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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.
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Non-Linearities
• Types of distortion…
• Harmonic
• Summation Tones
• Difference Tones
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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.
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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.
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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.
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• Non-linearities in
the spectral and time
domain.
Non-Linearities
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Non-Linearities
• Applications
• Amplifiers (including hearing aids)
• Inner Ear Distortion
• High intensities
• Cochlear damage
• Distortion Product Otoacoustic Emissions
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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.
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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).
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Sharply and broadly tuned resonators
• Sharply tuned …
• Low rate of damping, more definitive tonal quality
• Broadly tuned …
• High rate of damping, poor tonality
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Hemholtz Resonators
• Greater the volume the lower the resonant
frequency
• Greater the neck diameter the higher the
resonant frequency
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Wavelenth Resonator
• Greater the length the lower the resonant
frequency
• 1/2 wavelength resonator
• 1/4 wavelength resonator
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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
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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
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Transfer Function
• Background: Need to understand sound
system, which is anything that responds to
sound.
• E.g., vocal tract, amplification, auditory
system, filters, etc.
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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
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Transfer Function
• Head Related Transfer Function
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Summary
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