Devices and methods using the hermetic transform for transmitting and receiving signals using multi-channel signaling

An apparatus for spectral compacting, the apparatus comprising:

• a processor configured to:
• generate a set of orthogonal basis signals;
• modulate each of the basis signals with a complex modulation based on a constellation of complex symbols to produce modulated basis signals;
• sum the modulated basis signals to produce a frame of signal data;
• and
• apply a matrix transformation to the frame of signal data to produce a reduced bandwidth frame of signal data comprising non-orthogonal basis signals;
• and
• a transmitter configured to transmit the reduced bandwidth frame of signal data.

A method for spectral de-compacting, the method comprising:

• receiving a reduced bandwidth frame of signal data comprising non-orthogonal basis signals modulated with a complex modulation based on a constellation of complex symbols;
• applying an inverse transformation of a matrix transformation to the frame of signal data to produce a de-compacted frame of signal data comprising orthogonal basis signals modulated with the complex modulation;
• and
• applying a transformation to the de-compacted frame of signal data to remove the complex modulation and extract the constellation of complex symbols.

An apparatus for spectral de-compacting, the apparatus comprising:

• a receiver configured to receive a reduced bandwidth frame of signal data comprising non-orthogonal basis signals modulated with a complex modulation based on a constellation of complex symbols;
• and
• a processor configured to:
• apply an inverse transformation of a matrix transformation to the frame of signal data to produce a de-compacted frame of signal data comprising orthogonal basis signals modulated with the complex modulation;
• and
• apply a transformation to the de-compacted frame of signal data to remove the complex modulation and extract the constellation of complex symbols.