Questions tagged [stationary]
The stationary tag has no usage guidance.
78
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Weiner Filter - why does this computation explain that the necessary filter is a weiner filter?
$X_1(t), X_2(t)$ are random WSS processes with expectation 0, and correlation functions $R_{X_1}(\tau), R_{X_2}(\tau), R_{X_1,X_2}(\tau)$ $n(t)$ is a white noise with SPD $S_n(f) = \frac{N_0}{2}$ ...
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42
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Struggling with visualizing (drawing) a sample of a random process
I've had this question I don't really know how to answer.
let $t \ge 0$, $N_t$ is a possionian random process with parameter 1. let $-\infty < t < \infty$, $X_t$ is a random process that is ...
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70
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random signals through LTI systems, why are these two signals joint wide sense stationary?
I’m trying to solve this problem but I don’t understand an assumption the solution makes:
The question:
let $\hat{W}$ be the best linear approximation of $W_t$ out of $Y_t$, find $\text{CoV}(W_4, \...
2
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28
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Haykin - permissible region for asymptotic stationarity of 2 parameter AR process
My question is about an example in Adaptive Filter Theory, Haykin 4th ed (refer figures 1.8 and 1.10 of Haykin). We want to determine the region for asymptotic stationarity of an AR process in the 2D ...
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68
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How do I determine stationarity from a set of 50 complex values collected every 10 minutes?
I am trying to determine stationarity from a somewhat stochastic process. Every 10 minutes, I collect a set of 50 FFTs, i.e., 1 trial over $50$ seconds, so an FFT occurs every time second. I ...
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2
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0
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64
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Estimation of time-varying velocity
Objective:
Estimate the mechanical tension of a cable using the velocity of the waves travelling along it.
Experimental setup:
I have a cable in tension equipped with accelerometers. I measure a ...
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3
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1
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114
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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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104
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Why is a random process strictly stationary when its joint Probability density function is time invariant?
I don't understand what stationarity of random process mean.
I know they're statistical properties that are time invariant but I don't have intuition for it and I don't get what that has to do with ...
2
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0
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15
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Condition for these sequences to be stationary correlated (tipp for integration of exponential functions)
I have two sequences $s$ and $r$ defined as :
$s = \{s_n\}_{n \in \mathbb{Z}}$ where $s_n(t) = (M_{\beta}^n s)(t) = s(t) e^{int}$ with arbitrary $s \in L^2(\mathbb{R})$ and $\beta > 0$
$r = \{r_n\}...
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105
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Limiting value of autocorrelation of wide-sense stationary process
Let random process $X$ is wide-sense stationary process. Where could I find the source or verification of the statement that, when the limiting value of autocorrelation $\lim_{\tau\rightarrow\infty}...
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68
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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 $T$ ...
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79
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Why is Power spectral density of random walk noise defined despite it being non-stationary? [duplicate]
While reading up on oscillator stability, I noticed that authors characterize random walk noise (Brownian noise) as having a PSD of $S_y(f) = h_{-2} f^{-2} $ where $h_{-2}$ is some constant. This is ...
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468
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How to filter out noise from non-stationary signal
I have this non-stationary signal.
the mean is roughly constant but the second moment (autocorrelation) does not depend only on the time lag $tau$.
Correct me if I am wrong in the above statement.
...
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81
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When is the Correlation Coefficient Ergodic
Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \...
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3
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406
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How to find the output mean and autocorrelation of a non-linear system
I need help with this question. I am sure this is the right StackExchange forum for this type of question.
Consider a nonlinear device such that the output is $Y(t) = aX^2(t)$, where the input X(t) ...
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2
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375
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Wiener filtering/deconvolution for non-stationary noise
Consider a stationary discrete-time random process $x[k]$ which undergoes low pass filtering by a filter with impulse response $h[k]$ and is subject to additive, temporally uncorrelated noise $n[k]$ ...
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2
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85
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Intuitive definition of ergodicity for random signal
Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?
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2
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995
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Understanding kurtogram parameters
I am about to understand a kurtogram, and don't understand what means the value of "K" (presented in table 1),or especially why takes values of 1.6 ; 2.6 ; 3.6 etc.
Other question is how do ...
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78
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Relationship between wide sense cyclostationary process and jointly wide sense stationary processes
https://faculty.engineering.ucdavis.edu/gardner/wp-content/uploads/sites/146/2014/05/Cyclostationarity_Half_a_century_of_research.pdf
According to the paper above (page 654~655), a CT wide sense ...
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4
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212
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Conceptual Questions on Colored Noise Process
I am having a tough time finding answers to some specific questions and finding references where there is information regarding Brownian noise or Red Noise. I'm referring to white and colored noises ...
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3
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269
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Separating/recovering base signal from two mixed signals, given phase information
I have collected two signals, $B_1(x)$ and $B_2(x)$. The signals start and end at the same $x$-values. Each signal $B_i(x)$ contains:
a base signal $b(x)$, which is the same for both, and
a signal, ...
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85
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ARMA Filter Output Stationary and set up?
I have questions regarding ARMA Filters.
Is the output of a ARMA Filter stationary or just wide sense stationary?
I do know that you can obtain an ARMA filter by connecting an MA filter with an AR ...
0
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1
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100
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Stationarity, discrete-translation operator, and the power spectral density matrix
Let $\mathbf{T}$ be the translation operator/matrix in discrete-time domain which can be written as $\mathbf{T} = \mathbf{\Phi} \mathbf{P} \mathbf{\Phi}^*$ where $\mathbf{P} = \exp(-i Diag([w_0, w_1, \...
