Recent questions in Continuous-time Signals

Consider a system whose input $x$ and output $y$ are related by the equation\[ y(t)=\int_{-\infty}^{\infty} x(t-\tau) h(2 \tau) d \tau, \]where $h(t)$ is shown in the gra...

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...

Consider the pulse shape $s(t)$ as shown. The impulse response $h(t)$ of the filter matched to this pulse is ​​​​​​​

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...

For the compensated attenuator of the given figure, the impulse response under the condition $R_{1} C_{1} = R_{2} C_{2}$ is$\frac{R_{2}}{R_{1}+R_{2}}\left[1-e^{-\frac{1}{...

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...

An excitation is applied to a system at $\mathrm{t}=\mathrm{T}$ and its response is zero for $-\infty<t<T$. Such a system isnon-causal systemstable systemcausal systemuns...

The pole-zero pattern of a certain filter is shown in the figure below. The filter must be of the following type.low passhigh passall passband pass

A signal has frequency components from $300 \mathrm{~Hz}$ to $1.8 \; \mathrm{KHz}$. The minimum possible rate at which the signal has to be sampled is ___________.

(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...

(a) A signal $A \sin \omega_m \mathrm{t}$ is input to a square - law device $\left(e_0-e_{m 2}\right)$. The output of which is given to an $\mathrm{FM}$ modulator as the ...

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...

The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure.Statement $\text{I}:$ The system is necessarily a pure delay system f...

Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function.If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}...

The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure.Based on th...