Questions tagged [stationary]
The stationary tag has no usage guidance.
64
questions
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2answers
104 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) ...
1
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2answers
55 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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1answer
32 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
97 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
29 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 ...
2
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1answer
62 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
124 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
47 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
68 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
89 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.
...
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0answers
24 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
79 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
47 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
103 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
79 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
31 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
88 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
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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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1answer
172 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:
$$
\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\
y_t = ...
1
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1answer
203 views
Energy definition for Autocorrelation lag 0 and lag 1 for complex signals
I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix.
Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
1
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1answer
428 views
Any experiences for plotting a stationary wavelet transform?
I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides.
There are very nice plots for CWTs, but does anyone know a technique for producing ...
0
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0answers
71 views
Proof of weak stationary random process autocovariance always goes to zero?
Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero.
I can intuitively understand it, however, ...
1
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1answer
39 views
Is a pulse of white noise still properly described as stationary?
I understand that a signal that is white noise is stationary (or more properly that the process generating it is stationary).
What if the white noise is delivered as a single pulse or a series of ...
0
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1answer
35 views
Radio Signal Stationarity
A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise.
When working with such an RF signal, numerically transformed to a ...
3
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2answers
142 views
How to find a variance of sample sequence
I have a sequence such as
$$r[n] = y[n]v[n]$$
$y[n]$ and $v[n]$ are zero-mean and statistically independent.
I need to find a variance of $r[n]$ and show that it is white and equal to $\sigma ^2_y\...
0
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1answer
142 views
Converting a non-stationary random process into a WSS process by adding a random phase
Here is an example where this method has been implemented.
We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse)
The auto correlation function of the pulse ...
1
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2answers
27 views
Decimator effect on wide sense stationary input
I've seen that the output of a decimator when a WSS process is passed through remains WSS. I am not able to immediately see why this is. What is a good explanation of why the signal maintains ...
1
vote
2answers
93 views
Fourier-Analysis of Stationary Random Signals
Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated.
For such a signal, how can we determine ...
1
vote
2answers
192 views
Conversion from stationarity to non-stationarity
Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
0
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1answer
201 views
Why doesn't law of large numbers apply to this stationary time-series?
There's a paragraph in Wikipedia that states the following:
Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by
$$X_{t}=Y\qquad {\text{ for all }}t$$
Then $\{X_t\}$ is a ...
0
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1answer
254 views
Why does it mean that the process/signal is not stationary when its variance varied with time? [closed]
Why does it mean that the process/signal is not stationary when its variance varied with time? that is,
$VAR[X(t)]= \alpha \times t$,$t$ is time,and $\alpha$ is a constant,then $X(t)$ is not the WSS ...
2
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1answer
132 views
Identifying whether or not a cyclostationary signal is noisy or not using the cyclic autocorrelation
I am trying to determine whether or not a given signal has been corrupted by Gaussian noise, either bandlimited (with a filter) or not. The signal in question is a BPSK or PAM signal that is upsampled ...
1
vote
1answer
725 views
Autocorrelation of Addition of Two Independent Signals
Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $:
$$ Z (t) = aX(t) +...
1
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0answers
54 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
236 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
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2answers
869 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
397 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
387 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
2k 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
234 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
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2answers
711 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
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0answers
44 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
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1answer
2k 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
42 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
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2answers
703 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
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1answer
78 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 ...
2
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2answers
1k views
Why is $\sin(t)$ a stationary process?
I am trying to understand the meaning of the term Stationary Process.
For example, I was told that $\sin(t)$ is a stationary process.
Could someone try to explain, in simple words, why is $\sin(t)$ (...
0
votes
1answer
169 views
Z-transform of difference equations and stability of a process
According to this paper:
$y(t)$ is stationary if all of the roots (of characteristic equation) lie outside the unit circle
Here, $y(t)$ is causal.
To me it seems the case is exactly the opposite, ...
22
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2answers
26k views
Stationary vs non-stationary signals?
There are nice technical definitions in textbooks and wikipedia, but I'm having a hard time understanding what differentiates stationary and non-stationary signals in practice?
Which of the following ...
