Recent questions in Random Processes

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...

​​​​A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$....

Let $X(t)=A \cos \left(2 \pi f_{0} t+\theta\right)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distribut...

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...

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,...

Define $\operatorname{sign}(x)=0$ for $x=0, \operatorname{sign}(x)=1$ for $x>0$ and $\operatorname{sign}(x)=-1$ for $x<0$. For $n \geq 0$, let\[Y_{n}=\operatorname{sign}\...

The power spectral density of a deterministic signal is given by $\left[\sin (f) / f^{2}\right]$ where $f$ is frequency. The autocorrelation function of this signal in th...

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) & ...

The PSD and the power of a signal $g(t)$ are, respectively, $\mathrm{S}_{\text{g}}(\omega)$ and $\text{P}_{\text{g}}$. The PSD and the power of the signal $a \text{g}(t)$...

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

Noise with uniform power spectral density of $\text{N}_{0}$ $\mathrm{W / Hz}$ is passed through a filter $\mathrm{H}(\omega)=2$ exp $\left(-j \omega t_{d}\right)$ followe...

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$...

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