Chapter 1: Introduction to digital audio

Transcription

1 Chapter 1: Introduction to digital audio Applications: audio players (e.g. MP3), DVD-audio, digital audio broadcast, music synthesizer, digital amplifier and equalizer, 3D sound synthesis 1

2 Properties of Sound Sound is what we call the air pressure variations generated by moving objects. It is a continuous acoustics wave that travels through the air. Sound waves are longitudinal waves, which means the particle movement caused by the wave is parallel to the direction of propagation. They propagate in three dimensions with compressible gas as medium. Sound waves have normal wave properties (reflection, refraction, diffraction, etc.) 2

3 Properties of Sound Sound intensity is directly related to the acoustic power per unit area, we must consider both the pressure and velocity aspects of sound waves in order to explain the interaction of a sound wave with a microphone or an ear. The relationship between pressure change and volume change is described by the bulk modulus (B) of the gas: where is the change in pressure, is the percent change in volume. The bulk modulus and density determine the velocity of propagation: where ρ is density. The speed of sound is about 330m/s at room temperature and sea level atmosphere. The sound waves propagate outward as an expanding sphere of concentric pressure variations. The pressure variation decreases in amplitude as it occupies a larger and larger volume of air. 3

4 Properties of Sound When we hear sounds, the perceived loudness is determined by the amount of power transmitted from the source to our ears. The intensity of a sound is the power per unit area received at the sensing device. The intensity received from a point source decreases with the square of the distance from the source. We commonly use sound pressure levels (SPL) as the measure of sound amplitude. Unlike intensity, sound pressure levels decrease linearly with distance from the source. This results in a 6 db decrease in SPL for a doubling of distance Human has an audible SPL range from 0dB to about 140 db within the frequency range from 50Hz to 20kHz. 4

5 Properties of Sound Waves interact with objects based on the dimensions of the object relative to the wavelength of the sound. Wavelengths much longer than an object will smoothly bend around edges and spread out in space. Wavelengths shorter than the dimensions of an object will shadow like light: they behave more as beams. In between the extremes, waves may bend partially as they encounter a surface edge. This is known as diffraction. Reflection occurs when a wave strikes a fixed object and bounces back. Sound waves reflect at the same angle at which they encounter an object. Since each collision absorbs some of the sound energy, repeated reflections will ultimately cause the sound to decay and since each collision removes energy in a frequencydependent way, the timbre of the sound changes as well as the intensity. The shape and dimensions of a space largely determine how sounds are altered as they radiate and decay inside that space. The dimensions are important because the distance a sound must traverse on its path from source to sensor will shape the cancellations and reinforcements that occur as a function of the wavelengths present. The reinforcement of certain frequencies may occur is by resonance. The resonances of a room will color the sound of reverberation as certain frequencies reinforce and others do not. 5

6 Sound Transduction Conversion of vibrations in an instrument or loudspeaker into vibrations of air molecules Conversion of air vibrations into mechanical vibrations, then ultimately into electrical oscillations in a microphone or electrochemical signals in the nervous system Microphone Transduction of sound pressure waves into electromagnetic signals There are several types of microphone: dynamic (moving coil and ribbon), capacitor (also known as condenser) are the main types. Each type has particular strengths and weaknesses. Choosing a microphone is much like selecting an instrument: there is no single ideal microphone for a given situation, but some types of sound better than others for particular applications. 6

7 Sound Transduction Microphone 7

8 Sound Transduction Dynamic Microphone For moving coil dynamic microphone, the signal is created when a coil of wire attached to a diaphragm moves in and out, through a magnetic field, as the air pressure changes. An electrical signal is created by induction as the wires in the coil cut through the magnetic field. The mass of the moving parts must be very low, so that it does not require much energy to move the diaphragm. The mass of the assembly limits the high-frequency response of the dynamic microphone. Dynamic microphones tend to be quite sturdy and of low cost, so they are commonly used to record drums, amplifier outputs, human voices, and other sources which produce high sound pressure levels. 8

9 Sound Transduction Capacitor Microphone Commonly called condenser microphones, these microphones function by making the diaphragm one plate of a capacitor. As the diaphragm vibrates, it changes the capacitance of the capacitor in proportion to the sound pressure level. The capacitance is converted to a voltage by a special amplifier inside the microphone. Since this requires outside power, capacitor microphones require a battery or external power supply (known as phantom power because it is transmitted back over the same cable as the output signal by a special technique). The capacitor itself must be charged, so some electricity must be used to polarize the capacitor. The mass of the diaphragm can be much smaller than that of a dynamic diaphragm, the capacitor microphone is usually better suited to high-frequency sound transduction. Condenser microphones have very high impedances. Electret microphone replace the phantom voltage power with a permanently charged material, e.g. Telfon, so there is no need for external power supply 9

