Recent questions tagged signals-and-systems

Three functions $f_{1}(t), f_{2}(t)$ and $f_{3}(t)$, which are zero outside the interval $[0, T]$, are shown in the figure. Which of the following statements is correct?$...

The $\text{3-dB}$ bandwidth of the low-pass signal $e^{-t} u(t)$, where $u(t)$ is the unit step function, is given by$\frac{1}{2 \pi} \mathrm{Hz}$$\frac{1}{2 \pi} \sqrt{\...

A Hilbert transformer is anon-linear systemnon-causal systemtime-varying systemlow-pass system

The frequency response of a linear, time-invariant system is given by $H(f)=\dfrac{5}{1+j 10 \pi f}$. The step response of the system is$5\left(1-e^{-5 t}\right) u(t)$$5\...

A $5$-point sequence $x[n]$ is given as\[ x[-3]=1, \quad x[-2]=1, \quad x[-1]=0, \quad x[0]=5, \quad x =1 .\]Let $X\left(e^{j \omega}\right)$ denote the discrete-time Fou...

The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system?$y(t)=x...

The pole-zero plot given below corresponds to aLow pass filterHigh pass filterBand pass filterNotch filter

The signal $x(t)$ is described by$x(t)=\left\{\begin{array}{ll}1 & \text { for }-1 \leq t \leq+1 \\0 & \text { otherwise }\end{array}\right.$Two of the angular frequencie...

A discrete time linear shift-invariant system has an impulse response $h[n]$ with $h[0]=1, h =-1$, $h =2$, and zero otherwise. The system is given an input sequence $x[n]...

Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system rela...

$\{x(n)\}$ is a real-valued periodic sequence with a period N. $x(n)$ and $X(k)$ form $\mathrm{N}$-point Discrete Fourier Transform (DFT) pairs. The DFT $Y(k)$ of the seq...

Noise with double-sided power spectral density of $\mathrm{K}$ over all frequencies is passed through a $\text{RC}$ low pass filter with $3 \mathrm{~dB}$ cut-off frequenc...

The signal $\cos \omega_{c} t+0.5 \cos \omega_{m} t \sin \omega_{c} t$ is$\mathrm{FM}$ only$\mathrm{AM}$ onlyboth $\mathrm{AM}$ and $\mathrm{FM}$neither $\mathrm{AM}$ nor...

The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The output ...

The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e.$f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=...

Sketch the waveform (with properly markedaxes) at the output of a matched filter matched for a signal $S(t)$, of duration $T$, given by $$ S(t)= \begin{cases}\text { A } ...

The Fourier series of a real periodic function has onlycosine terms if it is evensine terms if it is evencosine terms if it is oddsine terms if it is oddWhich of the abov...

A function is given by $f(t)=\sin ^{2} t+\cos 2 t$. Which of the following is true?$f$ has frequency components at 0 and $1 / 2 \pi \; \mathrm{Hz}$$f$ has frequency compo...

A white noise process $X(t)$ with two-sided power spectral density $1 \times 10^{-10} \mathrm{~W} / \mathrm{Hz}$ is input to a filter whose magnitude squared response is ...

If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is

Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is$s F(s)-f(0)$$\dfrac{1}{s} F(s)$$\...

A small signal source $v_{i}(t)=A \cos 20 t+B \sin 10^{6} t$ is applied to a transistor amplifier as shown below. The transistor has $\beta=150$ and $h_{i e}=3 \; \mathrm...

Consider a system whose input $x$ and output $y$ are related by the equation\[ y(t)=\int_{-\infty}^{\infty} x(t-\tau) h(2 \tau) d \tau, \]where $h(t)$ is shown in the gra...

The trigonometric Fourier series for the waveform $f(t)$ shown below containsonly cosine terms and zero value for the $dc$ componentonly cosine terms and a positive value...

For an $\mathrm{N}$-point $\mathrm{FFT}$ algorithm with $\mathrm{N}=2^{\text {m}}$, which one of the following statements is $\text{TRUE}?$It is not possible to construct...

Consider the pulse shape $s(t)$ as shown. The impulse response $h(t)$ of the filter matched to this pulse is ​​​​​​​

The Nyquist sampling rale for the signal $s(t)=\dfrac{\sin (500 \pi t)}{\pi t} \times \dfrac{\sin (700 \pi t)}{\pi t}$ is given by$400 \mathrm{~Hz}$$600 \mathrm{~Hz}$$120...