System and method for signal decomposition, analysis and reconstruction

A method comprising:

• obtaining a component signal representative of a digitally filtered frequency-limited band from a quasi-periodic waveform, wherein the component signal includes a plurality of component values;
• reducing the plurality of component values into a fractional-phase representation of the component signal having a plurality of fractional phases, and wherein each fractional phase is associated with a phase label and includes one or more values representing at least one of an abscissa and an ordinate for each of one or more local cycles of the component signal;
• and
• storing the fractional-phase representation,
• wherein the plurality of component values are complex numbers, wherein the fractional-phase representation for each fractional phase is associated with an angular range of a complex argument of the component signal, wherein the fractional-phase representation for one cycle of the component signal includes a first fractional phase, a second fractional phase, a third fractional phase, and a fourth fractional phase, and wherein the reducing of the plurality of component values into the fractional-phase representation further comprises:
• obtaining, for the first fractional phase, a complex value representing an ordinate and a real value representing an abscissa of a zero crossing of a real part of the component signal;
• obtaining, for the second fractional phase, a complex value representing an ordinate and a real value representing an abscissa of a zero crossing of an imaginary part of the component signal;
• obtaining, for the third fractional phase, a complex value representing an ordinate and a real value representing an abscissa of another zero crossing of the real part of the component signal;
• and
• obtaining, for the fourth fractional phase, a complex value representing an ordinate and a real value representing an abscissa of another zero crossing of an imaginary part of the component signal,
• wherein the obtaining of the value of the abscissa for each zero crossing includes finding a change in sign and interpolating in a neighborhood of the sign change.