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CHAPTER
22 Audio Processing
Audio processing covers many diverse fields, all involved in presenting sound to human listeners.
Three areas are prominent: (1) high fidelity music reproduction, such as in audio compact discs,
(2) voice telecommunications, another name for telephone networks, and (3) synthetic speech,
where computers generate and recognize human voice patterns. While these applications have
different goals and problems, they are linked by a common umpire: the human ear. Digital Signal
Processing has produced revolutionary changes in these and other areas of audio processing.
Human Hearing
The human ear is an exceedingly complex organ. To make matters even more
difficult, the information from two ears is combined in a perplexing neural
network, the human brain. Keep in mind that the following is only a brief
overview; there are many subtle effects and poorly understood phenomena
related to human hearing.
Figure 22-1 illustrates the major structures and processes that comprise the
human ear. The outer ear is composed of two parts, the visible flap of skin
and cartilage attached to the side of the head, and the ear canal, a tube
about 0.5 cm in diameter extending about 3 cm into the head. These
structures direct environmental sounds to the sensitive middle and inner ear
organs located safely inside of the skull bones. Stretched across the end of
the ear canal is a thin sheet of tissue called the tympanic membrane or ear
drum. Sound waves striking the tympanic membrane cause it to vibrate.
The middle ear is a set of small bones that transfer this vibration to the
cochlea (inner ear) where it is converted to neural impulses. The cochlea
is a liquid filled tube roughly 2 mm in diameter and 3 cm in length.
Although shown straight in Fig. 22-1, the cochlea is curled up and looks
like a small snail shell. In fact, cochlea is derived from the Greek word for
snail.
The Scientist and Engineer's Guide to Digital Signal Processing 352
When a sound wave tries to pass from air into liquid, only a small fraction of
the sound is transmitted through the interface, while the remainder of the
energy is reflected. This is because air has a low mechanical impedance (low
acoustic pressure and high particle velocity resulting from low density and high
compressibility), while liquid has a high mechanical impedance. In less
technical terms, it requires more effort to wave your hand in water than it does
to wave it in air. This difference in mechanical impedance results in most of
the sound being reflected at an air/liquid interface.
The middle ear is an impedance matching network that increases the fraction
of sound energy entering the liquid of the inner ear. For example, fish do not
have an ear drum or middle ear, because they have no need to hear in air.
Most of the impedance conversion results from the difference in area between
the ear drum (receiving sound from the air) and the oval window (transmitting
sound into the liquid, see Fig. 22-1). The ear drum has an area of about 60
(mm)2, while the oval window has an area of roughly 4 (mm)2. Since pressure
is equal to force divided by area, this difference in area increases the sound
wave pressure by about 15 times.
Contained within the cochlea is the basilar membrane, the supporting structure
for about 12,000 sensory cells forming the cochlear nerve. The basilar
membrane is stiffest near the oval window, and becomes more flexible toward
the opposite end, allowing it to act as a frequency spectrum analyzer. When
exposed to a high frequency signal, the basilar membrane resonates where it is
stiff, resulting in the excitation of nerve cells close to the oval window.
Likewise, low frequency sounds excite nerve cells at the far end of the basilar
membrane. This makes specific fibers in the cochlear nerve respond to specific
frequencies. This organization is called the place principle, and is preserved
throughout the auditory pathway into the brain.
Another information encoding scheme is also used in human hearing, called the
volley principle. Nerve cells transmit information by generating brief
electrical pulses called action potentials. A nerve cell on the basilar membrane
can encode audio information by producing an action potential in response to
each cycle of the vibration. For example, a 200 hertz sound wave can be
represented by a neuron producing 200 action potentials per second. However,
this only works at frequencies below about 500 hertz, the maximum rate that
neurons can produce action potentials. The human ear overcomes this problem
by allowing several nerve cells to take turns performing this single task. For
example, a 3000 hertz tone might be represented by ten nerve cells alternately
firing at 300 times per second. This extends the range of the volley principle
to about 4 kHz, above which the place principle is exclusively used.
Table 22-1 shows the relationship between sound intensity and perceived
loudness. It is common to express sound intensity on a logarithmic scale,
called decibel SPL (Sound Power Level). On this scale, 0 dB SPL is a sound
wave power of 10-16 watts/cm2, about the weakest sound detectable by the
human ear. Normal speech is at about 60 dB SPL, while painful damage to the
ear occurs at about 140 dB SPL.
Chapter 22- Audio Processing 353
sound
waves
in air
ear
outer
canal
ear
tympanic membrane
(ear drum)
oval window
sound waves
in liquid
middle
ear bones
cochlea
basilar
membrane
high
frequency
detection
medium
frequency
detection
low
frequency
detection
FIGURE 22-1
Functional diagram of the human ear. The outer ear collects sound waves from the environment and channels
them to the tympanic membrane (ear drum), a thin sheet of tissue that vibrates in synchronization with the air
waveform. The middle ear bones (hammer, anvil and stirrup) transmit these vibrations to the oval window, a
flexible membrane in the fluid filled cochlea. Contained within the cochlea is the basilar membrane, the supporting
structure for about 12,000 nerve cells that form the cochlear nerve. Due to the varying stiffness of the basilar
membrane, each nerve cell only responses to a narrow range of audio frequencies, making the ear a frequency
spectrum analyzer.
The difference between the loudest and faintest sounds that humans can hear
is about 120 dB, a range of one-million in amplitude. Listeners can detect a
change in loudness when the signal is altered by about 1 dB (a 12% change in
amplitude). In other words, there are only about 120 levels of loudness that
can be perceived from the faintest whisper to the loudest thunder. The
sensitivity of the ear is amazing; when listening to very weak sounds, the ear
drum vibrates less than the diameter of a single molecule!
The perception of loudness relates roughly to the sound power to an exponent
of 1/3. For example, if you increase the sound power by a factor of ten,
listeners will report that the loudness has increased by a factor of about two
( ). This is a major problem for eliminating undesirable environmental 101/3 . 2
sounds, for instance, the beefed-up stereo in the next door apartment. Suppose
you diligently cover 99% of your wall with a perfect soundproof material,
missing only 1% of the surface area due to doors, corners, vents, etc. Even
though the sound power has been reduced to only 1% of its former value, the
perceived loudness has only dropped to about , or 20%. 0.011/3 . 0.2
The range of human hearing is generally considered to be 20 Hz to 20 kHz,
but it is far more sensitive to sounds between 1 kHz and 4 kHz. For example,
listeners can detect sounds as low as 0 dB SPL at 3 kHz, but require 40 dB
SPL at 100 hertz (an amplitude increase of 100). Listeners can tell that two
tones are different if their frequencies differ by more than about 0.3% at 3
kHz. This increases to 3% at 100 hertz. For comparison, adjacent keys on a
piano differ by about 6% in frequency.
