# Questions tagged [stochastic]

A "stochastic process" is another term for "random process".

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### Relation and differences between correlation sequence and correlation matrix

Suddenly I am stuck at a question while studying Statistical signal processing: What are the differences between correlation sequence and matrix (can be auto/cross), and how are the two related? When ...
1 vote
31 views

### Parameter value in bias instability modeling

In IMU error modeling, bias instability/flicker noise is often modeled by a first order Gauss-Markov process whose standard deviation is equal to the given BI coefficient [1, p.185][2, p.31]. Because ...
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1 vote
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### Minimum Number of Base Accelerations Needed to Simulate Gaussian White Noise in Structural Dynamics?

I am currently working on a scientific paper where I subject a structure to base accelerations modeled as Gaussian white noise. I am relatively new to signal processing and would appreciate some ...
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### Two meanings for "innovation" in Wiener filter are the same?

This is related question to A question about Wiener filter based on Linear Estimation by Kailath, based on the textbook Linear Estimation by Kailath. In that link I talk about how I first learned what ...
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1 vote
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### Probability distribution sampling from a trajectory

Disclaimer: this question was originally posted on Physics SE but with very limited replies and I am reproducing it here as a suggestion from one of the comments. Consider a sequence of random ...
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1 vote
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### Why are convolutions between those functions equivalent (signal processing for theoretical neuroscience)?

I'm reading a book on theoretical neuroscience [1], in which the following definitions are given: $\rho(t)=\sum_{i=1}^n \delta(t-t_i)$ where $\delta$ is Dirac's delta and the $t_i$ are timestamps at ...
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### Proof of the Wiener-Khintchine theorem in time domain

In a proof for the Wiener-Khintchine theorem (See p. 572-573) I have seen the following operation being done: \begin{align*} S_{xx}(f) &= \lim_{T \rightarrow \infty} \int_{-2T}^{2T} Rxx(\tau) e^{-...
1 vote
58 views

### Expectation and autocorrelation for modulated sinusoid

Given $$Y(t) = A X(t) \cos(\omega t + \phi)$$ with $X(t)$ is zero-mean WSS (wide-sense stationary) process, $\phi$ ~ Unif$(0,2\pi)$. Suppose $X(t)$ and $\phi$ are independent random variables. I ...
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### What happens if you use the Fourier transform of the autocorrelation of a non-WSS process to compute power spectral density?

The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e. ...
135 views

### If $X(t)$ is a WSS process with mean 5, what is the mean of $X(2t)$? [closed]

I know mean is constant for a WSS process but I am still confused about the mean for this process. My process was by integrating $X(2t)$ from $0$ to $T$, then substituting $t′=2t$. So the limits ...
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356 views

### Bandpass Stationary Stochastic Process

I was following this interesting post by a new user Rubem Pacelli and got stuck at Proakis' referenced definition (see Section 4-1-4 starting on page 159 here). The math, all repeated further below, ...
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### The frequency function for $Y_t-18=0.4X_t+0.9X_{t-1}+e_t$

I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white ...
104 views

### Approximate a Known System with Adaptive Filter and an Unknown System in a Series

I am using gradient descent on an adaptive IIR filter for the below system 1. At the moment I am just assuming the known system is not there and it works fine. However, occasionally when the known ...
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1 vote
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### Effect of sampling a cont. stochastic process on the variance

I am trying to understand the estimation of the power spectral density of a continuous time stochastic process from it's samples. Consider a normal wide-sense stationary white noise process with ...
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### Deterministic, stochastic and chaotic components of a signal ; their combined effect

If a signal contains deterministic, stochastic as well as chaotic components, does this generally represent a problem in the analysis of the signal? By a problem, I mean that a signal containing all ...
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### White noise does not contradicts Wide Sense Stationarity?

I am studying White Noise. But I am really beginner level, so I have a confusion with its construction. White Noise is usually defined as a Wide Sense Stationary process $N=\{N_t\}_{t\in T}$ (for $T$ ...
106 views

### Noise from irregular sampling pattern

In this paper the author says By using an irregular sampling pattern and filtering the irregular samples to create the pixels, featureless noise is produced from such high frequencies rather than ...
1 vote
182 views

### Calculating error of estimation of signal from noisy data (Explanation of result)

Given random varaible X with distribution $$\begin{cases} \mathbb{P}\left(X=1\right)=\alpha\\ \mathbb{P}\left(X=-1\right)=1-\alpha \end{cases}$$ Where $\alpha$ is a given parameter($X$ is a binary ...
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131 views

### Random Signal Energy

Why the energy of random signal(random process) is infinite? and why random signal can not be zero at infinity? I know that there is a relation between the tow questions but I'am still confused.
139 views

### How Could One Accelerate the Convergence of the Least Mean Squares (LMS) Filter?

How can the convergence of an LMS filter be accelerated? Can we do better than the Vanilla algorithm?
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1 vote
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### Find coefficients of optimal Wiener filter of length 2

I need to find the coefficients (impulse response) of a FIR Wiener filter with length equal to 2. I have a gaussian white noise signal that is generated using the Standard Normal Distribution (mean = ...
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833 views

### Sampling Noise Given Power Spectral Density

I am trying to write a Monte Carlo physics simulation which involves, given a power spectral density, sampling rate, and total number of samples, generating noise with such a power spectral density. I ...
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### Super basic questions on statistical process

Before starting: I am really a beginner in statistical process in time. I mainly do quantum information and while learning aspect of quantum noise I realized that I am actually too weak on basics of ...
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