Questions tagged [stationary]
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67
questions
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0answers
46 views
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 ...
0
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1answer
48 views
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.
...
0
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0answers
21 views
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} \...
1
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2answers
115 views
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) ...
3
votes
2answers
98 views
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 $n[k]$ ...
0
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2answers
48 views
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?
1
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2answers
147 views
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 ...
3
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0answers
31 views
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 ...
3
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1answer
81 views
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 ...
3
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1answer
140 views
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, ...
0
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1answer
57 views
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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1answer
71 views
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, \...
4
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1answer
94 views
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.
...
0
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0answers
25 views
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 ...
0
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1answer
97 views
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 ...
0
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1answer
75 views
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....
0
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0answers
142 views
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 ...
1
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2answers
94 views
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 ...
0
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1answer
32 views
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 ...
1
vote
1answer
101 views
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 ...
3
votes
1answer
1k views
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 ...
1
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2answers
223 views
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:
$$
\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\
y_t = ...
1
vote
1answer
233 views
Energy definition for Autocorrelation lag 0 and lag 1 for complex signals
I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix.
Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
1
vote
1answer
525 views
Any experiences for plotting a stationary wavelet transform?
I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides.
There are very nice plots for CWTs, but does anyone know a technique for producing ...
0
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0answers
75 views
Proof of weak stationary random process autocovariance always goes to zero?
Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero.
I can intuitively understand it, however, ...
1
vote
1answer
41 views
Is a pulse of white noise still properly described as stationary?
I understand that a signal that is white noise is stationary (or more properly that the process generating it is stationary).
What if the white noise is delivered as a single pulse or a series of ...
0
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1answer
35 views
Radio Signal Stationarity
A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise.
When working with such an RF signal, numerically transformed to a ...
3
votes
2answers
142 views
How to find a variance of sample sequence
I have a sequence such as
$$r[n] = y[n]v[n]$$
$y[n]$ and $v[n]$ are zero-mean and statistically independent.
I need to find a variance of $r[n]$ and show that it is white and equal to $\sigma ^2_y\...
0
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1answer
150 views
Converting a non-stationary random process into a WSS process by adding a random phase
Here is an example where this method has been implemented.
We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse)
The auto correlation function of the pulse ...
1
vote
2answers
30 views
Decimator effect on wide sense stationary input
I've seen that the output of a decimator when a WSS process is passed through remains WSS. I am not able to immediately see why this is. What is a good explanation of why the signal maintains ...
1
vote
2answers
101 views
Fourier-Analysis of Stationary Random Signals
Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated.
For such a signal, how can we determine ...
1
vote
2answers
204 views
Conversion from stationarity to non-stationarity
Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
0
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1answer
218 views
Why doesn't law of large numbers apply to this stationary time-series?
There's a paragraph in Wikipedia that states the following:
Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by
$$X_{t}=Y\qquad {\text{ for all }}t$$
Then $\{X_t\}$ is a ...
0
votes
1answer
288 views
Why does it mean that the process/signal is not stationary when its variance varied with time? [closed]
Why does it mean that the process/signal is not stationary when its variance varied with time? that is,
$VAR[X(t)]= \alpha \times t$,$t$ is time,and $\alpha$ is a constant,then $X(t)$ is not the WSS ...
2
votes
1answer
135 views
Identifying whether or not a cyclostationary signal is noisy or not using the cyclic autocorrelation
I am trying to determine whether or not a given signal has been corrupted by Gaussian noise, either bandlimited (with a filter) or not. The signal in question is a BPSK or PAM signal that is upsampled ...
2
votes
1answer
954 views
Autocorrelation of Addition of Two Independent Signals
Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $:
$$ Z (t) = aX(t) + ...
1
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0answers
55 views
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) ...
1
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1answer
257 views
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 ...
1
vote
2answers
927 views
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 ...
0
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1answer
2k views
Why is doing fft on a non-stationary signal a problem?
Why is it a problem to do frequency analysis on a non-stationary signal?
what makes the frequency interpretation incorrect?
0
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1answer
405 views
Auto-covariance of the product of deterministic and wide-sense stationary signal
Anybody give me an advice how to find the auto-covariance of the product of deterministic and wide-sense stationary signal. I couldn't find how to solve this, I have looked and searched the internet, ...
-1
votes
1answer
405 views
Stationary signal: time-domain vs frequency domain
If I understand correctly, a signal is stationary if:
time domain: it's generated from the same distribution at each instant time.
frequency domain: its frequency content does not change in time.
...
2
votes
1answer
3k views
If the mean of a random process is constant, does it imply the process is first order stationary?
If a random process is first order stationary, its mean is constant. However, if a random process has a constant mean say $3$ and an autocorrelation equal to $9 + 15e^{|-\tau|}$. The process is ...
0
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1answer
238 views
LTI filtering for wide-sense stationary process
Why is it that if $U[n]$ is wide-sense stationary and it is convolved with $h[n]$ to produce $W[n]$, the autocorrelation becomes $R_{WW}[n] = R_{UU}[n]*h[n]*h[-n]$?
I know that in general $R_{WW}[n_{...
6
votes
2answers
773 views
Why is $A\cos(2\pi f_ct)$ a non-stationary process?
I am studying analog communication and having Communication system - Simon Hykin as one of the reference.
There is a question
Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ...
2
votes
0answers
45 views
Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?
e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is?
Also, ...
4
votes
1answer
3k views
Cross-correlation or cross-covariance of non-zero mean signals
Cross-correlation for uniformly sampled signals is defined as [1]
$$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$
Cross-covariance for wide-sense stationary (...
0
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1answer
43 views
Testing for changes in auto-covariance
I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no ...
2
votes
2answers
737 views
Does the inverse Fourier transform only produce stationary time signals?
I have a question regarding the inverse Fourier transform and its relevance to non-stationary signals. And by non-stationary signal, I'm talking about a signals whose frequency content varies with ...
5
votes
1answer
80 views
Is there any computational method to prove whether a series is stationary or not?
I have a discrete series $x[n]$. It is extracted from real life and I do not have probability distribution of each value $x[n]$. Is there any computational method to prove whether the series is ...
