Patent ID: 8751552

Claim:
A method of generating a complex waveform using a processing device having a plurality of inputs, the method comprising: providing programming instructions for implementing a function on the processing device having the form y ( x )=[( a ( x ) X ( x−d)) n(x) +ƒ( x )] [b(x)−(a(x)X(x−d)) n(x) ] wherein: ƒ(x) comprises a window function for determining an output value of the waveform within at least one operational window defined by the function; X(x−d) comprises a positions locus parameter defining a location of the at least one operational window defined by the function, and d represents a phase shift applied to the location of the at least one operational window defined by the function; a(x) comprises an operational window defining a width of the at least one operational window; b(x) comprises a weighting factor; and n(x) comprises a slew rate parameter for determining a slope of transitions between output values of the waveform outside the operational window and values of the waveform within operational window; providing one or more inputs to the processing device for defining one or more input values for one or more of the parameters ƒ(x), X(x−d), a(x), and n(x); executing the function on the processing device using the one or more input values for the one or more values of the parameters ƒ(x), X(x−d), a(x) and n(x); and generating, with a hardware device, an output waveform corresponding to the output value of the function.