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Gaussianity of Signals

Reply #25
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Not quite the same. correlation matrix == covariance matrix only if you have a zero-mean process.
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Yeah I know, but I find the zero-mean thing as being trivial when we refer to correlation matrices as covariance matrices.  It only becomes important when we want to start calling covariance matrices as correlation matrices.
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I read that in signal estimation theory, it is very important that the input signal is of zero mean.. For example, in the case of Levinson-Durbin calculation, if the mean isn't zero, the correlation matrice would show a common DC offset in all the elements of the matrice which could cause the LD algorithm to wrongly estimate them as tones ?

In fact, the most important preprocessing step needed to be taken is to subtract the mean from the signal itself before any estimation process.

In a more general case, the term covariance matrices is more accurate.

Gaussianity of Signals

Reply #26
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I read that in signal estimation theory, it is very important that the input signal is of zero mean.. For example, in the case of Levinson-Durbin calculation, if the mean isn't zero, the correlation matrice would show a common DC offset in all the elements of the matrice which could cause the LD algorithm to wrongly estimate them as tones ?
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Well, a DC component *is* a tone, of frequency 0. The reason we remove it is that in audio, we're just never interested in it.

Gaussianity of Signals

Reply #27
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I read that in signal estimation theory, it is very important that the input signal is of zero mean.. For example, in the case of Levinson-Durbin calculation, if the mean isn't zero, the correlation matrice would show a common DC offset in all the elements of the matrice which could cause the LD algorithm to wrongly estimate them as tones ?
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Well, a DC component *is* a tone, of frequency 0. The reason we remove it is that in audio, we're just never interested in it.
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What I meant was, what will happened if the input process isn't a zero mean process? Will this cause a bias in the spectrum estimation of the process ? 

Gaussianity of Signals

Reply #28
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What I meant was, what will happened if the input process isn't a zero mean process? Will this cause a bias in the spectrum estimation of the process ? 
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Well, it's not a bias, but it is information that the ear doesn't much care about, so removing it will change the autocorrelation coef's, such that the DC component is not, for instance, coded so accurately.

But it's not a "bias" it is an accurate representation of part of the signal, just not perhaps a part that's remotely relevant?
-----
J. D. (jj) Johnston

Gaussianity of Signals

Reply #29
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What I meant was, what will happened if the input process isn't a zero mean process? Will this cause a bias in the spectrum estimation of the process ? 
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Well, it's not a bias, but it is information that the ear doesn't much care about, so removing it will change the autocorrelation coef's, such that the DC component is not, for instance, coded so accurately.

But it's not a "bias" it is an accurate representation of part of the signal, just not perhaps a part that's remotely relevant?
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I think bias will cause distortions to the low frequency components of the spectrum.
It is not as simple as just the DC component. 

Gaussianity of Signals

Reply #30
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What I meant was, what will happened if the input process isn't a zero mean process? Will this cause a bias in the spectrum estimation of the process ? 
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Well, it's not a bias, but it is information that the ear doesn't much care about, so removing it will change the autocorrelation coef's, such that the DC component is not, for instance, coded so accurately.

But it's not a "bias" it is an accurate representation of part of the signal, just not perhaps a part that's remotely relevant?
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I think bias will cause distortions to the low frequency components of the spectrum.
It is not as simple as just the DC component. 
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Of course, you always have to consider your aperture size and your window. Well, I do, I work in finite time.
-----
J. D. (jj) Johnston

 

Gaussianity of Signals

Reply #31
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What I meant was, what will happened if the input process isn't a zero mean process? Will this cause a bias in the spectrum estimation of the process ? 
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Well, it's not a bias, but it is information that the ear doesn't much care about, so removing it will change the autocorrelation coef's, such that the DC component is not, for instance, coded so accurately.

But it's not a "bias" it is an accurate representation of part of the signal, just not perhaps a part that's remotely relevant?
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I think bias will cause distortions to the low frequency components of the spectrum.
It is not as simple as just the DC component. 
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Of course, you always have to consider your aperture size and your window. Well, I do, I work in finite time.


I thought so too. Windowing the data will introduce a DC bias to the data segment that needed to be corrected. Otherwise, the low frequency region of the calculated spectrum will be distorted.

 
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