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Binning is performed by calculating the variance of each dimension, identifying the highest variance dimension, and dividing data at the median into two new bins for the high variance dimension.
Each daughter bin was then similarly split at the median of its highest variance dimension until the desired number of bins is achieved.
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C N ( 0, N 0 ) with the noise variance per dimension is N0/2.
stands for circularly symmetric complex Gaussian distribution with mean, variance per dimension.
circularly symmetric complex Gaussian random variables with zero mean and variance per dimension.
complex Gaussian random variables with zero-mean and 0.5 variance per dimension.
The noise components are independently identical complex Gaussian random variables with zero-mean and variance per dimension.
Murmur detection is based on features extracted from Shannon energy, CWT, DWT, singular value decomposition (SVD), MFCC, bispectrum, variance fractal dimension, and Lyapunove exponents.
This type of investigation demands an in-depth study of multiple parameters such as the chosen representation (feature generation), the distribution of the data, the representation's dimensionality and the detected variance per dimension.
where y ¯ ( ρ − 1 ) and y ¯ ( ρ + 1 ) are the ISI components from the previous and next symbol periods; n ¯ is the additive white Gaussian noise component with E ( n ¯ n ¯ H = 2 σ 2 I N R ( N + L − 1 ) and σ 2 = N 0 2 is the noise variance per dimension.
This phenomenon that was first introduced by Scott and Thompson [14] can be explained with the following example: draw samples from a normal distribution (zero mean and unit variance) in dimension, and consider the probability to have a sample at distance from the mean of the distribution (zero).
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