation-in-time radix-$2$ FFT is $\_\_\_\_\_\_\_$ (in integer).

Consider a filter defined by the difference equation$$ y[n]-0.5 y[n-2]=a x[n-4] $$where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude r...

A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0 \leq n \leq 3$. The zero lag auto-correlation value of $x[n]$ is$1$$10$$20$$30$

A signal $V_{M}=5 \sin (\pi t / 3) \mathrm{V}$ is applied to the circuit consisting of a switch $S$ and capacitor $C=0.1 \mu \mathrm{~F}$, as shown in the figure. The out...

Let $X\left(e^{j \omega}\right)$ represent the discrete time Fourier transform of a $4$-length sequence $x[n]$, where $x[0]=1, x =2, x =2$, and $x[3]=4 . X\left(e^{j \ome...

Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.$e^{j \frac{2 \pi}{3} t}$$\cos \left(\frac{2 \pi}{3} t\righ...

Let $f(t)$ and $g(t)$ represent continuous-time real-valued signals. If $h(t)$ denotes cross-correlation between $f(t)$ and $g(-t)$, its continuous-time Fourier transform...

Let $y[n]=\frac{1}{\alpha} y[n-1]+x[n]$, where $\alpha>1$ and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is ...

Let a continuous-time signal be $x(t)=e^{j 9 t}+e^{j 5 t}$, where $j=\sqrt{-1}$ and $t$ is in seconds. The fundamental period of magnitude of $x(t)$, in seconds, is$\pi$$...

A signal $x(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}.$A signal $y(t)$ is related to $x(t)$ as follows:$$y(t) = x (2t – 5)$$The statement that ...

A periodic function $f(x),$ with period $2,$ is defined as$f(x) = \left\{\begin{matrix} -1 -x & -1 \leq x < 0 \\ 1 – x & 0 < x \leq 1 \end{matrix}\right. $The Fourier ser...

Consider the transfer function$$H_{c}(S) = \frac{1}{(s+1)(s+3)}$$Bilinear transformation with a sampling period of $0.1 \; \text{s}$ is employed to obtain the discrete-ti...

The input-output relationship of an $\text{LTI}$ system is given below.For an input $x\left [ n \right ]$ shown belowthe peak value of the output when $x\left [ n \right ...

The signal $\sin\left ( \sqrt{2\pi t} \right )$ isperiodic with period $T=\sqrt{2\pi }$not periodic periodic with period $T=2\pi$periodic with period $T=4\pi ^{2}$

The step response of a circuit is seen to have an oscillatory behavior at the output with oscillations dying down after some time. The correct inference$\text{(s)}$ regar...

Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rig...

A differentiator has a transfer function whosephase increases linearly with frequencymagnitude remains constantmagnitude increases linearly with frequencymagnitude decrea...

The input x[n] and output y[n] of a discrete-time system are related as y[n] = $\alpha$y[n – 1] + x[n]. The condition of $\alpha$ for which the system is Bounded-Input B...

The output y(t) of a system is related to its input x(t) asy(t) = ${\displaystyle \int^t_0}$x(t – 2)dt, where, x(t) =0 and y(t) = 0 for t $\le$ 0. The transfer function o...

A signal cos(2$\pi$f${_m}$t) modulates a carrier cos(2$\pi$f${_c}$t) using the double -sideband-with-carrier (DSDWC) scheme to yield a modulated signal cos(2$\pi$f${_c}$t...

A discrete- time signal x[n] = e$^{j(\frac{5\pi}{3})n}$ + e$^{j(\frac{\pi}{4})n}$ is down-sampled to the signal x${_d}[n]$ such that x${_d}[n]$ = x[4n]. The fundamental...

The output of a continuous-time system y(t) is related to its input x(t) as y(t) = x(t) + $\frac{1}{2}$x(t-1). If the Fourier transforms of x(t) and y(t) are x($\omega$) ...

A signal x(t) has a bandwidth 2B about a carrier frequency of f${_c}$ = 2 GHz as shown in Figure (a) below. In order to demodulate this signal, it is first mixed (multipl...

Unit step response of a linear time invariant $(LTI)$ system is given by $y(t) = (1 – e^{-2t})u(t)$. Assuming zero initial condition, the transfer function of the system ...

For the sequence $x[n] = \{1, -1,1, -1\},$ with $n = 0,1,2,3,$ the DFT is computed as $X(k) = \displaystyle{}\Sigma^3_{n=0}x[n]e^{-j\frac {2\pi}{4}nk}$, for $k = 0,1,2,3....

Let y[n] = x[n] * h[n], where * denotes convolution and x[n] and h[n] are two discrete time sequences, Given that the z-transform of y[n] is y(z) = 2+ 3z$^{-1}$ + z$^{-2}...

The Fourier transform of a signal x(t), denoted by X(j$\omega$), is shown in the figure Let y(t) = x(t) + e$^{jt}...

An ideal square wave with period of 20ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accur...

Consider signal x(t) = . Let $\delta$(t) denote the unit impulse (Dirac-delta) function. The value of the integral $ \int^5_0$ 2x(t- 3)$\delta$(t-4)dt is 2103

Two periodic signals x(t) and y(t) have the same fundamental period of 3 seconds. Consider the signal z(t) = x(-t) + y(2t + 1). The fundamental period of z(t) in seconds ...