Apparatus and methods for watermarking using starting phase modulation

A non-transitory computer readable storage medium comprising computer readable instructions that, when executed, cause a processor to:

• calculate a first instantaneous phase value for a first watermark component of a watermarked media signal at a first time;
• calculate a second instantaneous phase value for a second watermark component of the watermarked media signal at the first time;
• determine a first sum of differences for the first and second instantaneous phase values relative to a first possible starting phase value;
• determine a second sum of differences for the first and second instantaneous phase values relative to a second possible starting phase value;
• in response to one of the first sum of differences or the second sum of differences satisfying a difference threshold:
• select a corresponding one of the first possible starting phase value or the second possible starting phase value to be a starting phase value;
• decode a bit value corresponding to the starting phase value;
• and
• determine a payload based on the bit value and a symbol represented by watermark components including the first watermark component and the second watermark component.

A watermark decoding method comprising:

• calculating a first instantaneous phase value for a first watermark component of a watermarked media signal at a first time;
• calculating a second instantaneous phase value for a second watermark component of the watermarked media signal at the first time;
• determining a first sum of differences for the first and second instantaneous phase values relative to a first possible starting phase value;
• determining a second sum of differences for the first and second instantaneous phase values relative to a second possible starting phase value;
• in response to one of the first sum of differences or the second sum of differences satisfying a difference threshold:
• selecting a corresponding one of the first possible starting phase value or the second possible starting phase value to be a starting phase value;
• decoding a bit value corresponding to the starting phase value;
• and
• determining a payload based on the bit value and a symbol represented by watermark components including the first watermark component and the second watermark component.