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# Questions tagged [independence]

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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 ...
1 vote
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 ...
• 175
78 views

Given is this Wiener filter: From this we take $$x[k]-a x[k-1]=v[k]$$ $v(k)$ is assumed to be a white gaussian noise. In the textbook it is then stated that The ...
• 328
84 views

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

Sampling the signalN 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) – ...
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 ...
1 vote
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 ...
• 161
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 ...
• 171
1 vote
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 ...
• 321
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 ...
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 ...
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?
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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 ...
• 311
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 ...
• 311