DPLL

complex rotating data (a vector)

parameters:
para(1) - alpha, the proportional loop constant
para(2) - beta, the integral loop constant
(optional, default: 0 which means first order loop)
para(3) - err_para (optional, default: 0, see PLLerr...)
para(4) - phase_register_length in bits
(optional, default: 0, which means floating point)
para(5) - table_prec, number of bits in phase table representation;
used to build PhaseTable if required
(optional, default: 0, which means floating point,
uses: Qrotate to build PhaseTable)
para(6) - freq_register_length in bits
(optional, default: 0, which means floating point)
para(7) - freq_register_shift in bits;
the number of bits to the right of the "decimal" bit
(optional, default: 0, which means no scale)
para(8) - delay; an inserted delay before the loop_error signal in the loop
(optional, default: 0)

current state:
[last_phase, last_freq, pipe]; pipe is loop_error delay register values
(can initialize with [] or last_phase or [last_phase, last_freq])
err_func (optional, default: 'PLLerr_sign_linear')

complex de-rotated data (a vector)

next state vector
theta - loop
phase estimate (optional)

loop error (optional)