Hearing. 1 Introduction. 1.1 Auditory system. 1.2 Psychoacoustics

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1 Hearing Sources: Rossing. (1990). The science of sound. Chapters 5 7. Karjalainen. (1999). Kommunikaatioakustiikka. Moore. (1997). An introduction to the psychology of hearing. Contents: 1. Introduction 2. Ear physiology 3. Masking 4. Sound pressure level 5. Loudness 6. Pitch 7. Spatial hearing Hearing 1 1 Introduction! Auditory system can be divided in two parts Peripheral auditory system (outer, middle, and inner ear) Auditory nervous system (in the brain) Hearing 2! Ear physiology studies the peripheral system! Psychoacoustics studies the entire sensation: relationships between sound stimuli and the subjective sensation 1.1 Auditory system Hearing Psychoacoustics Hearing 4! Dynamic range of hearing is wide ratio of a very loud to a barely audible sound pressure level is 1:10 5 (powers 1:10 10, 100 db)! Frequency range of hearing varies a lot between individuals only few can hear from 20 Hz to 20 khz sensitivity to low sounds (< 100Hz) is not very good sensitivity to high sounds (> 12 khz) decreases along with age! Selectivity of hearing listener can pick an instrument from among an orchestra listener can follow a speaker at a cocktail party One can sleep in background noise but still wake up to an abnormal sound! Perception involves information processing in the brain Information about the brain is limited! Psychoacoustics studies the relationships between sound stimuli and the resulting sensations Attempt to model the process of perception For example trying to predict the perceived loudness / pitch / timbre from the acoustic properties of the sound signal! In a psychoacoustic listening test Test subject listens to sounds Questions are made or the subject is asked to describe her sensasions

2 2 Ear physiology Hearing Outer ear Hearing 6! The human ear consists of three main parts: (1) outer ear, (2) middle ear, (3) inner ear! Outer ear consists of: pinna gathers sound; direction-dependent response auditory canal (ear canal) - conveys sound to middle ear Nerve signal to brain [Chittka05] 2.2 Middle ear Hearing Inner ear, cochlea Hearing 8! Middle ear contains Eardrum that transforms sound waves into mechanic vibration Tiny audtory bones: hammer (resting against the eardrum, see figure), anvil and stirrup! The bones transmit eardrum vibrations to the oval window of the inner ear! Acoustic reflex: when sound pressure level exceeds ~80 db, eardrum tension increases and stirrup is removed from oval window Protects the inner ear from damage! The inner ear contains the cochlea: a fluid-filled organ where vibrations are converted into nerve impulses to the brain.! Cochlea = Greek: snail shell.! Spiral tube: When stretched out, approximately 30 millimeters long.! Vibrations on the cochlea s oval window cause hydraulic pressure waves inside the cochlea! Inside the cochlea there is the basilar membrane,! On the basilar membrane there is the organ of Corti with nerve cells that are sensitive to vibration! Nerve cells transform movement information into neural impulses in the auditory nerve

3 2.4 Basilar membrane Hearing 9 Basilar membrane Hearing 10! Figure: cochlea stretched out for illustration purposes Basilar membrane divides the fluid of the cochlea into separate tunnels When hydraulic pressure waves travel along the cochlea, they move the basilar membrane! Different frequencies produce highest amplitude at different sites! Preliminary frequency analysis happens on the basilar membrane Travelling waves: Best freq (Hz) 2.5 Sensory hair cells Hearing 11 3 Masking Hearing 12! Distributed along the basilar membrane are sensory hair cells that transform membrane movement into neural impulses! When a hair cell bends, it generates neural impulses Impulse rate depends on vibrate amplitude and frequency! Each nerve cell has a characteristic frequency to which it is most responsive to (Figure: tuning curves of 6 different cells)! Masking describes the situation where a weaker but clearly audible signal (maskee, test tone) becomes inaudible in the presence of a louder signal (masker)! Masking depends on both the spectral structure of the sounds and their variation over time

