1 Non-Linearities Linear systems (e.g., filters) can change the intensity and phase of a signal input. Non-linear systems (e.g., amplfiers) not only can modify the existing input, but can add sinusoids to the output. These additional signals are referred to as distortion.

2 Non-Linearities Types of distortion… Harmonic Summation Tones Difference Tones

3 Non-Linearities Harmonic Distortion Input = f1 (where f1 is the input sinusoid) Output = 1f1, 2f1, 3f1, etc. That is, the input is a pure tone, where the output is the input + its harmonics.

4 Non-Linearities Summation Tones Input = f1 and f2 Output = f1 + f2, 2f1 + f2, f1 + 2f2 When you have two (or more) sinusoids as inputs, the output will be the addition of these tones.

5 Non-Linearities Difference Tones Input = f1 and f2 Output = f2 - f1, 2f1 - f2, 2f2 - f1, etc. When you have two (or more) sinusoids as inputs, the output will be the difference of these tones.

6 Non-Linearities Non-linearities in the spectral and time domain.

7 Non-Linearities Applications Amplifiers (including hearing aids) Inner Ear Distortion High intensities Cochlear damage Distortion Product Otoacoustic Emissions

8 Resonance General Principle of Resonance. When a periodically vibrating force is applied to an elastic system, the elastic system will be forced to vibrate initially at the frequency of the applied force. The nearer the frequency to the applied force to the natural (resonant) frequency of the elastic system, the greater will be the resulting amplitude of vibration.

9 Resonance The resonant frequency is directly related to the mass and stiffness reactance of the system. > mass, the lower the resonant frequency > stiffness, the greater the resonant frequency. Most vibrating objects have multiple resonant frequencies (e.g., harmonics).

10 Sharply and broadly tuned resonators Sharply tuned … Low rate of damping, more definitive tonal quality Broadly tuned … High rate of damping, poor tonality

11 Hemholtz Resonators Greater the volume the lower the resonant frequency Greater the neck diameter the higher the resonant frequency

12 Wavelenth Resonator Greater the length the lower the resonant frequency 1/2 wavelength resonator 1/4 wavelength resonator

13 Wavelength Resonator 1/2 wavelength resonators resonate at whole number multiples of the primary resonant frequency. …. e.g., 100, 200, 300, 400 Hz 1/4 wavelength resonators resonate at ODD multiples of the resonator frequency. … e.g., 100, 300, 500, 700 Hz

14 Resonator Applications Auditory system ear canal, tympanic membrane/ossicles, basilar membrane Amplification acoustic and electrical Tuning forks Vocal tract oral, nasal, and pharyngeal cavities. Other

15 Transfer Function Background: Need to understand sound system, which is anything that responds to sound. E.g., vocal tract, amplification, auditory system, filters, etc.

16 Transfer Function Transfer function reflects how the sound system changes the amplitude, frequency or phase of the signal. E.g., Transfer Function of Vocal Tract

17 Transfer Function Head Related Transfer Function

18 Summary