# Questions tagged [stationary]

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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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### 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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### 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) ...
375 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 $n[k]$ ...
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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?
1 vote
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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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### 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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### 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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### 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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### 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 ...
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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 $\mathbf{P} = \exp(-i Diag([w_0, w_1, \... 4 votes 1 answer 169 views ### Downsampling, shifting, high pass and low pass filter commutativity strong textI have been reading "The Stationary Wavelet Transform and some Statistical Applications" by Nason and Silverman, and there is a claim in the their paper of which I cannot convince myself. ... 0 votes 0 answers 29 views ### Proving that this process is weakly-stationary [duplicate] Let$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 1 answer 268 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 ... 1 vote 1 answer 119 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 0 answers 297 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 2 answers 146 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 1 answer 38 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 1 answer 379 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 1 answer 3k 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 ... 0 votes 2 answers 333 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: $$\cases{ s_t = 2s_{t-2} + 3w_{t-2} \\ y_t = ... 1 vote 1 answer 447 views ### Energy definition for Autocorrelation lag 0 and lag 1 for complex signals I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix. Consider a complex input signal x(k)=[x1,x2]^T and x(k-1)=[x0,... 2 votes 1 answer 1k views ### Any experiences for plotting a stationary wavelet transform? I am experimenting with wavelets for my thesis and am currently working with the stationary WT pywavelets provides. There are very nice plots for CWTs, but does anyone know a technique for producing ... 0 votes 0 answers 105 views ### Proof of weak stationary random process autocovariance always goes to zero? Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero. I can intuitively understand it, however, ... 1 vote 1 answer 62 views ### Is a pulse of white noise still properly described as stationary? I understand that a signal that is white noise is stationary (or more properly that the process generating it is stationary). What if the white noise is delivered as a single pulse or a series of ... 0 votes 1 answer 42 views ### Radio Signal Stationarity A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise. When working with such an RF signal, numerically transformed to a ... 3 votes 2 answers 165 views ### How to find a variance of sample sequence I have a sequence such as$$r[n] = y[n]v[n]$$y[n] and v[n] are zero-mean and statistically independent. I need to find a variance of r[n] and show that it is white and equal to \sigma ^2_y\... 0 votes 1 answer 226 views ### Converting a non-stationary random process into a WSS process by adding a random phase Here is an example where this method has been implemented. We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse) The auto correlation function of the pulse ... 1 vote 2 answers 48 views ### Decimator effect on wide sense stationary input I've seen that the output of a decimator when a WSS process is passed through remains WSS. I am not able to immediately see why this is. What is a good explanation of why the signal maintains ... 1 vote 2 answers 212 views ### Fourier-Analysis of Stationary Random Signals Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated. For such a signal, how can we determine ... 2 votes 1 answer 291 views ### Conversion from stationarity to non-stationarity Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one? 1 vote 1 answer 338 views ### Why doesn't law of large numbers apply to this stationary time-series? There's a paragraph in Wikipedia that states the following: Let Y be any scalar random variable, and define a time-series \{X_t\}, by$$X_{t}=Y\qquad {\text{ for all }}t$$Then \{X_t\} is a ... 0 votes 1 answer 414 views ### Why does it mean that the process/signal is not stationary when its variance varied with time? [closed] Why does it mean that the process/signal is not stationary when its variance varied with time? that is, VAR[X(t)]= \alpha \times t,t is time,and \alpha is a constant,then X(t) is not the WSS ... 2 votes 1 answer 211 views ### Identifying whether or not a cyclostationary signal is noisy or not using the cyclic autocorrelation I am trying to determine whether or not a given signal has been corrupted by Gaussian noise, either bandlimited (with a filter) or not. The signal in question is a BPSK or PAM signal that is upsampled ... 3 votes 1 answer 2k views ### Autocorrelation of Addition of Two Independent Signals Given a random signal Z \left( t \right) which is addition of two independent signals X \left( t \right) and Y \left( t \right) with constant parameters a and b :$$ Z (t) = aX(t) + ... 1 vote 0 answers 63 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) ...
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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 ...