4 3.1 Masking in frequency domain Hearing 13 Masking in frequency domain Hearing 14! Model of the frequency analysis in the auditory system subdivision of the frequency axis into critical bands frequency components within a same critical band mask each other easily Bark scale: frequency scale that is derived by mapping frequencies to critical band numbers! Narrowband noise masks a tone (sinusoidal) easier than a tone masks noise! Masked threshold refers to the raised threshold of audibility caused by the masker sounds with a level below the masked threshold are inaudible masked threshold in quiet = threshold of hearing in quiet! Figure: masked thresholds [Herre95] masker: narrowband noise around 250 Hz, 1 khz, 4 khz spreading function: the effect of masking extends to the spectral vicinity of the masker (spreads more towards high freqencies)! Additivity of masking: joint masked thresh is approximately (but slightly more than) sum of the components 3.2 Masking in time domain Hearing 15 Masking: Examples Hearing 16! Forward masking masking effect extends to times after the masker is switched off! Backwards masking masking extends to times before the masker is been switched on! Forward/backward masking does not extend far in time " simultaneous masking is more important phenomenon backward masking forward masking! A single tone is played, followed by the same tone and a higher frequency tone. HF tone is reduced in intensity first by 12 db, then by steps of 5 db. Sequence repeats twice: second time the frequency separation between the tones is increased.! Attempt to mask higher frequencies! Attempt to mask lower frequencies (not masked as easily)

5 Application to audio steganography Hearing 17 4 Sound pressure level Hearing 18! Idea: hide a message in the audio data, keeping the message inaudible yet decodable! Example Here robustness to environmental noise was important! Sound signal s 1 (t) at time t represents pressure deviation from normal atmospheric pressure 2! Sound pressure p is the (linear) RMS-level RMS = E{()} s t of the signal E{ } denotes expectation (RMS = root-mean-square level)! Due to the wide dynamic range, decibel scale is convenient p db = 20 log10 (p RMS / p 0 ) = L p where p 0 is a reference pressure 4.1 Threshold of hearing and db scale Hearing Multiple sources Hearing 20! Threshold of hearing Weakest audible sound pressure at 1 khz frequency is 20 µpa, which has been chosen to be the reference level p 0 of the dbscale L p = 20 log 10 (p/p 0 ) = 10 log 10 (p 2 /p 02 )! Threshold of pain Loudest sound that the auditory system can meaningfully deal with khz! Two sound sources: s(t) = s 1 (t) + s 2 (t)! RMS pressure level of the summary signal: p = E{()} s t = E{ s () t + 2 s () t s () t + s ()} t RMS ! If the signals are uncorrelated Es { 1( ts ) 2( t )} = 0 and the above formula simplifies to p = p + p RMS If p 1 = p 2, the sound pressure level of the summary signal is 3 db higher than that of p 1 (why?)

6 Multiple sources Hearing 21 5 Loudness Hearing 22! Two sources with 80 db sound pressure level Source signals uncorrelated: together produce 83 db level Sources correlate perfectly (same sound): results in 86 db level! Doubling the sound amplitude increases the sound pressure level by 6 db Because: L p = 20 log 10 (2 p/p 0 ) = 20 log 10 (p/p 0 ) + 6 [db] Equivalent to adding another identical source next to the first one! Intuitively: if the two sources do not correlate, the components of the two audio signals may amplify or cancel out each other, depending on their relative phases, and hence the level will be only 83 db! Loudness describes the subjective level of sound Perception of loudness is relatively complex, but consistent phenomenon and one of the central parts of psychoacoustics! The loudness of a sound can be compared to a standardized reference tone, for example 1000 Hz sinusoidal tone Loudness level (phon) is defined to be the sound pressure level (db) of a 1000 Hz sinusoidal, that has the the same subjective loudness as the target sound For example if the heard sound is perceived as equally loud as 40 db 1kHz sinusoidal, is the loudness level 40 phons 5.1 Equal-loudness curves Hearing Critical bands Hearing 24 Sound pressure level (db) Loudness level (phons)! Listening to two sinusoids with nearby frequencies and increasing their frequency difference, the perceived loudness increases when the frequency difference exceeds critical bandwidth Figure: 1 60 db, Critical bandwidth is 160 Hz at 1 khz! Ear analyzes sound at critical band resolution. Each critical band contributes to the overall loudness level Frequency (Hz)

