Recent questions tagged signals-and-systems

In the small circuit shown, the enhancement mode $n$-channel $\text{MOSFET}$ is biased in saturation with a transconductance $g_{m}.$ A small signal low-frequency voltage...

The input-output relationship of an $\text{LTI}$ system is given below.For an input $x\left [ n \right ]$ shown belowthe peak value of the output when $x\left [ n \right ...

The signal $\sin\left ( \sqrt{2\pi t} \right )$ isperiodic with period $T=\sqrt{2\pi }$not periodic periodic with period $T=2\pi$periodic with period $T=4\pi ^{2}$

The step response of a circuit is seen to have an oscillatory behavior at the output with oscillations dying down after some time. The correct inference$\text{(s)}$ regar...

Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rig...

The input signal shown belowis passed through the filter with the following tapsThe number of non-zero output samples is ________________.

A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $...

A signal having a bandwidth of $\text{5 MHz}$ is transmitted using the Pulse code modulation $\text{(PCM)}$ scheme as follows. The signal is sampled at a rate of $50\%$ a...

A sinusoid of $\text{10 kHz}$ is sampled at $\text{15 k samples/s}.$ The resulting signal is passed through an ideal low pass filter $(LPF)$ with cut-off frequency of $\t...

Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right. $ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \...

Consider the finite sequence $X=(1,1,1).$ The Inverse Discrete Fourier Transform (IDFT) of X is given as $\text{(x(0), x(1), x(2)).}$ The value of $x(2)$ is _______

A differentiator has a transfer function whosephase increases linearly with frequencymagnitude remains constantmagnitude increases linearly with frequencymagnitude decrea...

Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $The period of this signal $x[n...

The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ____...

Consider two discrete-time signals:$x_1(n)$={1,1} and $x_2(n)$={1,2} , for $n=0,1$.The Z-transform of the convoluted sequence $x(n)=x_1(n)^*x_2(n)$ is$1+2z^{-1}+3z^{-2}$$...

Three $DFT$ coefficients, out of five $DFT$ coefficients of a five-point reall sequence are given as: $X(0)=4$, $X(1)=1-j1$ and $X(3)=2+j2$. The zeroth value of the seque...

For a first order lowpass filter with unity $\text {d.c}$. gain and $-3\;\text {dB}$ corner frequency of $2000\pi \:\text {rad/s}$,the transfer function $H(j\omega)$ is $...

A periodic signal $\text{x(t)}$ is shown in the figure. The fundamental frequency of the signal $\text{x(t)}$ in $\text Hz$ is ____________.

If a continuous-time signal $x(t)=\cos(2\pi t)$ is sampled at $ \text{4 Hz}$, the value of the discrete-time sequence $x(n)$ at $n=5$ is$-0.707$$-1$$0$$1$

The Region of Convergence $\text {(ROC)}$ of the $\text Z$-transform of a causal unit step discrete-time sequence is $|z|<1$$|z|\leq1$$|z|>1$$|z|\geq1$

The output y(t) of a system is related to its input x(t) asy(t) = ${\displaystyle \int^t_0}$x(t – 2)dt, where, x(t) =0 and y(t) = 0 for t $\le$ 0. The transfer function o...

The input x[n] and output y[n] of a discrete-time system are related as y[n] = $\alpha$y[n – 1] + x[n]. The condition of $\alpha$ for which the system is Bounded-Input B...

The frequency response of a digital filter H($\omega$) has the following characteristicsPassband: 0.95$\le$|H($\omega$|$\le$1.05 for 0$\le$$\omega$$\le$0.3$\pi$ andStopba...

The output of a continuous-time system y(t) is related to its input x(t) as y(t) = x(t) + $\frac{1}{2}$x(t-1). If the Fourier transforms of x(t) and y(t) are x($\omega$) ...

A discrete- time signal x[n] = e$^{j(\frac{5\pi}{3})n}$ + e$^{j(\frac{\pi}{4})n}$ is down-sampled to the signal x${_d}[n]$ such that x${_d}[n]$ = x[4n]. The fundamental...

A signal x(t) has a bandwidth 2B about a carrier frequency of f${_c}$ = 2 GHz as shown in Figure (a) below. In order to demodulate this signal, it is first mixed (multipl...

The signal $x[n]$ shown in the figure below is convolved with itself to get $y[n]$. The value of $y[-1]$ is $\_\_\_\_\_\_\_\_.$

If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.

The signal $m(t)=cos(\omega_mt)$ is $SSB$ (single side-band) modulated with a carrier $\cos(\omega_ct)$ to get $s(t)$. The signal obtained by passing $s(t)$ through an id...

Let $s(t)=rect\left(\frac{t-3}{3}\right)$ be a signal passed through an $AWGN$ (additive white Gaussian noise) channel with noise power spectral density $(PSD)$ $\frac{N_...

For the periodic signal $x(t)$ shown below with period $T=8s$, the power in the 10th harmonic is __________.$0$$\frac{1}{2} \left (\frac{2}{10\pi} \right)^2$$\frac{1}{2} ...

The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.

Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.$P(s)-(3), Q(s)-(2), R(s)-(1)$$P(s)-(1), Q(s)-(2), R(s)-(3)$$...

The comparators (output=$’1’$, when input $\underline{>}$ and output=$’0’$, when input$<0$), exclusive-OR gate and the unity gain low-pass filter given in the circuit are...

The signal $m(t)=\frac{\sin(100\;\pi t)}{100\; \pi t}$ is frequency modulated $(FM)$ with an $FM$ Modulator of frequency deviation constant of $30\;kHz/V$. Using Carson’s...

A signal $m(t)$ varies from $-3.5\;V$ to $+3.5\;V$ with an average power of $3\;W$. The signal is quantized using a midtread type quantizer and subsequently binary encode...

The highest frequency present in the signal $x(t)$ is $f_{max}$. The highest frequency present in the signal $y(t)=x^2(t)$ is$\frac{1}{2}f_{max}$$f_{max}$$2f_{max}$$4f_{m...

The filter whose transfer function is of the form $G(s)=\frac{s^2-bs+c}{s^2+bs+c}$ isa high-pass filtera low-pass filteran all-pass filtera band-reject filter

Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is$3-4j$$\frac{3}{25}+\frac{4}{25}j$$\frac{3}{25}-...

A mass-spring-damper system with force as input and displacement of the mass as output has a transfer function $G(s)=1/(s^2+24s+900)$. A force input $F(t)=10\sin(70t)$ ne...