Recent questions tagged random-processes

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_{b} / N_{o}=8.4 \mathrm{~dB}$ at the input of a coherent QPSK demodula...

Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_{c} t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_{M}$ and ...

A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random vari...

Consider a real-valued random process$$f(t)=\sum_{n=1}^{N} a_{n} \: p(t-n T),$$where $T>0$ and $N$ is a positive integer. Here, $p(t)=1$ for $t \in[0,0.5 T]$ and $0$ othe...

Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t...

$X$ and $Y$ are jointly Gaussian random variables with zero mean.A constant-pdf contour is where the joint density function takes on the same value. If the constant-pdf c...

Let $R_{X}(\tau)$ be the autocorrelation function of a zero mean stationary random process $X(t)$. Which of following statements is FALSE.If $R_{X}(\tau)=0, \forall \tau,...

Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$

Zero mean white Gaussian noise with a two-sided power spectral density of $4 \mathrm{~W} / \mathrm{kHz}$ is passed through an ideal lowpass filter with a cut-off frequenc...

The power spectral density $\text{(PSD)}$ of a noise process is given by$\mathrm{S}_{\mathrm{N}}(f)=\left\{\begin{array}{cc}10^{-8}\left(1+\frac{|f|-10^8}{10^8}\right) & ...

If the variance $\sigma_{x}^{2}$ of $d(n)=x(n)-x(n-1)$ is one-tenth the variance $\sigma_{x}^{2}$ of a stationary zero-mean discrete-time signal $x(n)$, then the normaliz...

A DSBSC modulated signal $s(t)=10 \cos \left(2 \pi \times 10^{b} t\right. +\phi) m\left(t^{-}\right)$is corrupted by an additive white Gaussian noise of power spectral de...

The spectral density of a real valued random process hasan even symmetryan odd symmetrya conjugate symmetryno symmetry

The probability density function of the envelope of narrow band Gaussian noise isPoissonGaussianRayleighRician

Data for Q. 65-66 are given below. Solve the problems and choose the correct answers.Let $X$ be the Gaussian random variable obtained by sampling the process at $t=t_{i}$...

Let $Y$ and $Z$ be the random variables obtained by sampling $X(t)$ at $t=2$ and $t=4$ respectively. Let $W$ $=Y-Z$. The variance of $W$ is$13.36$$9.36$$2.64$$8.00$

For a narrow band noise with Gaussian Gradrature components, the probability density function of its envelope will beuniformGaussianexponentialRayleigh

A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t...

Statement for Linked Answer Questions 78 and 79The following two questions refer to wide sense stationary stochastic processesIt is desired to generate a stochastic proce...

Statement for Linked Answer Questions 78 and 79The following two questions refer to wide sense stationary stochastic processesThe parameters of the system obtained in $\t...

If $R(\tau)$ is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is $\text{NOT}$ true?$R(\tau)=R(-\tau)$$|R(\tau)...

If $S(f)$ is the power spectral density of a real, wide-sense stationary random process, then which of the following is $\text{ALWAYS}$ true?$S(0) \geq S(f)$$S(f) \geq 0$...

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

$\text{X}(t)$ is a stationary process with the power spectral density $\text{S}_{\text{X}}(f)>0$ for all $f$. The process is passed through a system shown below.Let $\tex...

Statement for Linked Answer Questions 54 and 55:Consider a baseband binary PAM receiver shown below. The additive channel noise $n(t)$ is white with power spectral densit...

Statement for Linked Answer Questions 54 and 55:Consider a baseband binary PAM receiver shown below. The additive channel noise $n(t)$ is white with power spectral densit...

(a) A Gaussian random variable with zero mean and variance $\sigma$ is input to a limiter with input output characteristic given by$$ \begin{array}{ll} e_{\text {out }}=e...

$\mathrm{X(t)}$ is a stationary random process with autocorrelation function $R_X(\tau)=\exp \left(-\pi \tau^2\right)$. This process is passed through the system shown be...

A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the...