Hierarchical audio coding and decoding method and system and hierarchical audio coding and decoding method for transient signals are provided. A trajectory can be used to identify a selected trajectory or path of an instrument to reach a tumor within a brain of a subject, reach a selected portion of the anatomy or spinal cord), or other appropriate target. First and second overlapping, rotatable rotors are disposed within the head portion and are operatively coupled to the drive source through a plurality of gears such that the first and second rotors rotate in opposite directions when the drive source is actuated. When the spectral data is then quantized to reduce bitrate, the earlier phase shifting reduces excess requantization error. The fixation surface is configured to fix the implant to a prepared bone surface of the pelvic bone. The optical parametric oscillator is contoured with a plurality of exterior planes with specific reflective characteristics to form a resonator of the idler beam while reflecting and diffracting the signal beam with a desired wavelength.