Recent questions in Signals and Systems

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...

A signal cos(2$\pi$f${_m}$t) modulates a carrier cos(2$\pi$f${_c}$t) using the double -sideband-with-carrier (DSDWC) scheme to yield a modulated signal cos(2$\pi$f${_c}$t...

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...

A current $i(t)$ shown in the figure below is passed through a $\text{1 F}$ capacitor that had zero initial charge. The voltage across the capacitor for $t>2s$ in $volt$ ...

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 input $i(t)$ = $2\sin(3t+\pi)$ is applied to a system whose transfer function $G(s)=\frac{8}{(s+10)^2}$.The amplitude of the output of the system 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 ____________.

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}-...

The $z-$transform of $x[n]=\alpha ^{|n|}, 0<|\alpha|<1,$ is $X(z).$ The region of convergence of $X(z)$ is$|\alpha|<|z|<\frac{1}{|\alpha|}$$|z|>\alpha$$|z|>\frac{1}{|\alp...

The signal $x[n]=\sin(\pi n/6)/(\pi n)$ is processed through a linear filter with the impulse response $h[n]=\sin(\omega_cn)/(\pi n)$ where $\omega_c>\pi/6$. The output o...

A signal is band-limited to $\text{0 to 12 kHz}$. The signal spectrum is corrupted by additive noise which is band-limited to $\text{10 to 12 kHz}$. Theoretically, the mi...

Given $x(t)=3\sin (1000\; \pi t)\; and\;y(t)=5\cos (1000\;\pi t+\frac{\pi}{4})$The $x-y$ plot will bea circlea multi-loop closed curvea hyperbolaan ellipse

Time domain expressions for the voltage $v_1(t)$ and $v_2(t)$ are given as$$v_1(t)=V_m\sin(10t-130^\circ)\; and\; v_2(t)=V_m\cos(10t+10^\circ)$$Which one of the following...

The system function of an LTI system is given by$$H(Z)=\frac{1-\frac{1}{3}Z^{-1}}{1-\frac{1}{4}Z^{-1}}$$The above system can have stable inverse if the region of converge...

The impulse response of an LTI system is given as:$h[n]=\left\{ \begin{array}{rcl} \frac{\omega_c}{\pi} & n=0\\ \frac{\sin \omega_cn}{\pi n} & n\neq 0 \end{array}\right.$...

A discrete-time signal $x[n]$ is obtained by sampling an analog signal at $10\;kHz$. The signal $x[n]$ is filtered by a system with impulse response $h[n]=0.5${$ \delta [...

In order to remove respiration related motion artifacts from an $ECG$ signal, the following filter should be used:low-pass filter with $f_c=0.5\;Hz$high-pass filter with ...

The transfer function of a digital system is given by:$$\frac{b_0}{1-z^{-1}+a_2z^{-2}},\text{ where $a_2$ is real.}$$The transfer function in $BIBO$ stable if the value o...

A signal $V_i(t)=10+10\sin 100\pi t+10\sin 4000 \pi t+10\sin 100000\pi t$ is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated fre...

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$

The impulse response of a system is $h(t)=t\;u(t)$. 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^2-1}{...

A band-limited signal with a maximum frequency of $5\;kHz$ is to be sampled. According to the sampling theorem, the sampling frequency in $kHz$ which is not valid is$5$$1...

The discrete-time transfer function $\frac{1-2 Z^{-1}}{1-0.5Z^{-1}}$ isnon-minimum phase and unstableminimum phase and unstableminimum phase and stablenon-minimum phase a...