10 Sound Transduction Microphone polar patterns Each microphone exhibits a pattern of directional sensitivity: that is, it is more sensitive to sounds arriving from certain directions. The sensitivity of the microphone to sounds from a particular direction is indicated by the radius from the center of the plot to the perimeter at the angle in question. Sensitivity is measured in terms of voltage output for a given sound pressure level input. In addition to the sensitivity, the frequency response of the microphone also varies as the angle of incidence of the sound changes. The so-called off-axis response affects the microphone sound as it colors the sounds coming from the sides and rear of the microphone. 10

11 Sound Transduction Selection of microphone 1. The main selection criterion is the microphone s sensitivity in volts/db SPL, eg. -75 db re: 1V/mbar, 10 mbar = 1 pascal = 94 db SPL 2. Noise inherent in the microphone, i.e., self-noise or equivalent input noise. Noise in dynamic microphones is generated by random thermal processes that are impedance related, hence the low-impedance of most microphones. Noise in capacitor microphones is mostly generated in the internal electronic circuitry. 3. Spacial sensitivity (i.e., polar pattern) 4. Maximum sound pressure that can be transduced. Overloads in dynamic mics are generated by the physical limits of the diaphragm, which is mechanically damped, allowing very high sound pressure levels (up to 140 db SPL) to pass undistorted. Overloads in capacitor mics usually occur at the limits of the electronics power supply voltage rather than due to physical excursion limits in the sensing capsule. Even capacitor mics can usually handle SPLs up to 130 db SPL, with many capable of transducing SPLs up to 160 db SPL with the use of internal pads (attenuators). 11

12 Sound Transduction Loudspeaker Loudspeakers convert electrical energy into sound pressure waves. Basic construction: a cone of paper or paper-like material is suspended within a frame, and connected to the loudspeaker's input. A permanent magnet surrounds the center of the cone, and as alternating current is applied to the loudspeaker cone, changes in the magnetic field potential causes the cone to move away from or towards the permanent magnet. 12

13 Sound Transduction Loudspeaker Most loudspeaker cabinets and their components share similar design characteristics. Because of the large range of frequencies that are needed to properly reproduce the audible range of sound, in most cases, more than one component is used. A loudspeaker component, called a driver, that reproduces the lower frequencies of sound is called a woofer, while a component that is dedicated to reproducing higher frequencies is called a tweeter. Midrange driver is the name given to a component that is designed to reproduce the middle frequencies. Since low frequency sounds have a larger wavelength, low-frequency drivers tend to be larger. Loudspeaker Enclosure A primary function of a speaker enclosure is to keep the sound coming from the back of a driver cone from going into the room. All drivers should have their own individual enclosures. Loudspeaker Placement Coverage angle, intended coverage, system designs. Sound reproduction is about creating illusions in our mind. 13

14 Sound Transduction Loudspeaker Characteristics Frequency response, Phase response, Shape, Impedance, Powered, unpowered, Coverage angle. A set of priorities for loudspeaker design: Low non-linear distortion, e.g. drivers that can move sufficient amounts of air linearly in all parts of the frequency range but especially at the low end. Minimal excitation of room resonances, particularly at low frequencies. This requires low frequency directional speakers such as dipoles. Low amounts of stored energy in drivers, cabinet, air cavities and filters for fast transient decays. Smooth, extended frequency response from 20 Hz on up and without exaggerated high frequencies, both on-axis and off-axis. Minimal rolloff in power response There are additional requirements, such as an acoustic center for the speaker at ear height, vertical extension of the source, etc. 14

15 Hearing and Human Auditory System The functional role of the central structures of the auditory system, namely, the nervous pathway and the parts of the brain that govern sound reception, is still not fully known. However, it is clear that the transformations of the acoustics environment produced by the peripheral structures are central to the sound processing functions of the auditory system. The nervous system s cognitive response to sound stimuli is known as psychoacoustics: it is partly acoustics and partly psychology. Human Ear partitioned into an outer, middle and inner ear Outer ear (pinna, ear canal) gathers and focuses sound onto the eardrum, Pinna: source elevation information, front-to-rear discrimination Ear canal: introduces nonlinear effects in the frequency domain. The resonant frequency falls in the same range as the peak in our sensitivity: around 3kHz, and creates a maximum boost of about 10 db. 15

