Recent questions in Continuous-time Signals

In the figure, $M(f)$ is the Fourier transform of the message signal $m(t)$ where $A = 100$ Hz and $B = 40$ Hz. Given $v(t)= \cos (2\pi f_{c}t)$ and $w(t)= \cos (2\pi (f_...

A $230\: V$ rms source supplies power to two loads connected in parallel. The first load draws $10 \: kW$ at $0.8$ leading power factor and the second one draws $10\: kVA...

Consider a discrete time periodic signal $x[n] = \sin(\frac{\pi n}{s}).$ Let $a_{k}$ be the complex Fourier series coefficients of $x[n].$ The coefficients $\{a_{k}\}$ ar...

The state diagram of a system is shown below. A system is described by the state-variable equations$$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state-variable equations of the sy...

The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$$1$$2$$3$

Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is$ e^{-\pi ...

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? All the poles of the system must lie on the left side of the $j\omeg...

For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/s$ is$100$$300$$500$$1500$

A band-limited signal with a maximum frequency of $5\: kHz$ is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is$5\: kHz $$12...

The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is$\frac{t^{2}}{2}u(t)$$\frac{t(t-1)}{2}u(t-1)$$\frac{(t-1)^{2}}{2}u(t-1)$$\frac{t...

Two systems with impulse responses $h_{1}(t)$ and $h_{2}(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by product of $...

Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y =\frac{1}{2}$, then $g $ equa...

The circuit shown is a low pass filter with $f_{3\:dB}=\frac{1}{(R_1+R_2)C}\: rad/s$high pass filter with $f_{3\:dB}=\frac{1}{R_1C}\: rad/s$low pass filter with $f_{3\:dB...

The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is$\frac{1}{4}$$\frac{1}{2}$$1$$2$

The state variable description of an LTI system is given by$$\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{pmatrix}=\begin{pmatrix} 0 & a_1 & 0\\ 0 & 0 & a_2\\a_...

A band limited low-pass signal $x(t)$ of bandwidth $5\:kHz$ is sampled at a sampling rate $f_{s}$.The signal $x(t)$ is reconstructed using the reconstruction filter $H(f)...

The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below: Here $\sin c \left...

A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE?It...

Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is$$x\left ( t \right )=...