The Scientist and Engineer's Guide to Digital Signal Processing 354
Watts/cm2 Decibels SPL Example sound
10-2 140 dB Pain
10-3 130 dB
10-4 120 dB Discomfort
10-5 110 dB Jack hammers and rock concerts
10-6 100 dB
10-7 90 dB OSHA limit for industrial noise
10-8 80 dB
10-9 70 dB
10-10 60 dB Normal conversation
10-11 50 dB
10-12 40 dB Weakest audible at 100 hertz
10-13 30 dB
10-14 20 dB Weakest audible at 10kHz
10-15 10 dB
10-16 0 dB Weakest audible at 3 kHz
10-17 -10 dB
10-18 -20 dB
TABLE 22-1
Units of sound intensity. Sound
intensity is expressed as power per
unit area (such as watts/cm2), or
more commonly on a logarithmic
scale called decibels SPL. As this
table shows, human hearing is the
most sensitive between 1 kHz and
4 kHz.
Softer Louder
The primary advantage of having two ears is the ability to identify the
direction of the sound. Human listeners can detect the difference between
two sound sources that are placed as little as three degrees apart, about the
width of a person at 10 meters. This directional information is obtained in
two separate ways. First, frequencies above about 1 kHz are strongly
shadowed by the head. In other words, the ear nearest the sound receives
a stronger signal than the ear on the opposite side of the head. The second
clue to directionality is that the ear on the far side of the head hears the
sound slightly later than the near ear, due to its greater distance from the
source. Based on a typical head size (about 22 cm) and the speed of sound
(about 340 meters per second), an angular discrimination of three degrees
requires a timing precision of about 30 microseconds. Since this timing
requires the volley principle, this clue to directionality is predominately
used for sounds less than about 1 kHz.
Both these sources of directional information are greatly aided by the ability
to turn the head and observe the change in the signals. An interesting sensation
occurs when a listener is presented with exactly the same sounds to both ears,
such as listening to monaural sound through headphones. The brain concludes
that the sound is coming from the center of the listener's head!
While human hearing can determine the direction a sound is from, it does
poorly in identifying the distance to the sound source. This is because there
are few clues available in a sound wave that can provide this information.
Human hearing weakly perceives that high frequency sounds are nearby, while
low frequency sounds are distant. This is because sound waves dissipate their
higher frequencies as they propagate long distances. Echo content is another
weak clue to distance, providing a perception of the room size. For example,
Chapter 22- Audio Processing 355
Time (milliseconds)
0 1 2 3 4 5
-2
-1
0
1
2
3
b. 1 kHz - 3 kHz sine waves
Time (milliseconds)
0 1 2 3 4 5
-2
-1
0
1
2
3
a. 1 kHz + 3 kHz sine waves
FIGURE 22-2
Phase detection of the human ear. The human ear is very insensitive to the relative phase of the component
sinusoids. For example, these two waveforms would sound identical, because the amplitudes of their
components are the same, even though their relative phases are different.
Amplitude
Amplitude
sounds in a large auditorium will contain echoes at about 100 millisecond
intervals, while 10 milliseconds is typical for a small office. Some species
have solved this ranging problem by using active sonar. For example, bats and
dolphins produce clicks and squeaks that reflect from nearby objects. By
measuring the interval between transmission and echo, these animals can locate
objects with about 1 cm resolution. Experiments have shown that some
humans, particularly the blind, can also use active echo localization to a small
extent.
Timbre
The perception of a continuous sound, such as a note from a musical
instrument, is often divided into three parts: loudness, pitch, and timbre
(pronounced "timber"). Loudness is a measure of sound wave intensity, as
previously described. Pitch is the frequency of the fundamental component in
the sound, that is, the frequency with which the waveform repeats itself. While
there are subtle effects in both these perceptions, they are a straightforward
match with easily characterized physical quantities.
Timbre is more complicated, being determined by the harmonic content of the
signal. Figure 22-2 illustrates two waveforms, each formed by adding a 1 kHz
sine wave with an amplitude of one, to a 3 kHz sine wave with an amplitude
of one-half. The difference between the two waveforms is that the one shown
in (b) has the higher frequency inverted before the addition. Put another way,
the third harmonic (3 kHz) is phase shifted by 180 degrees compared to the
first harmonic (1 kHz). In spite of the very different time domain waveforms,
these two signals sound identical. This is because hearing is based on the
amplitude of the frequencies, and is very insensitive to their phase. The shape
of the time domain waveform is only indirectly related to hearing, and usually
not considered in audio systems.
The Scientist and Engineer's Guide to Digital Signal Processing 356
The ear's insensitivity to phase can be understood by examining how sound
propagates through the environment. Suppose you are listening to a person
speaking across a small room. Much of the sound reaching your ears is
reflected from the walls, ceiling and floor. Since sound propagation depends
on frequency (such as: attenuation, reflection, and resonance), different
frequencies will reach your ear through different paths. This means that the
relative phase of each frequency will change as you move about the room.
Since the ear disregards these phase variations, you perceive the voice as
unchanging as you move position. From a physics standpoint, the phase of an
audio signal becomes randomized as it propagates through a complex
environment. Put another way, the ear is insensitive to phase because it
contains little useful information.
However, it cannot be said that the ear is completely deaf to the phase. This
is because a phase change can rearrange the time sequence of an audio signal.
An example is the chirp system (Chapter 11) that changes an impulse into a
much longer duration signal. Although they differ only in their phase, the ear
can distinguish between the two sounds because of their difference in duration.
For the most part, this is just a curiosity, not something that happens in the
normal listening environment.
Suppose that we ask a violinist to play a note, say, the A below middle C.
