Nonlinearity and Psychoacoustics Do We Measure What We Hear?

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1 Nonlinearity and Psychoacoustics Do We Measure What We Hear? Alex Voishvillo JBL Professional, Northridge, CA Presented at ALMA 2009 European Symposium Frankfurt, Germany April 4th, 2009

2 Motivation Attempt to explain why conventional measurement methods may not provide information well correlated with subjective sound quality. Discuss possible future developments of nonlinearity measurement in transducers and sound systems. 2

3 Background What is nonlinear distortion?? Perceived deterioration of sound quality? Nonlinear physical effects? Measured objective parameters and responses? 3

4 THD versus sound quality Quiz 1: Which system has less distortion? Undistorted musical signal Click this button! Nonlinear system 1 Nonlinear system 2 THD = 22.6 % THD = 2.8 % Common sense: the system 2 sounds worse, it must have higher harmonic distortion. Musical excerpt from Paul Anka It s My Life (by Jon Bon Jovi), CD Rock Swings, Verve Records,

5 THD versus sound quality Hard clipping THD = 22.6 % Soft zero crossing THD = 2.8% 5

6 THD versus sound quality Spectra of distorted sinusoidal signals Hard Zero THD = 2.9 % clipping THD = 22.6 % crossing Waveforms of musical signal Hard clipping Original signal Zero crossing 6

7 THD versus sound quality Quiz 2: Why do we measure harmonic distortion? Answer: Because we can! Philip Newell, Recording Studio Design, Focal Press,

8 Background Popular believe: second harmonic distortion ti is benign Second harmonics are in octave consonance ce with fundamental tones Second harmonics are masked by the musical instruments overtones Does a system that generates second harmonic distortion still sound good? 8

9 Second harmonic distortion versus second order distortion Fundamental tones Multitone E3 minor chord Multitone E4 minor chord y x Y=x+Kx 2 Second harmonics Signal and Second Signal and all second harmonics and distortion harmonics IM products products 9

10 Background Why don t conventional measurement methods correlate well with subjective sound quality? Complexity of nonlinear systems Complexity of human hearing system Complexity of musical signal Reaction to simple testing signals does not convey sufficient information Hearing system is not a mere spectrum analyzer Musical and tonal signals differ statistically, in time and dfrequency domains 10

11 Sound reproduction as a communication system Transmitter Signal Receiver 11

12 Sound reproduction as a communication system What we often think about this system is not what it really is Transmitter Signal Receiver 12

13 Sound reproduction as a communication system We typically think that: Transmitter loudspeaker produces harmonics and IM distortion Musical signal is accompanied by harmonic and IM products We hear these irritating harmonic and intermodulation products 13

14 Sound reproduction as a communication system Stereotypical picture of loudspeaker distortion measurements Pout Culprits Uin 14

15 Sound reproduction as a communication system In reality: Extremely complex dynamic system with plethora of nonlinear and parametric electromagnetic, mechanical and acoustical effects Very complex dynamic signal with instantaneously t changing level, waveform, and spectrum. Far cry from sinusoidal signal including totally t different statistical ti ti distribution. Distortion signal is just as complex Enormously complex nonlinear time-variant system characterized by numerous physiological, psychoacoustical and cognitive effects 15

16 Transmitter Sources of nonlinearity in a horn driver Electrodynamic nonlinear effects * Nonlinear Bl-product * Bl-product modulation by voice coil current * Voice coil inductance variation with displacement * Quadratic reluctance force * Inductance dependence on current. Magnetic hysteresis * Eddy currents. Modulation of resistive losses Mechanical nonlinear effects * Nonlinear mechanical suspension. Diaphragm and surround breakups * Non-harmonic effects. Acoustical nonlinear effects * Nonlinear sound propagation in phasing plug and horn * Nonlinearity and modulation of compression chamber air compliance * Nonlinearity and modulation of compression chamber air mass * Nonlinearity and modulation of air viscosity in compression chamber * Nonlinear relationship between particle velocity and sound pressure * Nonlinear air compression in rear chamber * Air turbulence in phasing plug? * Air turbulence in voice coil gap? * Air turbulence in compression chamber? 16

17 Transmitter Loudspeaker is a nonlinear dynamic system There is a significant difference between: Dynamic nonlinear system and static nonlinear system Dynamic nonlinear system and dynamic linear system 17

