Abstract: A method of generating an analytical signal for signal analysis. The method includes obtaining a digital signal, sectioning the digital signal into a series of overlapping windows in time domain, generating a plurality of energy pulses by evaluating a function that describes energy information within each window or set of windows, and generating a time-dependent analytical signal by generating an oscillating signal by multiplying each of the plurality of energy pulses by an oscillating function; and integrating the oscillating function across a band pass frequency filter.

Abstract: A method of generating an analytical signal for signal analysis. The method includes obtaining a digital signal, sectioning the digital signal into a series of overlapping windows in time domain, generating a plurality of energy pulses by evaluating a function that describes energy information within each window or set of windows, and generating a time-dependent analytical signal by generating an oscillating signal by multiplying each of the plurality of energy pulses by an oscillating function; and integrating the oscillating function across a band pass frequency filter.

Abstract: There is provided a system and method of pre-processing discrete datasets for use in machine learning. The method includes: determining a median and a standard deviation of an input discrete dataset; determining a probability mass function including a probability of finding a particular data point in the input discrete dataset within a particular bin of a histogram representative of the input discrete dataset; transforming the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, the parametric control function including a lognormal derivative of the probability density function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error of an objective function; and outputting the probability density function for use an input to a machine learning model.

Abstract: There is provided a system and method of pre-processing discrete datasets for use in machine learning. The method includes: determining a median and a standard deviation of an input discrete dataset; determining a probability mass function including a probability of finding a particular data point in the input discrete dataset within a particular bin of a histogram representative of the input discrete dataset; transforming the probability mass function into a continuously differentiable probability density function using the standard deviation, the probability density function determined using a parametric control function, the parametric control function including a lognormal derivative of the probability density function, the parameters within the control function are estimated using optimization that minimizes a mean-squared error of an objective function; and outputting the probability density function for use an input to a machine learning model.