Questions tagged [stochastic]

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PDF of a Shifted Rectangular Pulse

I wanted to determine the PDF of a Stochastic Process. I am familiar with the concept of PDF for a Random Variable which maps the outcomes to its probabilities but I am not able to find the PDF of a ...
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I am reading through the PAM transmission scheme and about the power spectral density of the signals. Given that the Average Power Spectral Density of PAM Signals is: $$\Phi_{ss}(f)=\Phi_{aa}\left(e^... 1answer 1k views Autocorrelation and Power Spectral Density (Discrete) The Autocorrelation, \phi_{aa}[\kappa], of a discrete time random process, a[k], is defined as:$$ \phi_{aa}[\kappa] = \mathrm{E}\left\{ a[k+\kappa]a^*[k] \right\} $$Taking its fourier ... 2answers 78 views Stochastic approximation algorithm The goal is to find the FIR filter coefficients \mathbf{h} = [5;3] with the help of the adaptive FIR filter \mathbf{w} of order p = 2. I have implemented the Stochastic approximation algorithm ... 2answers 1k views Understanding the definition of mean/autocorrelation I was studying about the definitions of mean, expected value and autocorrelation. I wanted to verify my understanding the evaluation of mean, expected value and autocorrelation. At the same time to ... 1answer 191 views Understanding of Random Process/Random Variable At a simpler level to my previous question, I wanted to confirm my understanding on Random Process based on Random Variables using an example. So, I took this example: If we consider a dice, which ... 1answer 3k views Understanding of Random Process, Random Variable and Probability Density Function I just wanted to confirm my understanding of a Random Process, Random Variable and the its Probability density Function. Here is the way that I looked a Random Process/Random Variable: If we ... 3answers 306 views What really means stochastic in field of signal processing I met two definitions of word stochastic, the first one (cited from wikipedia Stochastic) The word stochastic is an adjective in English that describes something that was randomly determined The ... 1answer 227 views LTI filtering for wide-sense stationary process Why is it that if U[n] is wide-sense stationary and it is convolved with h[n] to produce W[n], the autocorrelation becomes R_{WW}[n] = R_{UU}[n]*h[n]*h[-n]? I know that in general R_{WW}[n_{... 1answer 520 views How to treat noise (in the acceleration) in a Kalman filter when tracking position? I have an equation of motion for which I am wanting to track the position. The equation looks like this:$$\ddot{x}(t) = -a\dot{x}(t) - bx(t) + F(t)$$where F(t) is an external Stochastic force ... 2answers 620 views Why is A\cos(2\pi f_ct) a non-stationary process? I am studying analog communication and having Communication system - Simon Hykin as one of the reference. There is a question Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ... 2answers 2k views What's the meaning of ergodicity? [duplicate] I just read the topic about Ergodicity but I have ambiguity about its meaning (by intuition). What does mean: (for mean) Statistical average = Time average. Could you please explain it in detail. ... 1answer 157 views Analyzing fluctuations within the Signal I am trying to figure out how to analyze the signal shown below. It shows the fluctuation of number of review in for a product in Amazon, where positive means addition number of review while negative ... 2answers 504 views What does the frequency axis of a Power Spectral Density mean? I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ... 1answer 78 views Is there any computational method to prove whether a series is stationary or not? I have a discrete series x[n]. It is extracted from real life and I do not have probability distribution of each value x[n]. Is there any computational method to prove whether the series is ... 1answer 182 views Output of lowpass filter with damped sine wave input The random process$$Y(t)=\cos(\omega_0t)\cos(\omega_0t+\pi N(t))$$where N(t) is a Poisson process of parameter \lambda enters a lowpass filter with transfer function$$H(j\omega) = \left\{ \...
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Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Īf$, with PSD equal to some quantity $A$ which you would like to measure. So the way to ...
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generating white gaussian noise in matlab using two different functions

I want to know the difference between the two Gaussian noises generated below? Which one is white and how can i make the other one white? y=wgn(1,10000,0) and <...
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Ergodicity of joint process

If we have two processes and both of them are ergodic. Does this mean that the joint proces is ergodic? Or other way around? If we have the dynamics for both components of the joint process what are ...