hpa logo.jpg




White Noise.jpg 

White noise is the epitome of chaos and unpredictability and yet its amplitude distribution is completely defined and predicted by a Gaussian distribution.  To be a standard Gaussian distribution the mean must be zero, which is easily achieved in electronics.  The mean of a signal equates to the DC component which is zero if the signal has been passed through a capacitor. 



A standard Gaussian distribution will have a standard deviation of one.  It therefore follows that 68.26% of the action (or data samples) will occur within one standard deviation either side of the mean.  Suddenly the chaos of noise is becoming defined and predictable.


To illustrate a statistical detection system based on a Gaussian distribution, consider a year 4 class of 8 year old pupils.  Nationally, 8 year old children have a mean height of 128cm and a height range of 10cm either side of the mean.  If we look at one particular class of 30 pupils, it has a mean of 128.5cm which is very close to the national average.  If however a child is substituted with a 35 year old, their height of 178.cm only marginally increases the mean to 130.1cm. What is obvious to the teacherís eye, does not stand out mathematically.  A statistically superior intruder detector is required.





Kurtosis is the fourth standardised moment of a population.  Kurtosis exaggerates events furthest away from the mean.  For a Gaussian distribution, Kurtosis is equal to 3.  The pre-intruder classroom has a kurtosis of 3.04.  However the Kurtosis for the class with the intruder is 24.7.  This is a robust difference given the small sample size.  An observer might comment that a simple height alarm threshold, approximately four standard deviations from the mean could be employed just as effectively.  In many technology applications, the amplitude of a signal varies due to variations in transmission media − radiowave signal amplitude variation with atmospheric conditions.  A simple amplitude threshold is not appropriate in many cases.  An alarm level could be confidently set at a Kurtosis level of 5.0 and would work as an intruder alarm for any year of class, within all primary schools in the country.


Harrogate Power has employed processors to calculate the Kurtosis of a population which has produced a powerful detection tool in impaction detection applications and other infrequent extreme events.  Kurtosis is calculated using the standard deviation of a population which is equivalent to the root mean square voltage of a signal.  This fact has enabled Harrogate Power to produce a totally hardware based solution using dedicated electronic circuits, in addition to the software computational technique approach for the detection of infrequent extreme events.