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Questions tagged [independence]

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2 votes
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Scatter plot of two signals - Shows independence?

If we have 2 signals, and we want to show that they are independent, I came across a reference where the scatter plot for both was shown, and from the scatter plot, it was written that the signals are ...
Radhika A. Mathuria's user avatar
1 vote
4 answers
282 views

What is definition of independent random variable

I wan't to ask that if E{X}=0 E{Y}=0 and E{XY}=0 then how can I verify if the two random variables are independent or not. X , Y are both continuous random variables {I am not able to recall ...
Buzz bee's user avatar
  • 175
4 votes
2 answers
78 views

Intuition about independent signals

Given is this Wiener filter: From this we take \begin{equation} x[k]-a x[k-1]=v[k] \end{equation} $v(k)$ is assumed to be a white gaussian noise. In the textbook it is then stated that The ...
Mr.Sh4nnon's user avatar
0 votes
1 answer
84 views

SNR contains $\log N$ term where $N$ stands for number of samples

Sampling the signal$ $N times increases the signal energy by a factor of $N^2$ and the noise energy by a factor of $N$. Why? This explanation is written for SNR(dB) = signal peak(dB) – ...
Harshit's user avatar
0 votes
1 answer
152 views

Why does White Noise in images imply noise in adjacent pixels are independent?

My professor said in the class that for "Additive White noise, the noise in pixels adjacent to each other are independent". How? This is what I have got so far: White noise implies that PSD (Power ...
Nagabhushan S N's user avatar
1 vote
1 answer
126 views

DFT as an Orthogonal Basis Change

In one of the homeworks that I am dealing with for Linear Systems course, I have encountered with such a statement: Consider $\mathbb{C}^N$ the vector space of N dimensional complex vectors. We can ...
Canberk's user avatar
  • 161
7 votes
2 answers
213 views

Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$

Let us have a random vector $\mathbf{x} \sim \mathcal{CN} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$ with $\boldsymbol{\mu} \neq \mathbf{0}$. What can we say about the relationship between the elements ...
TheDon's user avatar
  • 171
1 vote
0 answers
62 views

The effect of the mixed signals probability distribution on the ICA performance

Does the mixed signals distribution affect the ICA performance? I mean the ability of ICA to get the sources. Assume that the mixed signals follows a Gaussian distribution and of course the sources ...
hbak's user avatar
  • 321
5 votes
1 answer
713 views

Finding dependence between two sparse signals

I am new to signal processing and would really appreciate your help. happy to provide more context/details. In my research, I have a system that has many sensors $X_1, \ldots, X_N$ and using this ...
newmathwhodis's user avatar
3 votes
1 answer
985 views

If MFCC vectors are speaker independent, then how can we reconstruct unique speech signals from them?

Reconstructing a speech signal from a collection of MFCC vectors seems to work pretty well, but I've heard that one advantage of MFCCs is speaker-independence i.e. they are more-or-less the same ...
orangebanana3's user avatar
0 votes
1 answer
73 views

Difference between 'spatially' and 'instantaneously' independent

For a multivariate time series $$\underline{y}(t)=[y_1(t) \dots y_n(t)]^T$$ What is the difference between the components $y_i(t)$ being spatially independent and instantaneously independent?
rwolst's user avatar
  • 351
6 votes
1 answer
5k views

How can I calculate the Expectation for a particular known vector?

Let us say I have a row vector $X = [x_1, x_2, x_3, \ldots, x_n]$ and another row vector $Y = [y_1, y_2, y_3, \ldots, y_n]$. I want to check whether the two vectors are statistically independent or ...
Rachel's user avatar
  • 311
15 votes
4 answers
5k views

ICA - Statistical Independence & Eigenvalues of Covariance Matrix

I am currently creating different signals using Matlab, mixing them by multiplying them by a mixing matrix A, and then trying to get back the original signals using FastICA. So far, the recovered ...
Rachel's user avatar
  • 311
22 votes
2 answers
6k views

Examples of Independent and uncorrelated data in real-life, and ways to measure/detect them

We always hear about this vector of data VS this other vector of data being independent from each other, or uncorrelated, etc, and while it is easy to come across the math regarding those two concepts,...
Spacey's user avatar
  • 9,837