Questions tagged [independence]
14 questions
22
votes
2 answers
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, I want to tie them into examples from…
Spacey
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14
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4 answers
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 signals are really bad when compared to the original…
Rachel
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7
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2 answers
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 of $\mathbf{x}$ in the following two separate…
TheDon
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6
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1 answer
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 not.
Now two vectors are said to be statistically…
Rachel
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5
votes
1 answer
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 information, the system makes a prediction on a…
dval
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4
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2 answers
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 input $v[k]$ at time $k$ and the output $x[k − 1]$ at…
Mr.Sh4nnon
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3
votes
1 answer
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 across different speakers for a given phoneme. How…
acannon828
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2
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0 answers
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 independent. I am unable to understand what a…
Radhika A. Mathuria
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1
vote
1 answer
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 define a basis
$F=\{f_1,\ldots,f_N\}$…
Canberk
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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 do not follow Gaussian distributions. Then, this…
hbak
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0
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1 answer
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
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0
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4 answers
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 the exact equations for X , Y but I am sure about the…
Buzz bee
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0
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1 answer
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) – noise floor(dB)- $10\log N$
Harshit
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0
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1 answer
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 Spectral Density) is flat which implies Covariance…
Nagabhushan S N
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