When the waveform is displayed on an oscilloscope, it appear much as the
sawtooth shown in Fig. 22-3a. This is a result of the sticky rosin applied to the
fibers of the violinist's bow. As the bow is drawn across the string, the
waveform is formed as the string sticks to the bow, is pulled back, and
eventually breaks free. This cycle repeats itself over and over resulting in the
sawtooth waveform.
Figure 22-3b shows how this sound is perceived by the ear, a frequency of 220
hertz, plus harmonics at 440, 660, 880 hertz, etc. If this note were played on
another instrument, the waveform would look different; however, the ear would
still hear a frequency of 220 hertz plus the harmonics. Since the two
instruments produce the same fundamental frequency for this note, they sound
similar, and are said to have identical pitch. Since the relative amplitude of the
harmonics is different, they will not sound identical, and will be said to have
different timbre.
It is often said that timbre is determined by the shape of the waveform. This
is true, but slightly misleading. The perception of timbre results from the ear
detecting harmonics. While harmonic content is determined by the shape of the
waveform, the insensitivity of the ear to phase makes the relationship very onesided.
That is, a particular waveform will have only one timbre, while a
particular timbre has an infinite number of possible waveforms.
The ear is very accustomed to hearing a fundamental plus harmonics. If a
listener is presented with the combination of a 1 kHz and 3 kHz sine wave,
they will report that it sounds natural and pleasant. If sine waves of 1 kHz and
3.1 kHz are used, it will sound objectionable.
Chapter 22- Audio Processing 357
Frequency (hertz)
0 200 400 600 800 1000 1200 1400 1600
0
1
2
3
4
b. Frequency spectrum
harmonics
fundamental
Time (milliseconds)
0 5 10 15 20 25
-8
-4
0
4
8
a. Time domain waveform
FIGURE 22-3
Violin waveform. A bowed violin produces a sawtooth waveform, as illustrated in (a). The sound
heard by the ear is shown in (b), the fundamental frequency plus harmonics.
Amplitude
Amplitude
B C D E F G B C D E F G B C D E F G B C D E F G B C D E F G B C D E F G B C D E F G B C
A- 27.5 Hz A- 55 Hz A- 110 Hz A- 880 Hz A- 1760 Hz A- 3520 Hz A- 440 Hz A- 220 Hz
C- 262 Hz
(Middle C)
FIGURE 22-4
The Piano keyboard. The keyboard of the piano is a logarithmic frequency scale, with the fundamental
frequency doubling after every seven white keys. These white keys are the notes: A, B, C, D, E, F and G.
This is the basis of the standard musical scale, as illustrated by the piano
keyboard in Fig. 22-4. Striking the farthest left key on the piano produces a
fundamental frequency of 27.5 hertz, plus harmonics at 55, 110, 220, 440, 880
hertz, etc. (there are also harmonics between these frequencies, but they aren't
important for this discussion). These harmonics correspond to the fundamental
frequency produced by other keys on the keyboard. Specifically, every seventh
white key is a harmonic of the far left key. That is, the eighth key from the left
has a fundamental frequency of 55 hertz, the 15th key has a fundamental
frequency of 110 hertz, etc. Being harmonics of each other, these keys sound
similar when played, and are harmonious when played in unison. For this
reason, they are all called the note, A. In this same manner, the white key
immediate right of each A is called a B, and they are all harmonics of each
other. This pattern repeats for the seven notes: A, B, C, D, E, F, and G.
The term octave means a factor of two in frequency. On the piano, one
octave comprises eight white keys, accounting for the name (octo is Latin
for eight). In other words, the piano’s frequency doubles after every seven
white keys, and the entire keyboard spans a little over seven octaves. The
range of human hearing is generally quoted as 20 hertz to 20 kHz,
The Scientist and Engineer's Guide to Digital Signal Processing 358
corresponding to about ½ octave to the left, and two octaves to the right of
the piano keyboard. Since octaves are based on doubling the frequency
every fixed number of keys, they are a logarithmic representation of
frequency. This is important because audio information is generally
distributed in this same way. For example, as much audio information is
carried in the octave between 50 hertz and 100 hertz, as in the octave
between 10 kHz and 20 kHz. Even though the piano only covers about 20%
of the frequencies that humans can hear (4 kHz out of 20 kHz), it can
produce more than 70% of the audio information that humans can perceive
(7 out of 10 octaves). Likewise, the highest frequency a human can detect
drops from about 20 kHz to 10 kHz over the course of an adult's lifetime.
However, this is only a loss of about 10% of the hearing ability (one octave
out of ten). As shown next, this logarithmic distribution of information
directly affects the required sampling rate of audio signals.
Sound Quality vs. Data Rate
When designing a digital audio system there are two questions that need to be
asked: (1) how good does it need to sound? and (2) what data rate can be
tolerated? The answer to these questions usually results in one of three
categories. First, high fidelity music, where sound quality is of the greatest
importance, and almost any data rate will be acceptable. Second, telephone
communication, requiring natural sounding speech and a low data rate to
reduce the system cost. Third, compressed speech, where reducing the data
rate is very important and some unnaturalness in the sound quality can be
tolerated. This includes military communication, cellular telephones, and
digitally stored speech for voice mail and multimedia.
Table 22-2 shows the tradeoff between sound quality and data rate for these
three categories. High fidelity music systems sample fast enough (44.1 kHz),
and with enough precision (16 bits), that they can capture virtually all of the
sounds that humans are capable of hearing. This magnificent sound quality
comes at the price of a high data rate, 44.1 kHz × 16 bits = 706k bits/sec.
This is pure brute force.
Whereas music requires a bandwidth of 20 kHz, natural sounding speech only
requires about 3.2 kHz. Even though the frequency range has been reduced to
only 16% (3.2 kHz out of 20 kHz), the signal still contains 80% of the original
sound information (8 out of 10 octaves). Telecommunication systems typically
operate with a sampling rate of about 8 kHz, allowing natural sounding speech,
but greatly reduced music quality. You are probably already familiar with this
difference in sound quality: FM radio stations broadcast with a bandwidth of
almost 20 kHz, while AM radio stations are limited to about 3.2 kHz. Voices
sound normal on the AM stations, but the music is weak and unsatisfying.
