PK 6 Oct 2010 Some fundamental concepts Periodicity and aperiodicity Fundamental frequency Harmonics Formants and spectra

Periodicity and aperiodicity Periodic waveforms repeat themselves Aperiodic waveforms do not repeat themselves The frequency of the periodic cycle is called the Fundamental Frequency, F0.

Periodicity and aperiodicity periodic wave aperiodic wave

Periodicity and aperiodicity The waveforms on the previous slide were taken from the following waveform in Praat: my pronunciationof "fish": f i S

PK 6 Oct 2010 Some fundamental concepts Periodicity and aperiodicity Fundamental frequency Harmonics Formants and spectra

The frequency of the periodic cycle is called the Fundamental Frequency, F0. The pink shaded area is one cycle, = 0.006432 seconds, = 1/ 0.006432 = 155.4726368 c.p.s = Hz.

PK 6 Oct 2010 Some fundamental concepts Periodicity and aperiodicity Fundamental frequency Harmonics Formants and spectra

Complex periodic waves and harmonics A periodic wave is made up of a (potentially very large) number of simple sine waves of different amplitudes. There is a simple mathematical relation between the fundamental frequency and the component sine waves: The F0 is the Greatest Common Demoninator (GCD)* of all the component sine waves – the largest number that divides exactly into the frequency of all the components. Another way of saying this is that the sine waves are harmonics of the F0. A harmonic is any whole-number multiple of the F0. The second harmonic is twice the F0, the third is three times, the nth is n times. (There is no “first harmonic”) * also called Greatest/Largest Common Factor/Divisor

PK 6 Oct 2010 Some fundamental concepts Periodicity and aperiodicity Fundamental frequency Harmonics Formants and spectra

Spectrum (pl. spectra) We calculate the number and amplitude of the component sine waves (the harmonics) in a complex periodic waveform using Fourier Analysis. This will give us a spectrum of the waveform.

Spectrum of a waveform Ladefoged Elements p.94 This vowel has been synthesized from a small number of harmonics (sine waves) The harmonics around 520 and 1400 have the greatest amplitude: these are the first and second formants.

Spectrum of a waveform Ladefoged Elements p.97 Actual not showing the actual harmonics, just the outline.

The density of the harmonics depends on the F0 Ladefoged Elements p.94 (b) 100 Hz (c) 120 Hx (d) 150 Hz

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel Low F0

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel F0 higher

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel and higher ....

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel

Spectrum of Ladefoged´s FLEECE vowel The density of the harmonics depends on the F0 Spectrum of Ladefoged´s FLEECE vowel very high F0

Spectra of various waveforms

Harmonics and formants Formants are the peaks where the harmonics have the greatest amplitude.