Recent questions in Continuous-time Signals

The direct form structure of an FIR (finite impulse response) filter is shown in the figure.The filter can be used to approximate alow-pass filterhigh-pass filterband-pas...

A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autoco...

The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________

The Discrete Fourier Transform (DFT) of the $4$-point sequence$x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \righ...

A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the ...

A continuous-time sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal ana...

A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, ...

Consider the signal $$x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$$ If $X(e^{jw})$ is the discrete-time Fourier transform o...

The impulse response of an LTI system can be obtained by differentiating the unit ramp response differentiating the unit step response integrating the unit ramp response ...

The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.

A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t +...

Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Whic...

A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is$4\left(-\df...

Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1...

Consider a continuous-time signal defined as$$x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$$where $’\ast’$ denotes the ...

The characteristic equation of an LTI system is given by $F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0.$ The number of roots that lie strictly in the left half $s...

The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the fou...

Two causal discrete-time signals $x[n]$ and $y[n]$ are related as $y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]$. If the $z$-transform of $y[n]$ is $\dfrac{2}{z(z-1)^{2}},$...

The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ The sampled signal is passed through a filter with impulse ...

Input $x(t)$ and output $y(t)$ of an LTI system are related by the differential equation $y’’(t) – y’(t) – 6y(t) = x(t).$ If the system is neither causal nor stable, the ...