Questions tagged [stochastic]
A "stochastic process" is another term for "random process".
113 questions
2 votes
1 answer
85 views
Is there a definition of local/windowed coherence?
I'm looking for resources discussing the differences between two interpretations -- "global" (classic) and "local" (like a weighted phase locking value) of a Welch estimate of ...
- 313
0 votes
1 answer
73 views
Trying to numerically obtain Welch Power Spectral Density for a noisy driven damped harmonic oscillator
I am trying to obtain the power spectral density using Welch of the system governed by the equation: $$\frac{d^2x}{dt^2}+b\frac{dx}{dt}+\omega_0^2x=f_0\sin(\omega t)+\zeta(t)$$ where $f_0$ is a ...
0 votes
1 answer
68 views
Discrepancy of Average Power Calculation (Freq vs Time Domain)
I'm working on the below problem Given a WSS random process $X(n) = K \cos(2\pi n + \Theta)$, where $K$ is a constant and $\Theta$ is a random variable with a uniform distribution between $0$ and $2\...
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1 vote
1 answer
593 views
What is the physical significance of the PSD and what is its practical benefit versus just look at the magnitude of the DFT?
I'm currently struggling to understand the physical significance of the PSD versus just calculating the DFT of a signal and looking at the amplitude. I think I'm struggling because I haven't found an ...
- 961
0 votes
1 answer
73 views
nonlinear Kalman-Bucy filter
The Kalman-Bucy filter gives the best estimates for a partially observable linear system ( here I show a simplified version for exposition) State $\theta_t $ of system: $d\theta_t = ( a_1\theta_t)dt +...
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0 votes
0 answers
61 views
How to decorrelate a stochastic process using a filter?
I was given a process $X(n)$ WSS whose autocorrelation function is given by: $$ \gamma_X(\ell) = \left( \frac{1}{2} \right)^{|\ell|} $$ I'm asked to find a filter with an amplitude response $|H(\phi)|$...
- 109
2 votes
1 answer
166 views
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 ...
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1 vote
0 answers
61 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
1 answer
103 views
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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1 vote
1 answer
77 views
Ergodicity clarification
On page 201 of https://stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf, it is mentioned that This observation suggests that the capacity result (5.89) holds for a ...
- 125
2 votes
1 answer
124 views
Signal Processing of Long Term Behavior in Stochastic Systems
I am quite new to techniques of signal processing. I have a fairly generic problem and wish to find information about topics and/or techniques that may help me address this problem. Let $x(t)$ and $y(...
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2 votes
1 answer
161 views
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 ...
- 121
1 vote
1 answer
109 views
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 ...
- 111
3 votes
1 answer
573 views
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^{-...
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1 vote
1 answer
78 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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