# Questions tagged [stochastic]

The tag has no usage guidance.

84 questions
Filter by
Sorted by
Tagged with
160 views

102 views

270 views

### Band-limited random signal with arbitrary distribution?

I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
I have an input signal x (assumed to be iid Gaussian with $\mu=0$, $\sigma^2$) which is fed into two linear systems: $y_1 = h_1 * x$ $y_2 = h_2 * x$ Now I would like to calculate $\mathbb{E}[y_1 y_2]... 0answers 28 views ### The mean value of phase noise as a stochastic process What is the mean value of phase noise as a stochastic process? Where can I get a theoretical analysis of this topic? PS: PLL produces cos(2*πfct+φ(t)). The phase noise refers to φ(t). The mean value ... 2answers 138 views ### Physical meaning of average values of random signals This question might be a bit stupid, anyway, i'll risk it, since i want to get better understanding of this subject. Let's consider random signal x(t), and let's say that we know that it is ergodic ... 1answer 405 views ### Higher-order moment of output of LTI system Assume a very simple LTI system. Assume$x$is white Gaussian i.i.d. with variance$\sigma^2$. The output variance is straightforward to obtain. For example, for a continuous-time system: $$\mbox{... 1answer 75 views ### When a stochastic process would be a beneficial model in terms of noise Let's say we have an image/signal with some noise in it. When would it be beneficial to model the signal as an outcome of a stochastic process? More specifically: How significant would noise have to ... 1answer 124 views ### Relationship between the autocorrelations of X(t) and X(nt) Defining: X(t) WSS random process with autocorrelation function R_{X}(\tau) = \mathbb{E}[X(t)X(t+\tau)]. Y[n] = X(nT) (sampling of X at a rate \frac1T) with autocorrelation function R_Y(\... 1answer 49 views ### Are there any signals with brickwall autocorrelation? Are there any signals whose autocorrelation R(\tau) has the following form? Assuming \tau_c > 0 and R_0 > 0 a constant,$$R(\tau) = \begin{cases}R_0, \text{ for$|\tau| < \tau_c$} \\ 0,... 1answer 881 views ### What is an “innovation filter”? I'm a math postgrad student working through a paper on eigenvalue decompositions of matrices of FIR filters (used for stuff like total decorrelation, convolutive mixing, MIMO). Towards the beginning, ... 2answers 14k views ### generating white gaussian noise in matlab using two different functions I want to know the difference between the two Gaussian noises generated below? Which one is white and how can i make the other one white? y=wgn(1,10000,0) and <... 0answers 32 views ### Is it safe to call this WSSUS channel a Gaussian process? BACKGROUND: Equation (3.6) of Wireless Communications by Goldsmith gives the baseband impulse response of a time-varying channel as:$$c(\tau,t) = \sum_{n=0}^{N(t)}\alpha_n(t)e^{-j\phi_n(t)}\delta(\... 1answer 78 views ### Null autocorrelation function and stationary I can show that a process$X(t)$is Wide Sense stationary (WSS) by showing that$E[X(t)]$is constant and that its autocorrelation function is in function of$\tau=t_1-t_2$, that is,$R_X(t+\tau,t)=...
The Ornstein-Uhlenbeck (OU) process $dX_t = -\frac{1}{\mu} X_t + \sqrt{\frac{2\sigma^2}{\mu}} dW_t$ generates coloured noise with autocorrelation function \$R(t) = \langle X_t,X_{t'}\rangle = \...