18 Static versus dynamic nonlinearity Static nonlinearity (simple) Dynamic nonlinearity (complex) a 0 a 0 x(t) () a 1 x(t) y(t) x(t) a 1 x, h1 a 2 x 2 (t) a 2 x, h2 y(t) a n x n (t) a n x, hn y(t) x(t) Linear and nonlinear responses do not depend on frequency Second-order nonlinear response of a loudspeaker. 18

19 Linear dynamic system measurement Input signal: Sweeping tone, impulse or noise Dynamic linear system under test Output reaction: Impulse response or complex transfer function Full description! Output reaction to any signal can be predicted 19

20 Nonlinear dynamic system measurement Input signal: Sweeping tone, two tones Dynamic nonlinear system under test Output reaction: harmonics, THD, two-tonetone IM products Harmonics and IM products are only symptoms of nonlinearity Output reaction to any signal cannot be predicted 20

21 Linear dynamic versus nonlinear dynamic system Linear dynamic system (simple) Length Nonlinear dynamic system (complex) A B G G C Draft F E D Diameter I H 21

22 Signal Musical signal Sinusoidal signal Statistical distribution Amplitude Musical signal remains at low levels most of the time and the peaks are rare Amplitude Sinusoidal signal is opposite. It remains at large levels most of the time Waveform 22

23 Receiver - hearing system, psychoacoustics Eardrum Hammer Anvil Vestibular canals Auditory nerve Cochlea Pinna Ear canal Middle ear Stirrup Oval window 23

24 Receiver - hearing system, psychoacoustics OUTER EAR MIDDLE EAR INNER EAR Pinna Eardrum Outer ear canal Ossicles Oval window Basilar membrane Fluid Hair cells Resonances in the ear canal Reflex protects inner ear from overload by the middle ear muscles contraction Spreading excitation of areas on basilar membrane in the vicinity of the location responsible for a particular signal Compression amplification of low-level sounds Transformation of mechanical vibrations into electrical impulses f t 24

25 Spreading Masking Critical bands Receiver - hearing system, psychoacoustics Loudness Compression 25

26 Receiver - hearing system, nonlinearity Middle ear nonlinearity and acoustic reflex Inner ear nonlinear compression Cochlea nonlinear otoacoustic emission Cochlea turbulence of the fluid Basilar membrane nonlinear mechanics Hair cells nonlinear excitation Nonlinear auditory filtering 26

27 L Simultaneous masking Masking versus level and frequency Masking curve becomes progressively asymmetric at higher levels of masker L f f Lower-frequency masking extends over wider frequency range. 27

28 Time-domain masking Intensity Short sinusoidal tone Masked threshold for the second lower-level short tone t msec Backward (pre) masking msec Forward (post) masking 28

29 Simultaneous masking Fastl and Zwicker, Psychoacoustics. Facts and Models, Springer

30 Distortion and masking y f x 2 khz crossover Distortion f f y x 2 khz high-pass f 2 khz crossover Distortion f Musical excerpt from The Beatles Because, CD Love, Capitol/Apple Records,

31 Distortion and masking THD THD before and after Low pass High pass connection of the f second high-pass filter Level Low pass High pass f Reaction to multitone stimulus before connection of the second high-pass filter It reveal difference-frequency frequency IM products invisible to THD Level Low pass High pass f Reaction to multitone stimulus after connection of the second high-pass filter 31

32 Distortion and masking f 300 Hz crossover y f x Distortion Musical excerpt from The Beatles Come Together, CD Love, Capitol/Apple Records, 2006 f 300 Hz crossover 300 Hz low-pass y f x f Distortion 32

33 Distortion and masking Nonlinear products that fall outside the spectrum of the signal are very noticeable and irritating. Masking plays significant role in mitigating irritating effect of nonlinear distortion. The same nonlinearity produces the following effect on 440 Hz tone: THD = 15% 33

34 Low and high-order nonlinearity Good speaker P Low-order nonlinearity f U f Harmonics Input signal High-order nonlinearity P Bad speaker f 34

35 Low and high-order nonlinearity Good speaker P Low-order nonlinearity U Snapshot of input signal f f Distortion Signal Masking U P High-order nonlinearity t f Bad speaker Possible problems 35