Voice-only systems also reduce the precision from 16 bits to 12 bits per
sample, with little noticeable change in the sound quality. This can be
reduced to only 8 bits per sample if the quantization step size is made
unequal. This is a widespread procedure called companding, and will be
Chapter 22- Audio Processing 359
TABLE 22-2
Audio data rate vs. sound quality. The sound quality of a digitized audio signal depends on its data rate, the product
of its sampling rate and number of bits per sample. This can be broken into three categories, high fidelity music (706
kbits/sec), telephone quality speech (64 kbits/sec), and compressed speech (4 kbits/sec).
Sound Quality Required Bandwidth Sampling
rate
Number
of bits
Data rate
(bits/sec)
Comments
High fidelity music
(compact disc)
5 Hz to
20 kHz
44.1 kHz 16 bit 706k Satisfies even the most picky
audiophile. Better than
human hearing.
Telephone quality speech 200 Hz to
3.2 kHz
8 kHz 12 bit 96k Good speech quality, but
very poor for music.
(with companding) 200 Hz to
3.2 kHz
8 kHz 8 bit 64k Nonlinear ADC reduces the
data rate by 50%. A very
common technique.
Speech encoded by Linear
Predictive Coding
200 Hz to
3.2 kHz
8 kHz 12 bit 4k DSP speech compression
technique. Very low data
rates, poor voice quality.
discussed later in this chapter. An 8 kHz sampling rate, with an ADC
precision of 8 bits per sample, results in a data rate of 64k bits/sec. This is
the brute force data rate for natural sounding speech. Notice that speech
requires less than 10% of the data rate of high fidelity music.
The data rate of 64k bits/sec represents the straightforward application of
sampling and quantization theory to audio signals. Techniques for lowering the
data rate further are based on compressing the data stream by removing the
inherent redundancies in speech signals. Data compression is the topic of
Chapter 27. One of the most efficient ways of compressing an audio signal is
Linear Predictive Coding (LPC), of which there are several variations and
subgroups. Depending on the speech quality required, LPC can reduce the data
rate to as little as 2-6k bits/sec. We will revisit LPC later in this chapter with
speech synthesis.
High Fidelity Audio
Audiophiles demand the utmost sound quality, and all other factors are treated
as secondary. If you had to describe the mindset in one word, it would be:
overkill. Rather than just matching the abilities of the human ear, these
systems are designed to exceed the limits of hearing. It's the only way to be
sure that the reproduced music is pristine. Digital audio was brought to the
world by the compact laser disc, or CD. This was a revolution in music; the
sound quality of the CD system far exceeds older systems, such as records and
tapes. DSP has been at the forefront of this technology.
The Scientist and Engineer's Guide to Digital Signal Processing 360
0.5 µm
pit width
1.6 µm
track spacing
0.8 µm minimum length 3.5 µm maximum length
direction
readout
FIGURE 22-5
Compact disc surface. Micron size pits
are burned into the surface of the CD to
represent ones and zeros. This results in
a data density of 1 bit per µm2, or one
million bits per mm2. The pit depth is
0.16 µm.
Figure 22-5 illustrates the surface of a compact laser disc, such as viewed
through a high power microscope. The main surface is shiny (reflective of
light), with the digital information stored as a series of dark pits burned on the
surface with a laser. The information is arranged in a single track that spirals
from the inside to the outside, the opposite of a phonograph record. The rotation
of the CD is changed from about 210 to 480 rpm as the information is read
from the outside to the inside of the spiral, making the scanning velocity a
constant 1.2 meters per second. (In comparison, phonograph records spin at a
fixed rate, such as 33, 45 or 78 rpm). During playback, an optical sensor
detects if the surface is reflective or nonreflective, generating the corresponding
binary information.
As shown by the geometry in Fig. 22-5, the CD stores about 1 bit per (µm)2,
corresponding to 1 million bits per (mm)2, and 15 billion bits per disk. This is
about the same feature size used in integrated circuit manufacturing, and for a
good reason. One of the properties of light is that it cannot be focused to
smaller than about one-half wavelength, or 0.3 µm. Since both integrated
circuits and laser disks are created by optical means, the fuzziness of light
below 0.3 µm limits how small of features can be used.
Figure 22-6 shows a block diagram of a typical compact disc playback system.
The raw data rate is 4.3 million bits per second, corresponding to 1 bit each
0.28 µm of track length. However, this is in conflict with the specified
geometry of the CD; each pit must be no shorter than 0.8 µm, and no longer
than 3.5 µm. In other words, each binary one must be part of a group of 3 to
13 ones. This has the advantage of reducing the error rate due to the optical
pickup, but how do you force the binary data to comply with this strange
bunching?
The answer is an encoding scheme called eight-to-fourteen modulation
(EFM). Instead of directly storing a byte of data on the disc, the 8 bits are
passed through a look-up table that pops out 14 bits. These 14 bits have the
desired bunching characteristics, and are stored on the laser disc. Upon
playback, the binary values read from the disc are passed through the inverse
of the EFM look-up table, resulting in each 14 bit group being turned back into
the correct 8 bits.
Chapter 22- Audio Processing 361
Reed-
Solomon
decoding
Sample
rate
converter
(×4)
14 bit
DAC
Bessel
Filter
Power
Amplifier
EFM
decoding
Optical
pickup
Speaker
Sample
rate
converter
(×4)
14 bit
DAC
Bessel
Filter
Power
Amplifier Speaker
(4.3 Mbits/sec)
serial data
(706 Kbits/sec)
16 bit samples
at 44.1 kHz 14 bit samples
at 176.4 kHz
Compact disc
Left channel
Right channel
FIGURE 22-6
Compact disc playback block diagram. The digital information is retrieved from the disc with an optical
sensor, corrected for EFM and Reed-Solomon encoding, and converted to stereo analog signals.
In addition to EFM, the data are encoded in a format called two-level Reed-
Solomon coding. This involves combining the left and right stereo channels
along with data for error detection and correction. Digital errors detected
during playback are either: corrected by using the redundant data in the
encoding scheme, concealed by interpolating between adjacent samples, or
muted by setting the sample value to zero. These encoding schemes result in
the data rate being tripled, i.e., 1.4 Mbits/sec for the stereo audio signals
versus 4.3 Mbits/sec stored on the disc.
After decoding and error correction, the audio signals are represented as 16 bit
samples at a 44.1 kHz sampling rate. In the simplest system, these signals
could be run through a 16 bit DAC, followed by a low-pass analog filter.