16 Hearing and Human Auditory System Human Ear The middle ear contains a complicated linkage of bones for the transformation of time variations in air pressure to time variations in fluid pressure in the cochlea. It acts as an impedance matching device. The cochlea is a coiled, fluid-filled structure located in the inner ear. It is a dual-purpose structure: it converts mechanical vibrations into neuronal electrical signals and it separates the frequency content of the incoming sound into discrete frequency bands. Signal processing in the cochlea Fluid variations are conveyed to the nervous system through sensory cells embedded in the basilar membrane, a fibrous tissue which extends through the middle of the cochlea. 16

17 Hearing and Human Auditory System Signal processing in the cochlea The basilar membrane supports travelling waves along its extent. The stationary envelope of the travelling wave reaches a maximum at specific sites along the membrane which are proportional to the frequency components of the sound. Because the basilar membrane is narrow and stiff at the base of the cochlea, and wide and flexible at the tip of the cochlea, the site of maximum excursion of the travelling wave is near the opening onto the middle ear for high frequencies, and toward the cochlea tip for low frequencies. 17

18 Hearing and Human Auditory System Signal processing in the cochlea Sensory receptors, known as hair cells, reside on the basilar membrane. There are approximately 3,500 inner hair cells and 20,000 outer hair cells The inner hair cells detect the velocity of the passing fluid. The motion induces an electrical potential change across the hair cell membranes. Each inner hair cell responds optimally to simulation at a characteristic frequency. Stimulation with tones on either side of the characteristic frequency results in diminished cellular response. Inner hair cells also display a form of contrast enhancement. In the auditory system, this effect is known as two-tone suppression. Cells which are stimulated with a tone at the characteristic frequency and with additional tones above and below the characteristic frequency will not respond as strongly for frequencies around the characteristic frequency. The outer hair cells are not sensory detectors. In fact, these cells receive efferent connections from higher centers within the auditory system. The outer hair cells form the terminal point in an Automatic Gain Control (AGC) loop. These cells provide positive feedback by pushing in the direction of motion. Inhibition from higher centers decreases the activity of the outer hair cells, resulting in natural signal damping. Thus, the outer hair cells act as effectors of an AGC loop which performs early signal processing resulting in an increased range of sensitivity. 18

19 Hearing and Human Auditory System Signal processing in the cochlea Communication of hair cell response to nervous system is achieved via the auditory nerve. Studies of the manner in which the auditory nerve conveys stimulus information have focus on two parallel representations. The classical interpretation of the auditory nerve representation is based on the premise that each ascending nerve fibre innervates a specific portion of the basilar membrane. Since each fibre innervates a single inner hair cell, and each inner hair cell is sensitive to a particular frequency in the stimulus, the fibers themselves are "labeled" by frequency. Thus the fibers of the auditory nerve fire optimally at a characteristics frequency, and these fibers are organized to preserve the innervation pattern on the basilar membrane. Therefore, the auditory nerve fibers are said to be organized tonotopically. In this interpretation, the auditory system conveys stimulus spectral content by the average firing rate in each of the fibers of the auditory nerve. This representation is called the rate-place representation. 19

20 Hearing and Human Auditory System Signal processing in the cochlea An alternative interpretation arises from the observation that the auditory nerve fibers are capable of firing in synchrony with the stimulus. Fibers which innervate the inner hair cells near the apex of the cochlea are stimulated by low-frequency components. If the duration of the stimulus is longer than the duration of an action potential (1 ms), then the fibers are phase-locked to the stimulus. These fibers are capable of representing the temporal properties of the signal because their activity is directly correlated with time-varying amplitude components of the signal. For stimuli whose period is shorter than 1 ms, the auditory fibers are able to phase-lock to multiples of the stimulus period. This suggests a representation of the firing patterns of the auditory nerve which is referred to as a "temporalplace" code because the "temporal" measure of synchronization is computed only for those fibers with a specific characteristic frequency. The pattern of firing activity across auditory nerve fibers reflects the power in the individual spectral components of the stimulus. Thus the rate-place code represents spectral peaks. The rate-place code is highly sensitive to stimulus and ambient noise level while the temporal-place code is relatively insensitive to stimulus amplitude. Temporal-place representation preserves spectrum peaks even for rapid spectral changes in sounds. The temporal-place representation is capable of retaining detailed spectral information for large stimulus amplitudes. The temporal-place representation appears to be more robust for periodic stimuli. The temporal-place representation is derived from the synchronization behavior of the auditory fibers, and this property is observed primarily in low to moderate frequency regions. 20

