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-1
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0answers
17 views

uniformly distributed random signal

i need to generate an uniformly distributed random signal.... i was seeing in the internet that "The uniform distribution (also called the rectangular distribution) " and " A uniform distribution has ...
-1
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2answers
59 views

The Standard Deviation of The Derivative of a Signal

Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz. What would be the Standard Deviation of its 1st, 2nd and 'n' derivative? For instance, let's say we measure the ...
2
votes
1answer
90 views

Difficulty in understanding ergodicity and ensemble averaging

Literature says that a stationary signal is ergodic, if its ensemble average = time averages. Should it be the statistics computed by time averaging = statistics computed by ensemble averaging?The way ...
1
vote
1answer
113 views

Digital Gaussian White noise signal generation in C++

I am trying to generate a band limited noise signal on a Raspberry Pi. I calculate samples at every 1/48000 sec on the Pi. If I generate normally distributed random numbers as data points at every ...
1
vote
1answer
75 views

Autocorrelation of the product of deterministic and random signal

I was wondering how to calculate the autocorrelation of a deterministic signal $x(t)$ multiplied by a stochastic process $M(t)$, whose autocorellation $R_M(\tau)$ is known a priori. In my case, $x(t)$ ...
0
votes
2answers
115 views

number of possible component in sinusoidal model

Suppose that we have the following model $y(t) = A_1\sin(\omega_1 t+\phi_1) + A_2\sin(\omega_2 t+\phi_2) + ... + A_p\sin(\omega_p t+\phi_p) + z(t)$ My question is not related to how to determine the ...
1
vote
1answer
33 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
560 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
votes
0answers
77 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] + ...
0
votes
1answer
106 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
944 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 ...
5
votes
0answers
101 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
738 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
votes
2answers
102 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
120 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
vote
0answers
74 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
83 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
344 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 $x(T)$ ...
9
votes
3answers
487 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
314 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
9k 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
votes
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?