However, this would require high performance analog electronics to pass
frequencies below 20 kHz, while rejecting all frequencies above 22.05 kHz, ½
of the sampling rate. A more common method is to use a multirate technique,
that is, convert the digital data to a higher sampling rate before the DAC. A
factor of four is commonly used, converting from 44.1 kHz to 176.4 kHz. This
is called interpolation, and can be explained as a two step process (although
it may not actually be carried out this way). First, three samples with a value
of zero are placed between the original samples, producing the higher sampling
rate. In the frequency domain, this has the effect of duplicating the 0 to 22.05
kHz spectrum three times, at 22.05 to 44.1 kHz, 41 to 66.15 kHz, and 66.15
to 88.2 kHz. In the second step, an efficient digital filter is used to remove the
newly added frequencies.
The sample rate increase makes the sampling interval smaller, resulting in a
smoother signal being generated by the DAC. The signal still contains
frequencies between 20 Hz and 20 kHz; however, the Nyquist frequency has
been increased by a factor of four. This means that the analog filter only needs
to pass frequencies below 20 kHz, while blocking frequencies above 88.2 kHz.
This is usually done with a three pole Bessel filter. Why use a Bessel filter if
the ear is insensitive to phase? Overkill, remember?
The Scientist and Engineer's Guide to Digital Signal Processing 362
Since there are four times as many samples, the number of bits per sample can
be reduced from 16 bits to 15 bits, without degrading the sound quality. The sin(x)/x
correction needed to compensate for the zeroth order hold of the DAC can be
part of either the analog or digital filter.
Audio systems with more than one channel are said to be in stereo (from the
Greek word for solid, or three-dimensional). Multiple channels send sound to
the listener from different directions, providing a more accurate reproduction
of the original music. Music played through a monaural (one channel) system
often sounds artificial and bland. In comparison, a good stereo reproduction
makes the listener feel as if the musicians are only a few feet away. Since the
1960s, high fidelity music has used two channels (left and right), while motion
pictures have used four channels (left, right, center, and surround). In early
stereo recordings (say, the Beatles or the Mamas And The Papas), individual
singers can often be heard in only one channel or the other. This rapidly
progressed into a more sophisticated mix-down, where the sound from many
microphones in the recording studio is combined into the two channels.
Mix-down is an art, aimed at providing the listener with the perception of
being there.
The four channel sound used in motion pictures is called Dolby Stereo,
with the home version called Dolby Surround Pro Logic. ("Dolby" and
"Pro Logic" are trademarks of Dolby Laboratories Licensing Corp.). The
four channels are encoded into the standard left and right channels, allowing
regular two-channel stereo systems to reproduce the music. A Dolby
decoder is used during playback to recreate the four channels of sound. The
left and right channels, from speakers placed on each side of the movie or
television screen, is similar to that of a regular two-channel stereo system.
The speaker for the center channel is usually placed directly above or below
the screen. Its purpose is to reproduce speech and other visually connected
sounds, keeping them firmly centered on the screen, regardless of the
seating position of the viewer/listener. The surround speakers are placed
to the left and right of the listener, and may involve as many as twenty
speakers in a large auditorium. The surround channel only contains
midrange frequencies (say, 100 Hz to 7 kHz), and is delayed by 15 to 30
milliseconds. This delay makes the listener perceive that speech is coming
from the screen, and not the sides. That is, the listener hears the speech
coming from the front, followed by a delayed version of the speech coming
from the sides. The listener's mind interprets the delayed signal as a
reflection from the walls, and ignores it.
Companding
The data rate is important in telecommunication because it is directly
proportional to the cost of transmitting the signal. Saving bits is the same as
saving money. Companding is a common technique for reducing the data rate
of audio signals by making the quantization levels unequal. As previously
mentioned, the loudest sound that can be tolerated (120 dB SPL) is about onemillion
times the amplitude of the weakest sound that can be detected (0 dB
Chapter 22- Audio Processing 363
EQUATION 22-1
Mu law companding. This equation
provides the nonlinearity for µ255 law
companding. The constant, µ, has a
value of 255, accounting for the name
of this standard.
y ' ln(1%µx)
ln(1%µ ) for 0 # x # 1
y ' 1%ln(Ax )
1%ln(A) for 1/A # x # 1
for 0 # x # 1/A y ' Ax
1%ln(A)
EQUATION 22-2
"A" law companding. The constant, A,
has a value of 87.6.
SPL). However, the ear cannot distinguish between sounds that are closer than
about 1 dB (12% in amplitude) apart. In other words, there are only about 120
different loudness levels that can be detected, spaced logarithmically over an
amplitude range of one-million.
This is important for digitizing audio signals. If the quantization levels are
equally spaced, 12 bits must be used to obtain telephone quality speech.
However, only 8 bits are required if the quantization levels are made unequal,
matching the characteristics of human hearing. This is quite intuitive: if the
signal is small, the levels need to be very close together; if the signal is large,
a larger spacing can be used.
Companding can be carried out in three ways: (1) run the analog signal through
a nonlinear circuit before reaching a linear 8 bit ADC, (2) use an 8 bit ADC
that internally has unequally spaced steps, or (3) use a linear 12 bit ADC
followed by a digital look-up table (12 bits in, 8 bits out). Each of these three
options requires the same nonlinearity, just in a different place: an analog
circuit, an ADC, or a digital circuit.
Two nearly identical standards are used for companding curves: µ255 law (also
called mu law), used in North America, and "A" law, used in Europe. Both
use a logarithmic nonlinearity, since this is what converts the spacing
detectable by the human ear into a linear spacing. In equation form, the curves
used in µ255 law and "A" law are given by:
Figure 22-7 graphs these equations for the input variable, x, being between -1
and +1, resulting in the output variable also assuming values between -1 and
+1. Equations 22-1 and 22-2 only handle positive input values; portions of the
curves for negative input values are found from symmetry. As shown in (a),
the curves for µ255 law and "A" law are nearly identical. The only significant
difference is near the origin, shown in (b), where µ255 law is a smooth curve,
and "A" law switches to a straight line.
