Questions tagged [stationary]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
45 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 ...
2
votes
1answer
106 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
votes
1answer
39 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
votes
1answer
57 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
votes
1answer
71 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
votes
0answers
23 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
votes
1answer
51 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
votes
1answer
42 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
votes
0answers
38 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
vote
1answer
46 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
votes
1answer
26 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
56 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 ...
2
votes
1answer
593 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
vote
1answer
90 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
152 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
275 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
votes
0answers
61 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
36 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
votes
1answer
34 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
139 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
votes
1answer
115 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
26 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
73 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
155 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
votes
1answer
163 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
166 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
116 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
583 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
vote
0answers
52 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
vote
1answer
183 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
740 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
votes
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
votes
1answer
326 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
356 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. ...
1
vote
1answer
1k 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
votes
1answer
218 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_{...
5
votes
2answers
528 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
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
votes
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
votes
1answer
39 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
641 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
77 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
votes
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
142 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, ...
21
votes
2answers
23k 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 ...
3
votes
2answers
95 views

How to show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$

I am trying to solve the following exercise: Show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ (i.e. $x_n = w_1 x_{n-1} + w_2 x_{n-2}$). ...
3
votes
1answer
181 views

Is $A\cos(\omega t+\theta)$ a Gaussian random process?

$Z(t) = A\cos(\omega t+\theta)$ where $A$~$\mathcal N(0,\sigma ^2) $ and $\theta $~$\mathcal U(0,2\pi)$ are independent. I'm trying to figure out if $Z(t)$ is a Gaussian random process and whether it ...
1
vote
1answer
476 views

How to calculate the noise power for a non-stationary noise?

With stationary noise we have constant mean and variance (let's assume it is Gaussian noise). My first question is, how is the noise power calculated and how it is related to the variance? Now, I ...
0
votes
1answer
565 views

separating stationary and non stationary parts of univariate signal

Does anyone know if there is a procedure as to separate the stationary and non stationary parts of a univariate signal. I have seen signal source separation and blind separation algorithms (all of ...
2
votes
1answer
230 views

Is jointly wss (wide sense stationary) a transitive relation?

I've been try to either prove or find a counter-example to the idea of jointly-wss being transitive. In other words: does ($x$ and $y$ are jointly wss) $\wedge$ ($y$ and $z$ are jointly wss) imply ...