Recent questions in Continuous-time Signals

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 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...

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...

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...

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 function $x(t)$ is $\mathrm{X}(f)$. The Fourier transform of $\frac{d \mathrm{X}(f)}{d f}$ will be$\frac{dX(f)}{d f}$$j 2 \pi f X(f)$$jf X(f)$$...

Flat top sampling of low pass signalsgives rise to aperture effectimplies oversamplingleads to aliasingintroduces delay distortion

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