Recent questions tagged signals-and-systems

A system with an input $x(t)$ and output $y(t)$ is described by the relation. $y(t)=t x(t)$. This system islinear and time-invariantlinear and time varyingnon-linear and ...

A linear time invariant system has an impulse response $e^{2 t}, t>0$. If the initial conditions are zero and the input is $e^{3 t}$, then output for $t>0$ is$e^{3 t}-e^{...

One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$...

Let $u(t)$ be the step function. Which of the Waveforms in given figure, $(a)$ - $(d)$ corresponds to the convolution of $u(t)-u(t-1)$ with $u(t)-u(t-2)$ ?

A message $m(t)$ bandlimited to the frequency $f_{m}$ has a power of $P_{m}$. The power of the output signal in given figure is$\frac{\mathrm{P}_{m} \cos \theta}{2}$$\fra...

The Hilbert transform of $\cos \omega_{1} t+\sin \omega_{2} t$ is$\sin \omega_{1} t-\cos \omega_{2} t$$\sin \omega_{1} t+\cos \omega_{2} t$$\cos \omega_{1} t-\sin \omega_...

A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ are respectively given b...

In an $\text{FM}$ system, a carrier of $100\; \mathrm{MHz}$ is modulated by a sinusoidal signal of $5 \; \mathrm{kHz}$. The bandwidth by Carson's approximation is $1 \; \...

A bandlimited signal $x(t)$ with $a^{\prime}$ spectrum $X(f)$ as shown in first figure is processed as shown in second figure is $p(t)$ is a periodic train of impulses as...

Zero mean white Gaussian noise with a two-sided power spectral density of $4 \mathrm{~W} / \mathrm{kHz}$ is passed through an ideal lowpass filter with a cut-off frequenc...

If $[f(t)]=\mathrm{F}(s)$, then $[f(t-\mathrm{T})]$ is equal to$e^{s \mathrm{T}} \mathrm{~F}(s)$$e^{-s \mathrm{T}} \mathrm{~F}(s)$$\frac{\mathrm{F}(s)}{1-e^{s T}}$$\frac{...

A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ isa real and even function of $\omega$a imaginary and o...

The Fourier series representation of an impules train denoted by\[s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text { is given by }\]$\frac{1}{\mathrm{~T}...

The Nyquist sampling frequency (in $\mathrm{Hz}$ ) of a signal given by$6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)$ is$200$$300$$500$$1000$

The input to a matched filter is given by$s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} ...

Input to a linear delta modulator is a sinusoidal signal whose frequency can vary from $200 \mathrm{~Hz}$ to $4000 \mathrm{~Hz}$. The input is sampled at eight times the ...

A bandlimited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples throughan RC filteran envelope detectora PLLan ideal low-pass filt...

If a signal $f(t)$ has energy $E$, the energy of the signal $f(2 t)$ is equal to$\text{E}$$\frac{\mathrm{E}}{2}$$2 \mathrm{E}$$4 \mathrm{E}$

The impulse response functions of four linear systems $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4}$ are given respectively by$\begin{array}{ll} h_{1...

The Nyquist sampling interval, for the signal $\text{Sin c } (700 t)+\text{Sin c } (500 t)$ is$\frac{1}{350} \mathrm{sec}$$\frac{\pi}{350} \sec$$\frac{1}{700} \mathrm{sec...

The PSD and the power of a signal $g(t)$ are, respectively, $\mathrm{S}_{\text{g}}(\omega)$ and $\text{P}_{\text{g}}$. The PSD and the power of the signal $a \text{g}(t)$...

The Fourier transform $G(\omega)$ of the signal $g(t)$ in the figure, given as $G(w)=\frac{1}{\omega^{2}}\left(\mathrm{e}^{j \omega}-j w e^{j \omega}-1\right)$. Using thi...

A baseband signal $\text{g}(t)$ bandlimited to $100 \mathrm{~Hz}$ modulates a carrier of frequency $f_{0} \mathrm{~Hz}$. The modulated signal $\text{g}(t) \cos 2 \pi f t$...

A periodic signal $\text{g}(t)$ is shown inthe figure. Determine the PSD of $\text{g}(t)$.

Convolution of $x(t+5)$ with impulse function $\delta(t-7)$ is equal to$x(t-12)$$x(t+12)$$x(t-2)$$x(t+2)$

Which of the following cannot be the Fourier series expansion of a periodic signal ?$x(t)=2 \cos t+3 \cos 3 t$$x(t)=2 \cos \pi t+7 \cos t$$x(t)=\cos t+0.5$$x(t)=2 \cos 1....

The Fourier transform $\mathrm{F}\left\{e^{-t} u(t)\right\}$ is equal to $\frac{1}{1+j 2 \pi f}$. Therefore, $\mathrm{F}\left\{\frac{1}{1+j 2 \pi t}\right\}$ is$e^f u(f)$...

A linear phase channel with phase delay $T_p$ and group delay $T_g$ must have$T_p=T_g=$ constant$T_p \propto f$ and $T_g \propto f$$T_p=$ constant and $T_g \propto f$$T_p...

A $1 \; \mathrm{MHz}$ sinusoidal carrier is amplitude modulated by a symmetrical square wave of period $100 \; \mu \mathrm{sec}$. Which of the following frequencies will ...

Consider a sampled signal $y(t)=5 \times 10^{\circ}$ ${ }^6 x(t) \sum_{(n-\infty}^{+\infty} \delta \left(t-n \mathrm{T}_x\right)$ where $x(t)=10 \cos \left(8 \pi \times 1...