Method for estimating sampling phase from synchronously demodulated samples of sinusoidal waveforms

Data storage disk drive apparatus for controlling a sampling clock having a sampling frequency and a sampling phase relative to a data signal having a data frequency and a data phase, comprising:

• an analog timing controller adjusting the sampling frequency during a first time period;
• a digital timing controller adjusting the sampling phase during a second time period;
• and
• a timing error extractor determining the sampling phase relative to the data phase during a time interval spanning a transition from the first time period to the second time period, the timing error extractor coacting with the digital timing controller to adjust the sampling phase to a predetermined angle relative to the data phase, the data signal having a cosine component of amplitude (v) and a sine component of amplitude (u), the timing error extractor comprising:
• a first lookup table storing a set of log(u) and log(v) values;
• at least a second lookup table storing a set of arctan(log(v)−log(u)) values;
• means for looking up a log(u) value in the first lookup table;
• a memory storing the log(u) value;
• means for looking up a log(v) value;
• a subtraction function subtracting the stored log(u) value from the log(v) value to form an intermediate result;
• and
• addressing means addressing the second lookup table with the intermediate result to return an arctan(v/u) value for determining the sampling phase relative to the data phase.