System and method of generating complex waveforms

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.