# Questions tagged [stationary]

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### 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 ...
1answer
75 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 ...
2answers
350 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 ...
1answer
2k views

### Cross-correlation or cross-covariance of non-zero mean signals

Cross-correlation for uniformly sampled signals is defined as  $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...
2answers
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0answers
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### 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, ...
2answers
686 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 $\sin(t)$ (...
1answer
607 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 ...
2answers
426 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 ...
2answers
22 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 ...
1answer
121 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 ...
2answers
48 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 ...
1answer
37 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 ...
2answers
108 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?
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### Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
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176 views

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### Signal Plus Weakly Stationary Noise

I was reading the book "Spectral Analysis of Time Series" By Herman Koopmans. On Page 55, he explains that a specific type of non-stationary signal which is the result of adding weakly stationary ...
0answers
46 views

### How to show that an ergodic process must be a strict-sense stationary one? [duplicate]

I have trouble to distinguish these two concepts namely ergodic process and strict-sense stationary process. I look at one of the books about the signal processing that says an ergodic process must be ...
1answer
267 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. ...