EE599-020Audio Signals and Systems

Kevin D. DonohueElectrical and Computer Engineering

University of Kentucky

Question!

If a tree falls in the forest and nobody is there to hear it, will it make a sound?

Sound provided by http://www.therecordist.com/downloads.html

Ambiguity!

• Merriam-Webster Dictionary:

• Sound a : a particular auditory impression b : the sensation perceived by the sense of hearing c : mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium (as air) and is the objective cause of hearing.

Electronic Audio Systems

Sound Sources – Vibrations at 20Hz-20kHz

Amplification, Signal

Conditioning

Electoacoustic Transducer

Processing for Intended

Application

Transmission Media

Storage

Information Extraction /

Measurement

Playback

Ultimate Target for Playback

http://www1.omi.tulane.edu/departments/pathology/fermin/Hearing.html http://www.ear-hearing.com/ http://ear.berkeley.edu/ http://www.chdr.org/advancedearfunction.html

Diagram from:http://hyperphysics.phy-astr.gsu.edu/hbase/sound/hearcon.html

Outer Ear

Pinna – Provides amplification and sound source localization cues.

Auditory (Ear) Canal – Provides pressure gain at the middle ear. A 10 dB pressure gain occurs over 2 to 5kHz from the opening of the canal to the middle ear.

Resonance of Auditory Canal

Recall that frequency = speed/wavelength

Assume the speed of sound in air is 331 m/s and the auditory canal is about 3 cm long. Resonance in a pipe will occur at odd multiples of the quarter wavelength. Find the 2 lowest resonant frequencies of the auditory canal modeled as a simple pipe (closed on one end and open on the other).

c

f

Resonance of Auditory CanalHow does the the result derived in the last example help explain the shape of of the equal-loudness curves of the human auditory system:

Middle Ear

Tympanic Membrane (Eardrum) – Transfers vibrations in air to the Ossicles.

Ossicles – 3 bones, the malleus (hammer), incus (anvil), and stapes (stirrup) that work as levers to transfer pressure to the oval window of the inner ear (fluid filled cochlea). Can also tighten system to improve dynamic range and protect from loud sounds.

Middle Ear

The middle ear provides an acoustic impedance match to improve the transfer of vibrations in air to vibrations in the cochlear fluid.

Power or intensity (I) of a sound wave in a material is related to its pressure (p) by:

where Zo is the acoustic impedance of the material related to the density () and acoustic velocity (v) of the material:

oZ

pI

2

vZo

Middle Ear

Compute the impedance mismatch between air and cochlear fluid (water) given that Water: velocity = 1500m/s, density = 1.0 Mg/m3

Air:      velocity = 330m/s, density = 1.293kg/m3

Compute the pressure gain required to compensate for the intensity loss due to the impedance mismatch.

Middle Ear

Given the area of the tympanic membrane at 80 mm2, oval window of the cochlea is 3mm2, and the mechanical advantage of the lever system of the ossicles vary between 1.3 and 3.1, compute the minimum and maximum pressure gain provided by the middle ear.

Inner Ear

Cochlea - mechanically filters the sound into subbands and converts mechanical energy into electrical energy for transmission to the brain over the auditory nerves.

Cochlea

Oval window – layer on Cochlea exterior for transducing vibrations into the cochlear fluid.

Basilar Membrane - layer suspended between cochlea fluid with local frequency sensitivity.

Organ of Corti – hair cells on the basilar membrane that depolarize nerve cells when displaced by the basilar membrane vibrations.

Diagram from:http://hyperphysics.phy-astr.gsu.edu/hbase/sound/hearcon.html

Critical Bands of Hearing

Hearing exhibits dynamic sensitivities. If various sound stimuli are close in frequency, the dominant sound can completely or partially mask the others.

The bandwidths over the hearing spectrum in which masking occurs are referred to as critical bands.

Experimentally measured bandwidths are approximated in terms of the equivalent rectangular bandwidth ERB in Hz as function of the center frequency (f) in kHz by:

52283993236 2 ... ffERB

ProblemWrite a program to compute a set of center

frequencies so that the hearing spectrum (20Hz to 20kHz) is completely and efficiently covered by a set of critical bands. Use a second order BPF as a model for the frequency bands.

iii bhERB

iii bhf ib ihif

A

2

A

f

Hearing Properties and Auditory Nerve Responses

Adaptation – Neural firing rate decreases exponentially in response to a steady state sound (designed to detect changes in sound field).

Tuning – Sensitivity of firing nerve fibers along the basilar membrane have band-pass-like responses to changes in frequency.

Synchrony – Low frequency (< 5kHz) neural firing is in phase with tonal stimulation (phase locking).

Non linearity – Saturation, two tone suppression, masking by noise, and combination tones.

Hearing Properties – Non linearity

Saturation – High spontaneous rate fibers reach a maximum firing rate for lower level stimulation and results in a loss of spectral definition, while low spontaneous rate fibers do not significantly increase with increasing stimulation level.

Two Tone Suppression – The firing rate of a stimulated nerve by a tone can be suppressed by the presence of another tone.

Masking by Noise – The presence of broad band stimulation (noise) reduces the nerve firing rate in response to a tone.

Combination Tones – Tones played simultaneous may cause other nerve fibers to fire in addition to those stimulated by the actual tones.

Matlab Exercise Use the sine/cosine function in Matlab along with vector and

matrix manipulation to write a function that generates a major scale (do not start with tones above 440 Hz and use a sampling rate of 8 kHz). Let the Matlab function input arguments be the starting frequency and the time interval in seconds for each note in the scale. Let the output be a vector of samples that can be played with Matlab command “soundsc(v,8000)” (where v is the vector output of your function).

A scale covers a one octave frequency range, which implies the end frequency is twice the beginning. There are 10 semi-tones or half steps between octave frequencies. A major scale consists of a series of tones increasing in frequency by a whole, whole, half, whole, whole, whole, and half step (8 notes altogether – don’t forget the starting note).

Matlab Exercise - ScalesJust Pythagorean Equal Temperament

Interval - 0 (1) 1/1 = 1 1 = 1 2^(0)=1

Interval - 1 16/15 256/243 2^(1/12)

Interval - 2 (2) 10/9 (or 9/8) 9/8 2^(2/12)

Interval - 3 6/5 32/27 2^(3/12)

Interval - 4 (3) 5/4 81/64 2^(4/12)

Interval - 5 (4) 4/3 4/3 2^(5/12)

Interval - 6 45/32 (or 64/45) 1024/729 (or 729/512) 2^(6/12)

Interval - 7 (5) 3/2 3/2 2^(7/12)

Interval - 8 8/5 128/81 2^(8/12)

Interval - 9 (6) 5/3 27/16 2^(9/12)

Interval - 10 7/4 (or 16/19 or 9/5) 16/9 2^(10/12)

Interval - 11 (7) 15/8 243/128 2^(11/12)

Interval - 12 (8) 2/1 = 2 2/1 = 2 2^(12/12) = 2

Matlab Exercise – Famous Notes

Middle C = 261.626 Hz (standard tuning)

Concert A (A above middle C) = 440 Hz

Middle C = 256 Hz (Scientific tuning)