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6. Uncertainty of estimated pitch (ncluded in An_aadf_pitch_estimator and conversaciones con Enrique Tomás)
The pitch value obtained in any method is always uncertain, the value will change slightly around a central value. Why does it occur? Discarding errors in the calculation or in the programming of the algorithm we have always some reasons for this errors.
1) The first one is the impossibility of ascertain the exact pitch of a periodic signal by using a time limited window of analysis; we would need an infinite length of time to assess the exact value of the signal pitch. This pertain to the nature of things, not to the quality of any algorithm. For instance, if we estimate the pitch within a signal fragment of 100 milliseconds, we have an inherent uncertainty error of 1000/100=10 hz. That represent only 1%, a sixth of a semitone for a 1000 hz signal; but for a signal of 100 hz it means more then one semitone of pitch uncertainty. The solution is to augment the signal duration and so the processing time. (see some solved questions on this in Algunas preguntas sobre incertidumbre del tono.
2) Besides that, the instant or point t where we calculate the local pitch can fall in different part of the pitch period (by the way an ambiguous concept since there is no such thing a beginning of the pitch period despite engineers take the maximum positive jump as arbitrary beginning). In any case if we displace point by point the analysis it will take place by calculating different parts of the pitch period, thus the calculus would be different and similarities would be different.
3) Actual signals like singing or playing signals have usually pitch variations, as vibrato or unprocessed edition or any other reasons.
4) Another motive of variation is the sampling frequency that limits the sifts in delay of compared segments to integer values being one, one sample. therefore this is the absolute value of resolution for the estimated pitch. This limit can be trespassed by means of interpolation techniques, an useful device by using the peaks of the autodissimilarity function or any other, to estimate a value situated in the middle of integer values (samples).
See also some considerations on the concept of peak (pico).
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