Acoustic Phonetics and the Source-Filter Model of Speech Production

The Oscillogram

An oscillogram plots amplitude over time. It is an excellent tool for measuring the duration of specific speech events, such as Voice-Onset Time (VOT)—the interval between a consonant's burst and the start of vocal fold vibration. However, an oscillogram is limited; it cannot easily show the specific frequency components that make up a sound.

Fourier Transformation and Spectra

The Fourier Transformation is the mathematical engine of acoustic analysis. It operates on the principle that any periodic complex signal can be decomposed into a combination of individual sine waves. This process moves the signal from the time domain (amplitude/time) to the frequency domain (power/frequency).

The result is a spectrum, which shows which frequencies are present in a signal. When analyzing spectra, researchers face a fundamental trade-off between spectral resolution (the ability to distinguish between two close frequencies) and temporal resolution (the ability to see exactly when a sound changes).

The Spectrogram

A spectrogram provides a way to view both time and frequency simultaneously by stacking sequential spectra side-by-side.

• Narrow-band spectrograms provide high spectral resolution, making it easy to see individual harmonics (the integer multiples of the fundamental frequency).
• Wide-band spectrograms provide high temporal resolution, which is better for observing rapid transitions between speech segments and individual glottal pulses.

The Source-Filter Model

The most influential framework for describing speech production is the Source-Filter Model. This model posits that speech is the result of a sound source being modified by a filter.

The Source: Vocal Fold Vibration

The primary glottal source in human speech is the vibration of the vocal folds within the larynx. For voicing to occur, the vocal folds must be sufficiently approximated (brought close together) and supported by enough subglottal air pressure. This vibration creates a periodic signal characterized by a fundamental frequency ($F_0$) and its harmonics.

The quality of the source can be measured by:

• Jitter: Short-term variation in frequency.
• Shimmer: Short-term variation in amplitude.
• Spectral Tilt: Information regarding how the vocal folds open and close.

Other sources can include "jiggling" articulators (like the tongue in a trill) or turbulent noise (as in fricatives).

The Filter: The Vocal Tract

The vocal tract (comprising the pharynx, oral cavity, and nasal cavity) acts as the filter. As the source signal passes through the vocal tract, the tract modifies the signal through resonance (amplifying certain frequencies) and damping (attenuating others).

The specific frequencies that are amplified by the vocal tract are called formants ($F_1, F_2$, etc.). It is crucial to distinguish formants from harmonics: harmonics are determined by the source ($F_0$), whereas formants are determined by the shape and size of the vocal tract.

Modeling the Filter: Cylindrical Tubes

To simplify the complex anatomy of the mouth, we can model sections of the vocal tract as cylindrical tubes. The resonance of these tubes depends on their length and whether the ends are open or closed.

In a "closed-open" model (where the glottis is closed and the lips are open), resonance occurs at quarter-wavelength intervals. In this system:

• The anti-node is the point of maximal pressure change.
• The node is the point of minimal pressure change.

For a tube of length $L$, the resonance frequencies can be calculated based on the wavelength ($\lambda$). The first resonance occurs at $1/4$ the wavelength, the second at $3/4$, and so on.

Worked Example: The Schwa [ə]

The vowel schwa is often modeled as a single, neutral cylindrical tube approximately 17 cm long. Using the quarter-wavelength principle, we can estimate its resonances:

1. First Resonance ($F_1$): Occurs at $1/4$ wavelength $\approx 500\text{ Hz}$.
2. Second Resonance ($F_2$): Occurs at $3/4$ wavelength $\approx 1500\text{ Hz}$.
3. Third Resonance ($F_3$): Occurs at $5/4$ wavelength $\approx 2500\text{ Hz}$.

By changing the shape of the vocal tract—moving the tongue or changing lip rounding—we change the length and shape of these "tubes," thereby shifting the formant frequencies and creating different vowel sounds.

Summary Table: Formants vs. Harmonics