Related Questions9 Items
Q1.MCQ
Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $-\omegac, \omegac$, where $\omegac$ is in rad/sec.
The signal $f(t)$ is uniformly sampled to obtain $y(t) = f(t) p(t)$. Here,
$$p(t) = \sum{n=-\infty}^{\infty} \delta(t - \tau - nTs),$$
with $\delta(t)$ being the Dirac impulse, $Ts > 0$, and $\tau > 0$. The sampled signal $y(t)$ is passed through an ideal lowpass filter $h(t) = \omegac Ts \frac{\sin(\omegac t)}{\pi \omegac t}$ with cutoff frequency $\omegac$ and passband gain $Ts$.
The output of the filter is given by .
Q2.MCQ
Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega) = \int{-\infty}^{\infty} f(t) \exp(-j \omega t) dt$ exists.
Which one of the following statements is always TRUE?
Q3.M-MCQ
Let $f(t)$ be a periodic signal with fundamental period $T0 > 0$. Consider the signal $y(t) = f(\alpha t)$, where $\alpha > 1$.
The Fourier series expansions of $f(t)$ and $y(t)$ are given by
$f(t) = \sum{k=-\infty}^{\infty} ck e^{j\frac{2\pi}{T0}kt}$ and $y(t) = \sum{k=-\infty}^{\infty} dk e^{j\frac{2\pi}{T0}\alpha kt}$.
Which of the following statements is/are TRUE?
Q4.M-MCQ
Let $xn$ be a discrete-time signal whose $z$-transform is $X(z)$.
Which of the following statements is/are TRUE?
Q5.MCQ
Consider the discrete-time system below with input $xn$ and output $yn$. In the figure, $h1n$ and $h2n$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\deltan$ is the unit impulse, and $b > 0$.
Assuming $h2n \neq \deltan$, the overall system (denoted by the dashed box) is .
!image(https://uadmin.udsfgecw.tech/file/download/public/public:47518a26-f6fc-4740-afb8-90966f192c78.jpg)
Q6.M-MCQ
The radian frequency value(s) for which the discrete time sinusoidal signal $xn = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are .
Q7.NUMERICAL
The relationship between any $N$-length sequence $xn$ and its corresponding $N$-point discrete Fourier transform $Xk$ is defined as
$$Xk = \mathcal{F}\{xn\}$$
Another sequence $yn$ is formed as below
$$yn = \mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{xn\}\}\}\}$$
For the sequence $xn = \{1, 2, 1, 3\}$, the value of $Y0$ is .
Q8.MCQ
A causal and stable LTI system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5t)$ is applied to another causal and stable LTI system with impulse response $h(0.5t)$. The resulting output is .
Q9.M-MCQ
For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2+3}{(z+\frac{1}{3})(z-\frac{1}{3})}$, which of the following statements is/are true?
Electronics EngineeringSignals and SystemsMultiple Choice (MCQ)2 Marks
Q1.
Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [−ωc,ωc], where ωc is in rad/sec.
The signal f(t) is uniformly sampled to obtain y(t)=f(t)p(t). Here, p(t)=∑n=−∞∞δ(t−τ−nTs), with δ(t) being the Dirac impulse, Ts>0, and τ>0. The sampled signal y(t) is passed through an ideal lowpass filter h(t)=ωcTsπωctsin(ωct) with cutoff frequency ωc and passband gain Ts.
The output of the filter is given by __________.
A
f(t) if Ts<π/ωc
B
f(t−τ) if Ts<π/ωc
C
f(t−τ) if Ts<2π/ωc
D
Tsf(t) if Ts<2π/ωc