Producing a stable nonlinearity is a difficult task for analog electronics. One
method is to use the logarithmic relationship between current and
The Scientist and Engineer's Guide to Digital Signal Processing 364
Input
-1.0 0.0 1.0
-1.0
0.0
1.0
Input
-0.05 0.00 0.05
-0.5
0.0
0.5
a. µ law and A law b. Zoom of zero crossing
µ law
A law
Output
FIGURE 22-7
Companding curves. The µ255 law and "A" law companding curves are nearly identical, differing only near
the origin. Companding increases the amplitude when the signal is small, and decreases it when it is large.
Output
voltage across a pn diode junction, and then add circuitry to correct for the
ghastly temperature drift. Most companding circuits take another strategy:
approximate the nonlinearity with a group of straight lines. A typical scheme
is to approximate the logarithmic curve with a group of 16 straight segments,
called cords. The first bit of the 8 bit output indicates if the input is positive
or negative. The next three bits identify which of the 8 positive or 8 negative
cords is used. The last four bits break each cord into 16 equally spaced
increments. As with most integrated circuits, companding chips have
sophisticated and proprietary internal designs. Rather than worrying about
what goes on inside of the chip, pay the most attention to the pinout and the
specification sheet.
Speech Synthesis and Recognition
Computer generation and recognition of speech are formidable problems; many
approaches have been tried, with only mild success. This is an active area of
DSP research, and will undoubtedly remain so for many years to come. You
will be very disappointed if you are expecting this section to describe how to
build speech synthesis and recognition circuits. Only a brief introduction to the
typical approaches can be presented here. Before starting, it should be pointed
out that most commercial products that produce human sounding speech do not
synthesize it, but merely play back a digitally recorded segment from a human
speaker. This approach has great sound quality, but it is limited to the
prerecorded words and phrases.
Nearly all techniques for speech synthesis and recognition are based on the
model of human speech production shown in Fig. 22-8. Most human speech
sounds can be classified as either voiced or fricative. Voiced sounds occur
when air is forced from the lungs, through the vocal cords, and out of the mouth
and/or nose. The vocal cords are two thin flaps of tissue stretched across
Chapter 22- Audio Processing 365
Noise
Generator
Pulse train
Generator
Digital
Filter
unvoiced
voiced
pitch
vocal tract
response
synthetic
speech
FIGURE 22-8
Human speech model. Over a short segment of time, about 2 to 40 milliseconds, speech can be modeled by
three parameters: (1) the selection of either a periodic or a noise excitation, (2) the pitch of the periodic
excitation, and (3) the coefficients of a recursive linear filter mimicking the vocal tract response.
the air flow, just behind the Adam's apple. In response to varying muscle
tension, the vocal cords vibrate at frequencies between 50 and 1000 Hz,
resulting in periodic puffs of air being injected into the throat. Vowels are an
example of voiced sounds. In Fig. 22-8, voiced sounds are represented by the
pulse train generator, with the pitch (i.e., the fundamental frequency of the
waveform) being an adjustable parameter.
In comparison, fricative sounds originate as random noise, not from vibration
of the vocal cords. This occurs when the air flow is nearly blocked by the
tongue, lips, and/or teeth, resulting in air turbulence near the constriction.
Fricative sounds include: s, f, sh, z, v, and th. In the model of Fig. 22-8,
fricatives are represented by a noise generator.
Both these sound sources are modified by the acoustic cavities formed from the
tongue, lips, mouth, throat, and nasal passages. Since sound propagation
through these structures is a linear process, it can be represented as a linear
filter with an appropriately chosen impulse response. In most cases, a
recursive filter is used in the model, with the recursion coefficients specifying
the filter's characteristics. Because the acoustic cavities have dimensions of
several centimeters, the frequency response is primarily a series of resonances
in the kilohertz range. In the jargon of audio processing, these resonance peaks
are called the formant frequencies. By changing the relative position of the
tongue and lips, the formant frequencies can be changed in both frequency and
amplitude.
Figure 22-9 shows a common way to display speech signals, the voice
spectrogram, or voiceprint. The audio signal is broken into short segments,
The Scientist and Engineer's Guide to Digital Signal Processing 366
say 2 to 40 milliseconds, and the FFT used to find the frequency spectrum of
each segment. These spectra are placed side-by-side, and converted into a
grayscale image (low amplitude becomes light, and high amplitude becomes
dark). This provides a graphical way of observing how the frequency content
of speech changes with time. The segment length is chosen as a tradeoff
between frequency resolution (favored by longer segments) and time resolution
(favored by shorter segments).
As demonstrated by the a in rain, voiced sounds have a periodic time domain
waveform, shown in (a), and a frequency spectrum that is a series of regularly
spaced harmonics, shown in (b). In comparison, the s in storm, shows that
fricatives have a noisy time domain signal, as in (c), and a noisy spectrum,
displayed in (d). These spectra also show the shaping by the formant
frequencies for both sounds. Also notice that the time-frequency display of the
word rain looks similar both times it is spoken.
Over a short period, say 25 milliseconds, a speech signal can be approximated
by specifying three parameters: (1) the selection of either a periodic or random
noise excitation, (2) the frequency of the periodic wave (if used), and (3) the
coefficients of the digital filter used to mimic the vocal tract response.
Continuous speech can then be synthesized by continually updating these three
parameters about 40 times a second. This approach was responsible for one the
early commercial successes of DSP: the Speak & Spell, a widely marketed
electronic learning aid for children. The sound quality of this type of speech
synthesis is poor, sounding very mechanical and not quite human. However,
it requires a very low data rate, typically only a few kbits/sec.
This is also the basis for the linear predictive coding (LPC) method of
speech compression. Digitally recorded human speech is broken into short
segments, and each is characterized according to the three parameters of the
model. This typically requires about a dozen bytes per segment, or 2 to 6
kbytes/sec. The segment information is transmitted or stored as needed, and
then reconstructed with the speech synthesizer.
Speech recognition algorithms take this a step further by trying to recognize
patterns in the extracted parameters. This typically involves comparing the
segment information with templates of previously stored sounds, in an
attempt to identify the spoken words. The problem is, this method does not
work very well. It is useful for some applications, but is far below the
capabilities of human listeners. To understand why speech recognition is
so difficult for computers, imagine someone unexpectedly speaking the
following sentence:
Larger run medical buy dogs fortunate almost when.
