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Questions tagged [independence]

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0
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1answer
37 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 ...
1
vote
1answer
26 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 ...
5
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2answers
141 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 ...
1
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0answers
46 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 ...
5
votes
1answer
325 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 ...
3
votes
1answer
720 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 ...
0
votes
1answer
67 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?
5
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1answer
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 ...
14
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4answers
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 ...
19
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2answers
5k 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,...