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169
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Downsampling, shifting, high pass and low pass filter commutativity
strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself.
...
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29
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Proving that this process is weakly-stationary [duplicate]
Let $X(t) = Acos(2\pi f_c t)$ be a random process where $A$ is a uniform random variable within $(-1,1)$. I'm trying to prove this is a weakly(i.e. wide sense) stationary process. I need to show two ...
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268
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Cyclostationary signal intuition
Images show a discussion I picked up from a PhD thesis about a cyclostationary process and need help interpreting it.
"In the time domain the upsampling process creates a signal whose distribution of ...
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119
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Build an inverse model for a train of gaussian pulses
I have a stationary signal from a train of Gaussian pulses.
My sampling window is too wide (cannot be reduced). In the example 1 ms. So it is not possible to clearly distinguish one pulse from another....
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297
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How to create a synthetic time series where power spectral density estimation is achieves better results than a direct Fourier transform?
I am trying to create a synthetic time series where PSD estimation is necessary and useful to recover the correct spectral information of the time series. But so far I can only create a time series ...
- 296
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2
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146
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How to create a wide-sense stationary time series with a frequency of 40 Hz?
I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
- 296
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38
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question related to something in karlin and taylor stochastic processes one text
This question is essentially a question about something in Karlin and Taylor's Stochastic Processes One text in the spectral chapter. Since this is a DSP list, Karlin and Taylor may not be so popular ...
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379
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System memory, causality, stability
im new into systems and im supposed to solve if the system has memory, us causal, linear, stationery, BIBO stable...The problem is i have never had experience with this type of system where the actual ...
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Autocorrelation of a uniform random process
i am currently learning the basics of signal processing.
As you may know the definition of the autocorrelation is different if you look at a random process or for example a deterministic signal
My ...
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333
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Questions about the stability (and stationarity) of a system and state space representations
i'm pretty new to the topic and I'm trying to understand how to determine the stability of a process. I'm giving this discrete-time stochastic system:
$$
\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\
y_t = ...
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447
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Energy definition for Autocorrelation lag 0 and lag 1 for complex signals
I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix.
Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
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1k
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Any experiences for plotting a stationary wavelet transform?
I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides.
There are very nice plots for CWTs, but does anyone know a technique for producing ...
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105
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Proof of weak stationary random process autocovariance always goes to zero?
Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero.
I can intuitively understand it, however, ...
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Is a pulse of white noise still properly described as stationary?
I understand that a signal that is white noise is stationary (or more properly that the process generating it is stationary).
What if the white noise is delivered as a single pulse or a series of ...
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42
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Radio Signal Stationarity
A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise.
When working with such an RF signal, numerically transformed to a ...
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3
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2
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165
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How to find a variance of sample sequence
I have a sequence such as
$$r[n] = y[n]v[n]$$
$y[n]$ and $v[n]$ are zero-mean and statistically independent.
I need to find a variance of $r[n]$ and show that it is white and equal to $\sigma ^2_y\...
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226
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Converting a non-stationary random process into a WSS process by adding a random phase
Here is an example where this method has been implemented.
We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse)
The auto correlation function of the pulse ...
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2
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48
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Decimator effect on wide sense stationary input
I've seen that the output of a decimator when a WSS process is passed through remains WSS. I am not able to immediately see why this is. What is a good explanation of why the signal maintains ...
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212
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Fourier-Analysis of Stationary Random Signals
Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated.
For such a signal, how can we determine ...
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291
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Conversion from stationarity to non-stationarity
Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
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338
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Why doesn't law of large numbers apply to this stationary time-series?
There's a paragraph in Wikipedia that states the following:
Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by
$$X_{t}=Y\qquad {\text{ for all }}t$$
Then $\{X_t\}$ is a ...
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414
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Why does it mean that the process/signal is not stationary when its variance varied with time? [closed]
Why does it mean that the process/signal is not stationary when its variance varied with time? that is,
$VAR[X(t)]= \alpha \times t$,$t$ is time,and $\alpha$ is a constant,then $X(t)$ is not the WSS ...
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1
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211
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Identifying whether or not a cyclostationary signal is noisy or not using the cyclic autocorrelation
I am trying to determine whether or not a given signal has been corrupted by Gaussian noise, either bandlimited (with a filter) or not. The signal in question is a BPSK or PAM signal that is upsampled ...
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1
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2k
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Autocorrelation of Addition of Two Independent Signals
Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $:
$$ Z (t) = aX(t) + ...
- 197
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63
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A wide sense stationary random process that is not second order stationary [duplicate]
I have been reading Peebles Probability, Random Variables, and Random Signal Principles and it claims that second-order stationarity is sufficient to guarantee:
$E[X(t)]$ is a constant
$R_{XX}(t1,t2) ...
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363
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Doubt about wide sense stationary random process
I have white Gaussian noise $F[n]$ with zero mean and autocorrelation $R_F[n_1,n_2]=\delta[n_1-n_2]$.
If now I consider the random process defined as
$$X[n]=u[n]e^{-kn}F[n]$$ Is $X[n]$ a wide-ense ...
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2
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1k
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What is the difference between Kalman filter algorithm and stationary Kalman filter algorithm?
I want to compute the stationary Kalman filter algorithm but I haven't found any information about that algorithm ( not even the pseudo code ) so, I wonder what is the difference between the Kalman ...
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