Of course, you will not understand the meaning of this sentence, because it has
none. More important, you will probably not even understand all of the
individual words that were spoken. This is basic to the way that humans
Chapter 22- Audio Processing 367
Time (seconds)
0 0.5 1 1.5 2 2.5
0
1
2
3
4
5
The rain bow was seen after the rain storm
Frequency (kHz)
0 1 2 3 4 5
0
200
400
600
800
1000
d. Frequency domain: s in storm
Time (milliseconds)
0 2 4 6 8 10 12 14 16 18 20 22
1200
1400
1600
1800
2000
2200
2400
2600
2800
a. Time domain: a in rain
Time (milliseconds)
0 2 4 6 8 10 12 14 16 18 20 22
2000
2020
2040
2060
2080
2100
c. Time domain: s in storm
Frequency (kHz)
0 1 2 3 4 5
0
500
1000
1500
2000
2500
b. Frequency domain: a in rain
Frequency (kHz)
Amplitude Amplitude
Amplitude Amplitude (×10) FIGURE 22-9
Voice spectrogram. The spectrogram of the phrase: "The rainbow was seen after the rain storm." Figures
(a) and (b) shows the time and frequency signals for the voiced a in rain. Figures (c) and (d) show the time
and frequency signals for the fricative s in storm.
The Scientist and Engineer's Guide to Digital Signal Processing 368
perceive and understand speech. Words are recognized by their sounds, but
also by the context of the sentence, and the expectations of the listener. For
example, imagine hearing the two sentences:
The child wore a spider ring on Halloween.
He was an American spy during the war.
Even if exactly the same sounds were produced to convey the underlined words,
listeners hear the correct words for the context. From your accumulated
knowledge about the world, you know that children don't wear secret agents,
and people don't become spooky jewelry during wartime. This usually isn't a
conscious act, but an inherent part of human hearing.
Most speech recognition algorithms rely only on the sound of the individual
words, and not on their context. They attempt to recognize words, but not to
understand speech. This places them at a tremendous disadvantage compared
to human listeners. Three annoyances are common in speech recognition
systems: (1) The recognized speech must have distinct pauses between the
words. This eliminates the need for the algorithm to deal with phrases that
sound alike, but are composed of different words (i.e., spider ring and spy
during). This is slow and awkward for people accustomed to speaking in an
overlapping flow. (2) The vocabulary is often limited to only a few hundred
words. This means that the algorithm only has to search a limited set to find
the best match. As the vocabulary is made larger, the recognition time and
error rate both increase. (3) The algorithm must be trained on each speaker.
This requires each person using the system to speak each word to be
recognized, often needing to be repeated five to ten times. This personalized
database greatly increases the accuracy of the word recognition, but it is
inconvenient and time consuming.
The prize for developing a successful speech recognition technology is
enormous. Speech is the quickest and most efficient way for humans to
communicate. Speech recognition has the potential of replacing writing,
typing, keyboard entry, and the electronic control provided by switches and
knobs. It just needs to work a little better to become accepted by the
commercial marketplace. Progress in speech recognition will likely come from
the areas of artificial intelligence and neural networks as much as through DSP
itself. Don't think of this as a technical difficulty; think of it as a technical
opportunity.
Nonlinear Audio Processing
Digital filtering can improve audio signals in many ways. For instance, Wiener
filtering can be used to separate frequencies that are mainly signal, from
frequencies that are mainly noise (see Chapter 17). Likewise, deconvolution
can compensate for an undesired convolution, such as in the restoration of old
Chapter 22- Audio Processing 369
Frequency
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
6
7
8
9
10
a. Signal spectrum
Frequency
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
6
7
8
9
10
b. Noise spectrum
FIGURE 22-10
Spectra of speech and noise. While the frequency spectra of speech and noise generally overlap, there is some
separation if the signal segment is made short enough. Figure (a) illustrates the spectrum of a 16 millisecond
speech segment, showing that many frequencies carry little speech information, in this particular segment.
Figure (b) illustrates the spectrum of a random noise source; all the components have a small amplitude.
(These graphs are not of real signals, but illustrations to show the noise reduction technique).
Amplitude
Amplitude
recordings (also discussed in Chapter 17). These types of linear techniques are
the backbone of DSP. Several nonlinear techniques are also useful for audio
processing. Two will be briefly described here.
The first nonlinear technique is used for reducing wideband noise in speech
signals. This type of noise includes: magnetic tape hiss, electronic noise in
analog circuits, wind blowing by microphones, cheering crowds, etc. Linear
filtering is of little use, because the frequencies in the noise completely overlap
the frequencies in the voice signal, both covering the range from 200 hertz to
3.2 kHz. How can two signals be separated when they overlap in both the time
domain and the frequency domain?
Here's how it is done. In a short segment of speech, the amplitude of the
frequency components are greatly unequal. As an example, Fig. 22-10a
illustrates the frequency spectrum of a 16 millisecond segment of speech (i.e.,
128 samples at an 8 kHz sampling rate). Most of the signal is contained in a
few large amplitude frequencies. In contrast, (b) illustrates the spectrum when
only random noise is present; it is very irregular, but more uniformly
distributed at a low amplitude.
Now the key concept: if both signal and noise are present, the two can be
partially separated by looking at the amplitude of each frequency. If the
amplitude is large, it is probably mostly signal, and should therefore be
retained. If the amplitude is small, it can be attributed to mostly noise, and
should therefore be discarded, i.e., set to zero. Mid-size frequency components
are adjusted in some smooth manner between the two extremes.
Another way to view this technique is as a time varying Wiener filter. As
you recall, the frequency response of the Wiener filter passes frequencies
that are mostly signal, and rejects frequencies that are mostly noise. This
The Scientist and Engineer's Guide to Digital Signal Processing 370
requires a knowledge of the signal and noise spectra beforehand, so that the
filter's frequency response can be determined. This nonlinear technique uses
the same idea, except that the Wiener filter's frequency response is recalculated
for each segment, based on the spectrum of that segment. In other words, the
filter's frequency response changes from segment-to-segment, as determined by
the characteristics of the signal itself.
One of the difficulties in implementing this (and other) nonlinear techniques is
that the overlap-add method for filtering long signals is not valid. Since the
frequency response changes, the time domain waveform of each segment will
no longer align with the neighboring segments. This can be overcome by
remembering that audio information is encoded in frequency patterns that
change over time, and not in the shape of the time domain waveform. A typical
approach is to divide the original time domain signal into overlapping
segments. After processing, a smooth window is applied to each of the overlapping
segments before they are recombined. This provides a smooth transition
of the frequency spectrum from one segment to the next.
