Psycho-acoustics (Sound characteristics, Masking, and Loudness)

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1 Psycho-acoustics (Sound characteristics, Masking, and Loudness) Tai-Shih Chi ( 冀泰石 ) Department of Communication Engineering National Chiao Tung University Mar. 20, 2008

2 Pure tones Mathematics of the pure tone xt ( ) = Asin(2 π ft+ φ) f in Hz (cycles/sec) where = Asin( ωt+ φ) ω in rad/sec = Asin Θ Θ in radians Θ=Θ ( t) = ωt+ φ RMS (Root-Mean-Square) value: x = A/ 2 = 0.707A RMS Unique nature of a pure tone Wave shape unchanged after linear operation eigen function Easy to retain control in psychoacoustic experiments Sound of a pure tone Low frequency (<200 Hz) pure tone: dull High frequency (>2000 Hz) pure tone: bright f = [300,500,1000,1500, 2000, 2500];

3 Measurement of sound level db (decibel) L L (in Bels) = log( P / P) L L (in decibels) = 10log( P / P) = 20log( A / A ) 2 1 Sound intensity Sound intensity is defined as acoustical power per unit area. Sound pressure level (SPL): a reference sound intensity in air, which was chosen to be close to the average absolute threshold of humans for a 1000 Hz sinusoid (10 W/m ). Sensation level (SL): a reference level above the threshold of a particular subject for a particular sound. Sound pressure level decreases about 6 db each time the distance from the source doubles.

4 Sound level demonstration Broadband noise is reduced in 10 steps of 6 db. Broadband noise is reduced in 15 steps of 3 db. Constant power speech at [25, 50, 100, 200] cm from the mic.

5 Loudness (Size) Constancy Is the sound source moved further away or just with decreased intensity? Other cues (timbre, reflections, etc.) would help in reality

6 Fourier analysis of the complex sound for a periodic complex sound S ( t) = A sin(2 π f t + φ ) f = i f i i i i i 1 1st harmonic f1= fundamental frequency ( 基頻 ) 2nd harmonic f2= first overtone ( 泛頻 )

7 Filters and their properties Filters are used to manipulate the spectra of the stimuli in a certain way. Filters are generally linear devices: sinusoidal input sinusoidal output with the same frequency Lowpass, bandpass and highpass filters. Peripheral auditory system (cochlea) is likened to a bank of (constant Q) bandpass filters with different center frequencies. Impulse response versus bandwidth Bandwidth: 3dB (-3 db) bandwidth 10 db bandwidth ERB (equivalent rectangular bandwidth): the bandwidth of a perfect rectangular filter with the same maximum response and transmitting the same power of white noise The Q to measure the sharpness of the filter: Q = CF/Bandwidth; Q3db, Q10dB and QERB.

8 Filtered noise demonstration White noise Lowpass filtered white noise with cutoff frequency at [10000, 4000, 2000, 1000, 500] Hz. Highpass filtered white noise with cutoff frequency at [500, 1000, 2000, 4000, 10000] Hz. 1/3-octave bandpass filtered white noise with center frequency at [500, 1000, 2000, 4000, 8000] Hz. White noise and pink noise with the same power.

9 Musical measure of frequency Octave notation for relative musical scale Octaves = log2(f2/f1) 12 semitones per octave 100 cents per semitones Absolute musical scale Section of a piano keyboard including the central octave starting on C4 ( Middle C and including A4 ( Concert A )

10 Masking Definition of masking (American Standards Association, 1960): The process by which the threshold of audibility for one sound is raised by the presence of another (masking) sound. The amount by which the threshold of audibility of a sound is raised by the presence of another (masking) sound. The unit customarily used is the decibel. Different kinds of masking: Simultaneous masking Forward masking: signal is masked by a preceding masker Backward masking: the masker follows the signal Simultaneous masking reflects the limits of frequency selectivity.

11 Critical band Fletcher (1940) measured the threshold of a sinusoidal signal as a function of the bandwidth of a bandpass noise masker and called the bandwidth at which the signal threshold ceased to increase the critical bandwidth.

12 Critical band demonstration 2000 Hz tone in 5 db decreasing steps Signal is masked by broadband noise Signal is masked by noise with 1000 Hz bandwidth Signal is masked by noise with 250 Hz bandwidth Signal is masked by 10 Hz narrowband noise CF = 2000 Hz, CB ~ 280 Hz

13 Shape of the auditory filter Psychophysical tuning curves in masking The low level signal is assumed to have activity primarily at the output of only ONE auditory filter. The masker produces a constant output at threshold from the same auditory filter to mask the fixed signal. However, humans do the off-frequency listening when it is advantageous to do so.

14 Notched-noise method To limit the offfrequency listening ERB = 24.7(4.37F + 1) (in Hz; F in khz) N constant Q filter bank (1ERB N 0.9mm BM)

15 Excitation pattern Frequency (Hz) Asymmetric excitation pattern of a given sound (1 khz)

16 Masking pattern A masking pattern (masked audiogram) is a graph showing the masked threshold as a function of the frequency of the signal.

