Recent questions tagged signals-and-systems

The RLC filter shown below acts as a $\_\_\_\_$.low pass filterhigh pass filterband pass filterband stop filter

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 $\_...

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$

The maximum signal to quantization noise ratio (SQNR) for a $16$-bit analog-todigital converter is approximately $\_\_\_\_\_\_$ $\mathrm{dB}$.$48$$68$$88$$98$

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

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{...

A closed Lissajous pattern observed on an oscilloscope in the $\mathbf{X}-\mathbf{Y}$ mode has three horizontal tangencies and two vertical tangencies in steady state. If...

Given a differential equation $\dfrac{d^{2} x}{d t^{2}}+x=0$ with $x(0) \neq 0$.Which of the following statements is/are true?$\mid x(t) \mid ^{2}+\left|\dfrac{d x(t)}{d ...

A linear time invariant (LTI) system has a transfer function$$G(s)=\frac{10(s+1)}{s\left(s^{2}+2 s+5\right)}$$The system is placed in unity negative feedback configuratio...

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$$...

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 ...

A chopper amplifier shown in the figure is designed to process a biomedical signal $v_{\text {in }}(t)$ to generate conditioned output $v_{\text {out }}(t)$. The signals ...

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...

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 $X\left(e^{j \omega}\right)$ 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...

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$

The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is$1-j \omega T$$\dfrac{1-j \omega T}{1+j \omega T}$$1+j \omega T$$\dfrac...

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...

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

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 $\_\_\_\...

​​​​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 $z$...

​​​​​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 an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ vol...

The $4$-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the $4$ -point circular...

A system has the transfer-function$\frac{Y(s)}{X(s)}=\frac{s-\pi}{s+\pi}$Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t...

Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3],$ where $u[n]=\left\{\begin{array}{l}1 ; n \geq 0 \\ 0 ; n<0\end{array}\right . $ The smallest $n$ for which $x[n]=...

Let $y(t)=x(4 t),$ where $x(t)$ is a continuous-time periodic signal with fundamental period of $100 \mathrm{~s}.$ The fundamental period of $ y(t)$ is___________$s$ (rou...

The impulse response of an LTI system is $h(t)=\delta(t)+0.5 \delta(t-4)$, where $\delta(t)$ is the continuous-time unit impulse signal. If the input signal $x(t)=\cos \l...

The Laplace transform of the continuous-time signal $x(t)=e^{-3 t} u(t-5)$ is_____________, where $u(t)$ denotes the continuous-time unit step signal.$\frac{e^{-5 s}}{s+3...

A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0, \forall \; t<0.$ From the list given below, select ALL the signals whose continuous-time Fo...

The input $x(t)$ to a system is related to its output $y(t)$ as$$\frac{dy(t)}{dt} + y(t) = 3x (t-3)u (t-3)$$Here $u(t)$ represents a unit-step function.The transfer funct...

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...

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 __________Linear and time-variantNon-l...

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 ...

The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$$2 + G...

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...

A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at $t=0 \; \text{s}$ is received back by the transceiver $100 \; \text{ns}$ ...

The signal $x(t) = (t-1)^{2}u(t-1),$ where $u(t)$ is the unit-step function, has the Laplace transform $X(s).$ The value of $X(1)$ is ________$\frac{1}{e}$$\frac{2}{e}$$2...

A proportional-integral-derivative $\text{(PID)}$ controller is employed to stably control a plant with transfer function$$P(s) = \frac{1}{(s+1)(s+2)}$$Now, the proportio...