[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: two cycles

Dear List,

Rabiner and Schafer (1978: 145, Digital Processing of Speech Signals) state that "to get any indication of periodicity in the autocorrelation function, the window must have a duration of at least two periods of the waveform."

Using an autocorrelation (ACC) function with a 39.37 ms rectangular window, I tested this proposition with three 2.5 s sawtooth waves at 27.5 Hz (pitch period = 36.36 ms), 38.9 Hz (25.71 ms), and 55 Hz (18.18 ms).

R&S's statement holds if the ACC function is scanned for its maximum value. Only the F0 of the 55 Hz sawtooth is accurately determined (mean calculated over the 2.5 s waveform = 54.74 Hz). The other F0s are severely overestimated, the mean estimated F0s of the 27.5 and 38.9 Hz sawtooths being respectively 281.19 and 179.54 Hz. Because two periods of the 55 Hz sawtooth are equal to 36.36 ms, R&S are clearly correct if the ACC maximum value detection method is employed, given the 39.37 ms rectangular window.

On the other hand, using the ACC peak-peaking method developed in Section 4.2.2 of my thesis (p. 96-98), I found that the respective mean F0s of the 27.5, 38.9, and 55 Hz sawtooths to be 31.52, 41.30, and 54.69 Hz (Table 5.1, p. 115). These results indicate that it is possible to obtain reasonable F0 estimates even when the pitch period is nearly of the same duration as the analysis window, on the condition that the appropriate ACC peak-peaking procedure is used.


Thesis URL:


The "pitch in two cycles" phenomenon is exactly what would be predicted by an
autocorrelation model of pitch. With two copies of a pulse, you can measure a consistent interval as a peak in the ACF.


Hi list,

In many of the papers published by Georg von Békésy he makes the statement that the
fundamental frequency was determined by the auditory system "even when the stimulus was
only two cycles" in length. In at least one of his publications {The Missing Fundamental
and Periodicity Detection in Hearing JASA 1972 512) 631-637) he attributes this to his
own experiments and to a paper by Savart.[Annalen der Physik und Chemie 1840 53 ( )
555-561 in german]. It is quite true that Savart found that the fundamental was
determined in two cycles but it was published in an earlier paper by Savart (Ueber die
Empfindlichkeit des Gehörorgans Felix Savart Annalen der Physik und Chemie 1830 20( )
290-304 in german)and no mention of the two cycles is mentioned in the citation by
Békésy. Actually from a historical point of view the original paper by Felix Savart was
published in French in: Annales de chimie et de Physique 1830 44 ( ) 337-352 in French.

Can anyone point me to literature which shows how the auditory system performs the "two
cycle" feat, or to papers which show how such a "two cycle" feat might be acomplished
mathematically or to any papers of a more recent origin which discusses this ability.