36 Low and high-order nonlinearity 2 nd order nonlinearity, THD = 15% Nonlinear function Tone waveforms Tone spectrum Original musical signal Distorted musical signal Distortion signal only Musical excerpt from Janis Ian His Hands, CD Breaking Silence, Morgan Creek Records,

37 Low and high-order nonlinearity 4 th order nonlinearity, THD = 15% Nonlinear function Tone waveforms Tone spectrum Original musical signal Distorted musical signal Distortion signal only Musical excerpt from Janis Ian His Hands, CD Breaking Silence, Morgan Creek Records,

38 Three approaches to assessment of nonlinearity in audio Identification Distortion measurement Perceptual methods Obtaining enough information to predict reaction to an arbitrary signal Obtaining certain symptoms of nonlinearity Simulation of psychoacoustical effects responsible for perception of sound quality Klippel analyzer IMD, THD, harmonics, multitone, coherence function PEAQ, PESQ 38

39 History - measurement Non-coherence and broadband stimuli. S. Temme and P. Brunet, The authors introduced a Non-Coherent Distortion (NCD) measure. The measure is based on consideration of weakly nonlinear systems and the assumption that the output signal is a superposition of the linear component, nonlinear component and noise. They demonstrated t d that t the non-coherence [1-γ 2 (iω)] applied to the overall output t signal s autospectrum G yy (ω) is the autospectrum G NN (ω) of the uncorrelated (distortion+noise) signal. Based on this, the NCD was introduced as: η ( ω ) = G G 2 NN ω ( ω) ( ω) YY a c b Example of testing 6 x 9 car loudspeaker: a Normalized THD, b Difference Frequency IM distortion, c - NCD 39

40 Classification of semi-perceptual and perceptual p methods Semi- perceptual Perceptual methods Harmonics weighting. Gedd-Lee metric. Pass-band noise weighting Codecs measurement Transducers measurement Better correlation with sound quality than harmonics and 2-tone IM, but limited application Psychoacoustics- based Hearing system physiology-based Significantly better correlation with perceived quality 40

41 Semi-perceptual methods Gedd-Lee metric. E. Geddes, L. Lee, 2003 This metric stays between objective and perceptual methods because the metric does not use explicitly models of auditory system, but is based on the following psychoacoustical assumptions: High-order nonlinearity T(x) produces wide spectrum of distortion products that are poorly masked Nonlinearity that affects signal at low levels (e.g. zero crossing) is worse than nonlinearity that affects only high level signal (e.g. hard clipping) because low-level signals are poor maskers xπ d Subjective rating G m = cos T ( x) dx 2 versus Gm 2 1 dx T(x) static nonlinearity 41

42 Semi-perceptual methods Measurement of distortion using musical signal, V. Wolf, 1953 Output signal and distortion Input signal t Stop-band filter ω 1 ω 2 Device under test t Band-pass filter Band-pass filtered input signal t ω 1 ω 2 U S (ω) R = k ω 2 ω 1 U U D S ( ω) d ω ( ω) Comparison U D (ω) ω 1 ω 2 Band-pass filter Distortion only in frequency band ω 1 ω 2 t 42

43 Semi-perceptual methods Alternative semi- perceptual methods using weighting functions, Voishvillo, 2007 Band-pass filtered input signal t Output signal and distortion t Weighting functions Input noise N in ω 1 ω 2 Device under test N out S L1 (ω) S H1 (ω) W L1 (ω) L1( ) W H1 (ω) H1( ) K(ω 12 ) Band-pass filter ω 1 ω 2 ω L ω H ω 12 Repeat for different frequencies and different levels Comparison ωh K(ω 12 ) = k [ S L1 ( ω) W dω ω * L1 (ω) + S H1 (ω )* W H1 ( ω ) ] L R(ω 12 ) =K(ω 12 ) / N in (ω 12 ) R(ω 12) ) ω 12 R(ω) N 1 N 2 N 1 <N 2 <N 3 N 3 ω 43

44 Perceptual methods Noise-to-mask ratio Internal representations Explicit simulation of masking processes Simulation of physiological and psychoacoustical effects in hearing system Energy of error signal is compared with masking threshold in each critical band and time frame Distorted and original audio signals are mapped on reaction of basilar membrane 44

