What effects the estimation of a sample covariance matrix?
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
add a comment |
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
add a comment |
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
3,09621038
asked Dec 3 '18 at 14:17
bidbybidby
876
asked Dec 3 '18 at 14:17
bidbybidby
876
asked Dec 3 '18 at 14:17
bidbybidby
876
876
add a comment |
add a comment |
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