7 5.4 Loudness of a complex sound Hearing 25 6 Pitch Hearing 26! Loudness of a complex sound is calculated by using so-called loudness density as intermediate unit! Loudness density at each critical band is (roughly) proportional to the log-power of the signal at the band (weighted according to sensitivity of hearing and spread slightly by convolving over frequency)! Overall loudness is obtained by summing up loudness density values from each critical band! Figure: integration of loudness for a sinusoidal tone and for wideband noise Loudness density (sones / Bark) Frequency / Bark! Pitch Subjective attribute of sounds that enables us to arrange them on a frequency-related scale ranging from low to high Sound has a certain pitch if human listaners can consistently match the frequency of a sinusoidal tone to the pitch of the sound! Fundamental frequency vs. pitch Fundamental frequency is a physical attribute Pitch is a perceptual attribute Both are measured in Hertz (Hz) In practise, perceived pitch fundamental frequency! "Perfect pitch" or "absolute pitch" - ability to recognize the pitch of a musical note without any reference Minority of the population can do that 6.1 Harmonic sound Hearing Pitch perception Hearing 28! For a sinusoidal tone Fundamental frequency = sinusoidal frequency Pitch sinusoidal frequency! Harmonic sound Trumpet sound: * Fundamental frequency F = 262 Hz * Wavelength 1/F = 3.8 ms! Pitch perception has been tried to explain using two competing theories Place theory: Peak activity along the basilar membrane determines pitch (fails to explain missing fundamental) Periodicity theory: Pitch depends on rate, not place, of response. Neurons fire in sync with signals! The real mechanism is a combination of the above Sound is subdivided into subbands (critical bands) Periodicity of the amplitude envelope (see lowest panel) is analyzed within bands Results are combined across bands

8 6.3 Perceptually-motivated frequency scales Hearing 29 Subjective attributes of sound Hearing 30 mm. on basilar membrane frequency / khz frequency / mel! Sounds are typically described using four main attributes loudness, pitch, timbre, and duration! Table: dependence of the subjective attributes on physical parameters = strongly dependent, = to some extent = weak dependency Subjective attribute Loudness Pitch Timbre Duration frequency / Bark Physical parameter Pressure Frequency Spectrum Duration Envelope 7 Spatial hearing Hearing Monaural source localization Hearing 32! The most important auditory cues for localizing a sound sources in space are 1. Interaural time difference 2. Interaural intensity difference 3. Direction-dependent filtering of the sound spectrum by head and pinnae! Terms Monaural : with one ear Binaural : with two ears Interaural : between the ears (interaural time difference etc) Lateralization : localizing a source in horizontal plane! Diretional hearing works to some extent even with one ear! Head and pinna form a direction-dependent filter Direction-dependent changes in the spectrum of the sound arriving in the ear can be described with HRTFs HRTF = head-related transfer function! HRTFs are crucial for localizing sources in the median plane (vertical localization)

9 Monaural source localization Hearing Localizing a sinusoidal Hearing 34! HRTFs can be measured by recording Sound emitted by a source Sounds arriving to the auditory canal or eardrum (transfer function of the auditory canal does not vary along with direction)! In practice left: microphone in the ear of a test subject, OR right: head and torso simulator! Experimenting with sinusoidal tones helps to understand the localization of more complex sounds! Angle-of-arrival perception for sinusoids below 750 Hz is based mainly on interaural time difference Localizing a sinusoidal Hearing Localizing complex sounds Hearing 36! Interaural time difference is useful only up to 750 Hz Above that, the time difference is ambiguous, since there are several wavelengths within the time difference Moving the head (or source movement) helps: can be done up to 1500 Hz! At higher frequencies (> 750 Hz) the auditory system utilizes interaural intensity difference Head causes and acoustic shadow (sound level is lower behind the head) Works especially at high frequencies! Complex sounds refer to sounds that involve a number of different frequency components and vary over time! Localizing sound sources is typically a result of combining all the above-described mechanisms 1. Interaural time difference (most important) 2. Interaural intensity difference 3. HRTFs! Wideband noise: directional hearing works well

10 7.4 Lateralization in headphone listening Hearing 37! When listening with headphones, the sounds are often localized inside the head, on the axis between the ears Sound does not seem to come from outside the head because the diffraction caused by pinnae and head is missing If the sounds are processed with HRTFs carefully, they move outside the head