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# Questions tagged [stationary]

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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) ...
184 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 $n[k]$ ...
67 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 vote
379 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 ...
49 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 ...
121 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 ...
178 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, ...
68 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 ...
81 views

1 vote
320 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
1k 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 ...
3k 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?
422 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, ...
448 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. ...
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 ...
276 views

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 $R_{WW}[n_{... 6 votes 2 answers 953 views ### Why is$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 ...
46 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, ...
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 (...