Recent questions tagged signals-and-systems

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...

The Laplace transform of a continuous-time signal $x(t)$ is $X(s)=\frac{5-s}{s^{2}-s-2}$. If the Fourier transform of this signal exists, then $x(t)$ is$e^{2 t} u(t)-2 e^...

In the figure $m(t)=\frac{2 \sin 2 \pi t}{t}, s(t)=\cos 200 \pi t$ and $n(t)$ $=\frac{\sin 199 \pi t}{t}$. The output $y(t)$ will be$\frac{\sin 2 \pi t}{t}$$\frac{\sin 2 ...

A signal $x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t$ is ideally sampled with a sampling period of $50 \; \mu \mathrm{sec}$ and then passed through an ideal lowpas...

A deterministic signal $x(t)=\cos 2 \pi t$ is passed through a differentiator as shown in the figure isDetermine the autocorrelation $R_\mathrm{xx}(T)$ and the power spec...

A continuous-time signal with finite energy, band limited from $3 \; \mathrm{MHz}$ to $5 \; \mathrm{MHz}$, is ideally sampled, encoded by a fixed length PCM coder and the...

If $f(t)=\frac{\omega}{s^2+\omega^2}$, then the value of $\lim _{t \rightarrow \infty} f(t)$cannot be determinedis zerois unityis infinite

The trigonometric Fourier series of a periodic time function can have onlycosine termssine termscosine and sine terms$d.c$. and cosine terms

A periodic signal $x(t)$ of period $T_0$ is given by$$ x(t)= \begin{cases}1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2}\end{cases} $$The $\text{d.c}$. component of $x(t)$ is...

The unit impulse response of a linear time-invariant system is the unit step function $u(t)$. For $t>0$, the response of the system to an excitation $e^{-a t} u(t), a>0$ ...

A distorted sinusoid has the amplitudes $\mathrm{A}_{1}, \mathrm{A}_{2}, \text{A}_3 \ldots \ldots$ of the fundamental, second harmonic, third harmonic, ...... respectivel...

The amplitude spectrum of a Gaussian pulse isuniforma sine functionGaussianan impulse function

The $\text{ACF}$ of a rectangular pulse of duration $\mathrm{T}$ isa rectangular pulse of duration $\mathrm{T}$a rectangular pulse of duration $\mathrm{2T}$a triangular p...

The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ isvoltvolt-secvolt/secvolt $^{2}$

Consider a rectangular pulse $g(t)$ existing between $t=-\frac{T}{2}$ and $t=-\frac{T}{2}$. Find and sketch the pulse obtained by convolving $g(t)$ with itself. The Fouri...

If the input to the ideal comparator shown in the figure is a sinusoidal signal of $8 \mathrm{~V}$ (peak to peak) without any DC component, then the output of the compara...

The Fourier series expansion of a real periodic signal with fundamental frequency $\mathrm{f}_0$ is given by $$ g_p(t)=\sum_{n=-\infty}^{\infty} c_n e^{j 2 \pi n f_\omega...

Let $x(t)$ be the input to a linear, time-invariant system. The required output is $4 x(t-2)$. The transfer function of the system should be$4 e^{j4 \pi f}$$2 e^{-j8 \pi ...

Let $\mathrm{P}$ be linearity, $\mathrm{Q}$ be time-invariance, $\mathrm{R}$ be causality and $\mathrm{S}$ be stability. A discrete-time system has the input-output relat...

Let $x(t)=2 \cos (800 \pi t)+\cos (1400 \pi t) . x(t)$ is sampled with the rectangular pulse train shown in the figure. The only spectral components(in $\mathrm{kHz}$ ) p...

The data for Q. 75-76 are given below. Solve the problems and choose the correct answers.Let $m(t)=\cos \left[\left(4 \pi \times 10^{3}\right) t\right]$ be the message si...

The Fourier transform of a conjugate symmetric function is alwaysimaginaryconjugate anti-symmetricrealconjugate symmetric

A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a$\text{DC}...

Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$The conjugate anti-symmetric part of the sequence is$[-4-j 2.5 \quad j...

Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...