21 Human Auditory Perception Our auditory system is incredibly sensitive, allowing perception over many orders of magnitude in both amplitude and frequency. We can discriminate tiny changes in sound timbres and accurately determine where in space a sound originates. We process sound information through our hearing organs and our perception includes distortions: alterations in the way sounds are transmitted and converted to neuronal signals and in the way our brain interprets these inputs and renders for us what we refer to as hearing. Human ears can hear in the range of 16 Hz to about 20 khz. This will change with age. Hence, wavelengths vary from 21.3 m to 1.7 cm. The intensity of sound can be measured in terms of Sound Pressure Level (SPL) in decibels (dbs). Intensity level = db, Where and are values of acoustic power, and will deliver an intensity of sound at the threshold of hearing, which is W/m2 (watts per square meter). The ear is a remarkably complex device. Through it our perception of sound is characterized by a high frequency resolution and excellent frequency discrimination (tones differing by as little as 0.3% being discriminable), a wide dynamic range of over 120 db, a fine temporal resolution (able to detect differences as small as 10 µs in the timing of clicks presented to the two ears), and rapid temporal adaptation (faint sounds being audible as little as 10 ms after the cessation of a moderately loud sound). 21

22 Human Auditory Perception Loudness Perception The sensitivity of the human ear is not the same for tones of all frequencies. It is most sensitive to frequencies in the range 1000 to 4000 Hz. Low- and high-frequency sounds require a higher intensity sound to be just audible, and our concept of loudness also varies with frequency. The diagram below shows the hearing threshold curve as a function of frequency. 22

23 Human Auditory Perception Pitch Perception Distinguishing audible tones by pitch enables us to order them on a musical scale. The pitch perception may be explained by two different theories. The place theory relates the pitch of a tone to the place of maximum excitation on the basilar membrane. The temporal theory relates pitch to the time patterns of neural impulses. For pure tones, the ear can detect a frequency difference of about 2 Hz for a 1000 Hz tone at about db SPL. Accuracy is better for middle range frequencies and for longer duration tones. For complex tones, the ear is able to hear out some of the individual partials within a complex tone. Frequency Selectivity and Masking The perception of frequency components in a sound can be detected by a series of overlapping bandpass filters centred continuously at frequencies throughout the normal range of hearing. The ability to discriminate between two simultaneously presented sounds which contain frequencies that are very close is limited to the width of one of these auditory bandpass filters the critical band. The concept of frequency selectivity explains a very common perceived effect that of masking. Briefly, a sound is masked if it cannot be heard in the presence of another sound. The hearing threshold can be changed when there is another sound appeared. 23

24 Human Auditory Perception More on critical bands and frequency masking Human auditory system has a limited, frequency-dependent resolution. The perceptually uniform measure of frequency can be expressed in terms of the width of the Critical Bands. It is less than 100 Hz at the lowest audible frequencies, and more than 4 khz at the high end. All together, the audio frequency range can be partitioned into 25 critical bands. Bark Scale A new unit for frequency bark (after Barkhausen) can be defined according to the critical bands: 1 Bark = width of one critical band 24

25 Human Auditory Perception An Experiment: Put a person in a quiet room. Raise the magnitude level of 1 khz tone until just barely audible. Vary the frequency and plot Play 1 khz tone (masking tone) at fixed level of 60 db. Play a second tone (test tone) at a different level (e.g., 1.1 khz), and raise the level until it is just distinguishable. Vary the frequency of the test tone and plot the threshold when it becomes audible: Repeat for various frequencies of masking tones 25

26 Human Auditory Perception Temporal masking If we hear a loud sound, then it stops, it takes a little while until we can hear a soft tone nearby. Experiment: Play 1 khz masking tone at 60 db, plus a test tone at 1.1 khz at 40 db. Test tone can't be heard (it's masked). Stop masking tone, then stop test tone after a short delay. Adjust delay time to the shortest time when test tone can be heard (e.g., 5 ms). Repeat with different level of the test tone and plot: Total effect of both frequency and temporal maskings 26