Recent questions tagged continuous-time-signals

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$. A unit ste...

The signal $x(t)$ is described by$x(t)=\left\{\begin{array}{ll}1 & \text { for }-1 \leq t \leq+1 \\0 & \text { otherwise }\end{array}\right.$Two of the angular frequencie...

Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system rela...

In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The samples $x(n) \quad(n=0,1,2,...

The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The frequen...

The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The output ...

Fourier series of the periodic function (period $2 \pi$ ) defined by$f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ is$\frac{\pi}{4}+\sum_1...

The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e.$f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=...

Six independent low pass signals of bandwidth $3\mathrm{W}, \mathrm{W}, \mathrm{W}, 2 \mathrm{W}, 3 \mathrm{W}$, and $2 \mathrm{W} \mathrm{~Hz}$ are to be time-division-m...

The Fourier series of a real periodic function has onlycosine terms if it is evensine terms if it is evencosine terms if it is oddsine terms if it is oddWhich of the abov...

A function is given by $f(t)=\sin ^{2} t+\cos 2 t$. Which of the following is true?$f$ has frequency components at 0 and $1 / 2 \pi \; \mathrm{Hz}$$f$ has frequency compo...

Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is$s F(s)-f(0)$$\dfrac{1}{s} F(s)$$\...

An $\text{LTI}$ system having transfer function $\frac{s^{2}+1}{s^{2}+2 s+1}$ and input $x(t)=\sin (t+1)$ is in steady state. The output is sampled at a rate $\omega_{s} ...

The trigonometric Fourier series for the waveform $f(t)$ shown below containsonly cosine terms and zero value for the $dc$ componentonly cosine terms and a positive value...

A continuous time $\text{LTI}$ system is described by\[ \frac{d^{2} y(t)}{d t^{2}}+4 \frac{d y(t)}{d t}+3 y(t)=2 \frac{d x(t)}{d t}+4 x(t) \]Assuming zero initial conditi...

The Nyquist sampling rale for the signal $s(t)=\dfrac{\sin (500 \pi t)}{\pi t} \times \dfrac{\sin (700 \pi t)}{\pi t}$ is given by$400 \mathrm{~Hz}$$600 \mathrm{~Hz}$$120...

If $G(f)$ represents the Fourier transform of a signal $g$ (t) which is real and odd symmetric in time, then$\mathrm{G}(f)$ is complex$G(f)$ is imaginary$\mathrm{G}(f)$ i...

The voltage across an impedance in a network is $V(s)=z(s) I(s)$, where $V(s)$, $Z(s)$ are the Laplace transforms of the corresponding time function $v(t), z(t)$ and $i(t...

A linear second order single input continuous time system is described by the following set of differential equations$$ \begin{aligned} &x_1(t)=-2 x_1(t)+4 x_2(t) \\ &x_2...

Referring to the figure. The switch $S$ is in position $1$ initially and steady state conditions exist from time $\mathrm{t}=0$ to $t=t_0$. The switch is suddenly thrown ...

(a) Find the Laplace transform of the waveform $x(t)$ shown in figure.(b) The network shown in figure is initially under steady state condition with the switch in positio...

In figure, the operational amplifier is ideal and its output can swing between $-15$ and $+15$ volts. The input $v_\rho$ which is zero for $t<0$, is switched to $5$ volts...

In figure, the operational amplifiers are ideal and their output can swing between $-15$ and $+15$ volts. Sketch on same diagram, the waveform of voltages $V_1$ and $V_2$...

The differential equation $100 \dfrac{d^2 y}{d t^2}-20 \dfrac{d y}{d t}+y=x(t)$ describes a system with an input $x(t)$ and an output $y(t)$. The system, which is initial...

The trigonometric Fourier series of an even function does not have thedc termcosine termssine termsodd harmonic terms

An input $\mathrm{x(t)}=\exp (-2 \mathrm{t)u(t})+\delta(\mathrm{t}-6)$ is applied to an LTI system with impulse response $\mathrm{h(t)=u(t})$. The output is$[1-\exp (-2 \...

The Fourier transform $X(j \omega)$ of the signal$$x(t) = \frac{t}{(1+t^{2})^{2}}$$is ______________.$\frac{\pi}{2j} \omega e^{– |\omega|}$$\frac{\pi}{2} \omega e^{– |\om...

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi...