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1answer
28 views

A special case of 2 jointly WSS stochastic processes

I know that 3 conditions must be met in order a pair of stochastic processes X(t) and Y(t) to be characterized as jointly WSS: 1. X(t) WSS 2. Y(t) WSS 3. Rxy(t1,t2) = Rxy(t1 - t2) = Rxy(t2 - t1) ...
2
votes
2answers
242 views

Sampling low pass filtered white noise

If we filter out ideal white noise using an ideal LPF of cutoff frequency 10 KHz and then sample it at 30 KHz , is the resulting discrete signal statistically independent? I would like to know the ...
0
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0answers
50 views

Variance of this random discrete sequence

If $x[n]$ is a discrete random sequence with uniform distribution having mean $\mu = 2$ and variance $\sigma^2 = 3$ if passed through a moving average filter to get an output of $(x[n] + x[n-1] + ...
1
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1answer
91 views

Why is random noise amplitude inversely proporional to the frequency?

http://astarte.csustan.edu/~tom/SFI-CSSS/info-theory/info-lec.pdf compares a bacteria DNA vs a random string: My first step was to generate for myself a "random genome" of comparable size to ...
2
votes
1answer
378 views

Why the RMS of a PSD curve is the root of the area below

I will try to explain what is my level of understanding of this problem, please correct me if I'm wrong: RMS is the Root Mean Square, it represent the mean value of the input signal. PSD is the ...
4
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0answers
93 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
3
votes
2answers
432 views

Gaussian random generator

I have quite a straight-forward question. What I aim for is the generation of a certain set of random numbers with a normal distribution (mu = 0, ...
0
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2answers
95 views

Random signal power spectrum

I have a signal $X(t)=\sum_{n=-\infty}^{\infty} Z_n \delta(t-n\tau)$, $Z_n$ is a random variable with equal possibility of +-1 and I know the power spectrum of this signal is $\frac {1}{\tau}$ from ...
6
votes
1answer
113 views

How to tell how likely a signal is present in another one? (variance unknown)

I know this is probably a simple question, but I haven't been able to find a satisfactory answer anywhere... Say you have a time series signal of finite length N. Call it $y[n]$. It is stationary, ...
1
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0answers
72 views

Gauss Markov Process

I am trying to generate a random signal that represents a gyroscope drift. I know the Allan Variance characteristics of the signal (ARW, RRW, Bias Instability and Cluster Time for for Bias ...
1
vote
1answer
79 views

Probability of random numbers

This is the question i found on internet under DSP section so thats why i am posting it here. Help me understand it please. "A computer adds 1000 random numbers that have each been rounded off to ...
3
votes
2answers
276 views

Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ ...
8
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3answers
448 views

Implementing Gaussian random variable by using a uniform random variable

I'm trying to write a C++ function that will return Gaussian random values, given their means and variances. There is a library function rand(), which returns ...
6
votes
2answers
269 views

Probability distribution of windowed cross-correlation

This question is in the context of time-delay estimation. Say I have a stationary Gaussian stochastic process $g$, and I know its autocorrelation function $R_g(\tau)$. To do time-delay estimation, I'm ...
15
votes
5answers
6k views

What is the distinction between ergodic and stationary?

I have trouble distinguishing between these two concepts. This is my understanding so far. A stationary process is a stochastic process whose statistical properties do not change with time. For a ...
11
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2answers
1k views

Pink ($1/f$) pseudo-random noise generation

What are some algorithms for generating a good pseudo-random approximation to $1/f$ (pink) noise, yet suitable for implementation with low computational cost on an integer DSP?