System and method for statistically separating and characterizing noise which is added to a signal of a machine or a system

A method for an electronic noise estimation unit to characterize noise in a signal, the method comprising:

• using the electronic noise estimation unit, numerically differentiating the signal within a window at least m number of times to obtain an m-order differentiated signal;
• providing a histogram having a distribution that approximates the m-order differentiated signal;
• providing a probability density function type that approximates the distribution of the histogram, wherein said providing a probability density function type includes selecting a probability density function type from a library of probability density function types available to the noise estimation unit;
• determining a variance of the histogram;
• determining a zero-order variance using the variance of the histogram and the probability density function type;
• and
• outputting at least one of the probability density function type or the zero-order variance on an output line of the electronic noise estimation unit.

An apparatus for estimating noise in a signal, the apparatus comprising:

• a differentiation module configured to receive the signal and numerically differentiate the signal within a range of a window at least m number of times to obtain an m-order differentiated signal;
• a first module configured to determine a histogram that approximates the m-order differentiated signal;
• a second module configured to determine a probability density function type that approximates the distribution of the histogram;
• a third module configured to determine a variance of the histogram;
• a fourth module configured to determine a zero-order variance using the variance of the histogram and the probability density function type;
• and
• an interface module configured to output at least one of the zero-order variance or the probability density function type.

A system for estimating a pure signal component of a raw signal that includes the pure signal component and a noise signal component, the system comprising:

• an electronic noise estimation unit including:
• a differentiation module configured to receive a raw signal and numerically differentiate the raw signal within a range of a window at least m number of times to obtain an m-order differentiated signal;
• a first module configured to determine a histogram that approximates the m-order differentiated signal;
• a second module configured to determine a probability density function type that approximates the distribution of the histogram;
• a third module configured to determine a variance of the histogram;
• and
• a fourth module configured to determine a zero-order variance using the variance of the histogram and the probability density function type;
• and
• a filter coupled to the noise estimation unit, wherein the filter is configured to receive the zero-order variance and the raw signal and to output the estimated pure signal component of the raw signal.