17 Asymmetry of masking demonstration (1200 & 2000 Hz) A pure tone masks tones of higher frequency more effectively than tones of lower frequency.

18 Non-simultaneous masking Backward masking: the signal precedes the masker (a.k.a. prestimulatory masking or premasking). This phenomenon is poorly understood. The practice of the subjects affects the amount of backward masking. Forward masking: the signal follows the masker (a.k.a. poststimulatory masking or postmasking). It is greater the nearer in time to the masker that the signal occurs. The amount of forward masking for a 4 khz signal, as a function of time delay.

19 Backward and forward masking demonstration A brief sinusoidal tone (2000 Hz). The signal is followed by a noise burst (backward masking: t=100, 20 and 0 ms). The noise burst precedes the signal (forward masking: t=100, 20 and 0 ms).

20 Pure tones close together in frequency mask each other more than tones widely separated in frequency. A pure tone masks tones of higher frequency more effectively than tones of lower frequency. The greater the intensity of the masking tone, the broader the range of frequency it can mask. Masking by a narrow band of noise shows many of the same features (as mentioned above) as masking by a pure tone; while avoiding the occurrence of beats. Masking of tones by broadband (white) noise shows an approximately linear relationship between masking and noise level (e.g., increasing the noise level 10 db raises the hearing threshold by the same amount). Broadband noise masks tones of all frequencies. Conclusions from many simultaneous masking experiments

21 Conclusions for forward and backward masking Forward masking refers to the masking of a tone by a sound that ends a short time (up to 20 or 30 ms) before the tone begins. Forward masking suggests that recently stimulated cells are not sensitive as fully-rested cells. Backward masking refers to the masking of a tone by a sound that begins a few ms later. A tone can be masked by a noise that begins (up to 10 ms) later, although the amount of masking decreases as the time interval increases (Elliot, 1962). Backward masking apparently occurs at higher centers of processing where the later-occurring stimulus of greater intensity overtakes and interferes with the weaker stimulus.

22 Frequency selectivity of the hearing impaired Many studies found the loss of frequency selectivity (resolution) associated with cochlear damage. Perceptual consequences of a loss in frequency selectivity: Greater susceptibility to masking by interfering sounds (more noise gets through the broader filter). difficulty experienced by the hearing impaired in noisy environments such as in bars or at parties. Difficulty in the perceptual analysis of complex sounds (the perception of timbre depends on the frequency selectivity). difficulty to distinguish different vowels or musical instruments.

23 Application of the masking: MP3 coding Simultaneous masking Spectral masking Non-simultaneous masking Temporal masking

24 Spectro-temporal masking of MP3 coding Combined spectro-temporal masking

25 The perception of loudness Sound intensity: a physical quantity which can be measured by acoustical instrumentation. Loudness: a psychological quantity which can only measured by human listeners.

26 Psychophysics studies on loudness Psychophysics: the study of the relationship between the magnitude of sensation and the magnitude of a stimulus as measured in conventional physical units. Psychological magnitude M of loudness M = ki p where I is the sound intensity and k, p are constant. log M = log k+ plog I

27 Loudness of broad-band stimuli (uniform exciting noise) 64 subjects, 9 noise levels over a 40 db range (Hartmann, 1993) exponent p=0.22 Underestimate p? (regression effect) average between the magnitude estimation and magnitude production experiment results (Stevens and Greenbaum, 1966, p=( )/2=0.3)

28 Loudness of tones A common assumption: loudness is somehow related to the total neural activity evoked by a sound. Increasing neural count rate for tones compared with uniform exciting broadband noise larger p (Fletcher, 1953, p=1/3) Average of many experiments p=0.3 (Stevens, 1955)

29 Effect of bandwidth on loudness If the frequencies of the tones lie within the critical bandwidth, the loudness is calculated from the total intensity: I=I1+I2+I3+ If the bandwidth exceeds the critical bandwidth, the resulting loudness is greater than obtained from a simple summation of intensities. It approaches (but less than) a value that is the sum of the individual loudness: M=M1+M2+M3+

30 Critical band demo by loudness comparison Noise with 1000 Hz center frequency and 15% bandwidth ( Hz). The bandwidth of the test signal is increased of 15% in each step. CF = 1000 Hz, CB ~ 160 Hz

31 Temporal integration of loudness and demonstration At a given intensity, loudness increases with duration for up to ms. Demo: bursts of broadband noise with durations of [1000, 300, 100, 30, 10, 3, 1] ms are presented at 8 decreasing levels (0, -16, -20, -24, -28, -32, -36, and -40 db) in the presence of a broadband masking noise.

32 References Moore, B. C. J. (2003). An Introduction to the Psychology of Hearing, 5th ed. (Academic Press). Hartmann, W. M. (1997). Signals, Sound, and Sensation, (AIP Press). Auditory Demonstrations on CD, (Acoustical Society of America, 1989)

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