The second nonlinear technique is called homomorphic signal processing.
This term literally means: the same structure. Addition is not the only way
that noise and interference can be combined with a signal of interest;
multiplication and convolution are also common means of mixing signals
together. If signals are combined in a nonlinear way (i.e., anything other than
addition), they cannot be separated by linear filtering. Homomorphic
techniques attempt to separate signals combined in a nonlinear way by making
the problem become linear. That is, the problem is converted to the same
structure as a linear system.
For example, consider an audio signal transmitted via an AM radio wave. As
atmospheric conditions change, the received amplitude of the signal increases
and decreases, resulting in the loudness of the received audio signal slowly
changing over time. This can be modeled as the audio signal, represented by
, being multiplied by a slowly varying signal, , that represents the a[ ] g[ ]
changing gain. This problem is usually handled in an electronic circuit called
an automatic gain control (AGC), but it can also be corrected with nonlinear
DSP.
As shown in Fig. 22-11, the input signal, , is passed through the a [ ]×g [ ]
logarithm function. From the identity, log (x y) ' log x % log y, this results in
two signals that are combined by addition, i.e., . In other log a [ ] % log g [ ]
words, the logarithm is the homomorphic transform that turns the nonlinear
problem of multiplication into the linear problem of addition.
Next, the added signals are separated by a conventional linear filter, that is,
some frequencies are passed, while others are rejected. For the AGC, the
gain signal, , will be composed of very low frequencies, far below the g[ ]
200 hertz to 3.2 kHz band of the voice signal. The logarithm of these signals
will have more complicated spectra, but the idea is the same: a high-pass
filter is used to eliminate the varying gain component from the signal.
Chapter 22- Audio Processing 371
Logarithm
Linear
Filter
Anti- Logarithm
log a [ ] log a [ ] % log g [ ]
a [ ] × g [ ] a [ ]
FIGURE 22-11
Homomorphic separation of multiplied signals. Taking the logarithm of the input signal transforms
components that are multiplied into components that are added. These components can then be separated by
linear filtering, and the effect of the logarithm undone.
Fourier
Transform Logarithm
Linear
Filter
Anti- Inverse
Fourier
Transform
Logarithm
Homomorphic Transform Inverse Homomorphic Transform
X [ ]
log X [ ]
log X [ ] % log Y [ ]
X [ ] × Y [ ]
FIGURE 22-12
Homomorphic separation of convolved signals. Components that have been convolved are converted into
components that are added by taking the Fourier transform followed by the logarithm. After linear filtering
to separate the added components, the original steps are undone.
x [ ] x [ ] t y [ ]
In effect, is converted into . In the last step, the log a [ ] % log g [ ] log a[ ]
logarithm is undone by using the exponential function (the anti-logarithm, or
), producing the desired output signal, e
x a [ ].
Figure 22-12 shows a homomorphic system for separating signals that have
been convolved. An application where this has proven useful is in removing
echoes from audio signals. That is, the audio signal is convolved with an
impulse response consisting of a delta function plus a shifted and scaled delta
function. The homomorphic transform for convolution is composed of two
stages, the Fourier transform, changing the convolution into a multiplication,
followed by the logarithm, turning the multiplication into an addition. As
before, the signals are then separated by linear filtering, and the homomorphic
transform undone.
An interesting twist in Fig. 22-12 is that the linear filtering is dealing with
frequency domain signals in the same way that time domain signals are usually
processed. In other words, the time and frequency domains have been swapped
from their normal use. For example, if FFT convolution were used to carry out
the linear filtering stage, the "spectra" being multiplied would be in the time
domain. This role reversal has given birth to a strange jargon. For instance,
cepstrum (a rearrangment of spectrum) is the Fourier transform of the
logarithm of the Fourier transform. Likewise, there are long-pass and shortpass
filters, rather than low-pass and high-pass filters. Some authors even use
the terms Quefrency Alanysis and liftering.
The Scientist and Engineer's Guide to Digital Signal Processing 372
Keep in mind that these are simplified descriptions of sophisticated DSP
algorithms; homomorphic processing is filled with subtle details. For example,
the logarithm must be able to handle both negative and positive values in the
input signal, since this is a characteristic of audio signals. This requires the
use of the complex logarithm, a more advanced concept than the logarithm
used in everyday science and engineering. When the linear filtering is
restricted to be a zero phase filter, the complex log is found by taking the
simple logarithm of the absolute value of the signal. After passing through the
zero phase filter, the sign of the original signal is reapplied to the filtered
signal.
Another problem is aliasing that occurs when the logarithm is taken. For
example, imagine digitizing a continuous sine wave. In accordance with the
sampling theorem, two or more samples per cycle is sufficient. Now consider
digitizing the logarithm of this continuous sine wave. The sharp corners
require many more samples per cycle to capture the waveform, i.e., to prevent
aliasing. The required sampling rate can easily be 100 times as great after the
log, as before. Further, it doesn't matter if the logarithm is applied to the
continuous signal, or to its digital representation; the result is the same.
Aliasing will result unless the sampling rate is high enough to capture the sharp
corners produced by the nonlinearity. The result is that audio signals may need
to be sampled at 100 kHz or more, instead of only the standard 8 kHz.
Even if these details are handled, there is no guarantee that the linearized
signals can be separated by the linear filter. This is because the spectra of the
linearized signals can overlap, even if the spectra of the original signals do not.
For instance, imagine adding two sine waves, one at 1 kHz, and one at 2 kHz.
Since these signals do not overlap in the frequency domain, they can be
completely separated by linear filtering. Now imagine that these two sine
waves are multiplied. Using homomorphic processing, the log is taken of the
combined signal, resulting in the log of one sine wave plus the log of the other
sine wave. The problem is, the logarithm of a sine wave contains many
harmonics. Since the harmonics from the two signals overlap, their complete
separation is not possible.
In spite of these obstacles, homomorphic processing teaches an important
lesson: signals should be processed in a manner consistent with how they are
formed. Put another way, the first step in any DSP task is to understand how
information is represented in the signals being processed.