45 Perceptual methods Perceptual models based on noise-to-mask ratio x(t) Time frame Audio signal x(t) Time frame Codec under test y(t) e(t) () Temporal difference Delay x(t-τ) Explicit simulation of masking process e(f) [FFT] 2 Critical bands Spectral difference [FFT] 2 Critical bands x(f) R. Beaton et. al. Objective Measurement of Audio Quality, Collected Papers on Audio Bit-Rate Reduction, AES, 1996 Noise to Mask Rti Ratio Perceptual model dl Output 45

46 Perceptual methods Perceptual models based on internal representations Delay Time frame [FFT] 2 z f a z s t L E x(t) x(t-τ) w i (t) Spectrum power Hz to Bark Outer and middle ear Spreading z Audio signal Noise disturbance Scaling Comparison Compression x(t) y(t) w i (t) Codec under test Time frame [FFT] 2 z f f f f a z s t L E R. Beaton et. al. Objective Measurement of Audio Quality, Collected Papers on Audio Bit-Rate Reduction, AES, 1996 Simulation of physiological, psychoacoustical, and cognitive processes of hearing system 46

47 Perceptual methods PEAQ Result of using basic version of PEAQ Result of using advanced version of PEAQ T. Thiede et. al. PEAQ The ITU Standard for Objective Measurement of Perceived Audio Quality, JAES, vol. 48, No.1/2, 2000, January/February 47

48 Perceptual methods C. Tan, B. Moore, N. Zakharov, 2004 Perceptual measurement model based on musical and speech signals. Input Distortion t Ear correction f f Ear correction i-th 30-ms frame 40 ERB filters 40 ERB filters i-th 30-ms frame 1st 40th 1st 40th x i, 1 x x i, 40 y i, j i, 1 yi, y i, 40 j r i,1 (x, y) r i,40 (x, y) Cross-correlation Cross-correlation Frames output summation and r i, j max weighting and averaging Σ r i,j max Σ Filters output summation Maximum cross-correlation for each i-th frame and j-th filter R nonlin 48

49 Perceptual methods C. Tan, B. Moore, N. Zakharov, 2004 Perceptual measurement model based on musical and speech signals. Subjective ratings versus predicted ratings. Static nonlinearity Subjective ratings versus predicted ratings. Real transducers 49

50 Perceptual methods Benefits of using perceptual measurement for loudspeakers Replacement of labor- and dtime-consuming i subjective listening i tests t with computerized perceptual evaluation of sound quality Higher accuracy of estimation of transducers sound quality compared to traditional objective measurements Different approach to the design of transducers and loudspeaker systems. Linearization of psychoacoustically relevant nonlinear effects rather than minimization of all possible nonlinearities Using perceptual criteria rather than THD and other objective metrics in nonlinear correction of transducers 50

51 Future possible developments Further development of the methods initiated by Tan, Moore, and Zakharov by possibly adding more components to the model (loudness, nonlinear compression, etc.). Work on the problem of separation of linear and nonlinear distortion Investigate feasibility of using existing methods, such as Opera and PEAQ directly without modifications Using sound quality criteria not lumped into a single number, but kept separately for each individual critical band, therefore providing perceptual frequency response of distortion valuable information for engineers Investigate viability of using semi-perceptual methods 51

52 Conclusions Conventional measurement methods often fail to correlate with perceived sound quality in transducers The reason for the dismal correlation includes: The complexity of nonlinear dynamic systems The complexity of the human auditory system Some approaches in existing perceptual methods may be applicable to loudspeakers Early experiments applying these perceptual models to measurement of transducers show promise Semi-perceptual method seem to be a promising addition to the trueperceptual methods Continuing using only conventional method, the loudspeaker industry lags several years behind the state of art in perceptual technology 52

53 Conclusions Conventional measurement methods often fail to correlate with perceived sound quality in transducers The reason for the dismal correlation includes: The complexity of nonlinear dynamic systems The complexity of the human auditory system Some approaches in existing perceptual methods may be applicable to loudspeakers Early experiments applying these perceptual models to measurement of transducers show promise Semi-perceptual method seem to be a promising addition to the trueperceptual methods Continuing using only conventional method, the loudspeaker industry lags several light years behind the state of art in perceptual technology 53

54 Conclusions 55 years ago: If any manufacturer or group of manufacturers can carry out the necessary research required to correlate listening tests with various methods of measuring nonlinear distortion, it will be a great and valuable service for the industry. Herman Hosmer Scott, Intermodulation Distortion, JAES,

55 END 55

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