Speech amplitude statistics and the gamma density function as a theoretical approximation

Area of Science:

• Speech processing
• Acoustic phonetics
• Statistical analysis of speech signals

Background:

• Understanding speech waveform statistics is crucial for speech analysis.
• Speech amplitude density provides fundamental data on speech signal characteristics.
• Characterizing long-time speech amplitude density requires a substantial dataset.

Purpose of the Study:

• To present data characterizing long-time speech amplitude density.
• To analyze the distribution of speech amplitude density using a large dataset.
• To fit a theoretical gamma density function to experimental speech amplitude data.

Main Methods:

• Collected approximately 45 minutes of recorded speech from 25 speakers.
• Estimated two parameters of a theoretical gamma density function.
• Performed curve fitting to compare experimental data with the gamma density function.

Main Results:

• Identified significant differences in speech amplitude density between male and female speakers.
• Observed distinct speech amplitude density patterns for positive and negative speech amplitudes.
• Determined that the gamma probability density function better approximates full-wave rectified speech than unidirectional amplitudes.

Conclusions:

• Speech amplitude density varies significantly based on speaker sex.
• Asymmetry exists between positive and negative speech amplitude distributions.
• The gamma probability density function serves as a robust model for full-wave rectified speech amplitude.