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The Dynamic Response of the Basal Membrane to Short Acoustic Pulses
Abstract
We present results of studies of extremely short acoustic pulses as recorded by an artificial ear in an anechoic chamber. Two types of ultrashort acoustic pulses have been used: cosine signal with the Gaussian envelope and the Gaussian envelope itself. All pulses had duration times between 0.14 ms and 27.21 ms. The recorded spectra exhibited a maximum whose position shifted towards higher frequencies with decreasing duration time. This corroborates the concept of the effective pitch sensation produced by pulses beyond the uncertainty principle. Two mathematical models have been used to reveal the reaction of the basilar membrane to the pulses, and their distortions by electronic devices.
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We quantified the relative simplicity of frequency ratios axed reanalyzed data from several studies on the perception of simultaneous and sequential tones. Simplicity of frequency ratios accounted for judgments of consonance and dissonance and for judgments of similarity across a wide range of tasks and listeners. It also accounted for the relative ease of discriminating tone patterns by musically experienced and inexperienced listeners . These findings confirm the generality of previous suggestions of perceptual processing advantages for pairs of tones related by simple frequency ratios .
The time-frequency uncertainty principle states that the product of the
temporal and frequency extents of a signal cannot be smaller than $1/(4\pi)$.
We study human ability to simultaneously judge the frequency and the timing of
a sound. Our subjects often exceeded the uncertainty limit, sometimes by more
than tenfold, mostly through remarkable timing acuity. Our results establish a
lower bound for the nonlinearity and complexity of the algorithms employed by
our brains in parsing transient sounds, rule out simple "linear filter" models
of early auditory processing, and highlight timing acuity as a central feature
in auditory object processing.
In this project, Spectral Envelopes in Sound Analysis and Synthesis, various methods for estimation, representation, file storage, manipulation, and application of spectral envelopes to sound synthesis were evaluated, improved, and implemented. A prototyping and testing environment was developed, and a function library to handle spectral envelopes was designed and implemented. For the estimation of spectral envelopes, after defining the requirements, the methods LPC, cepstrum, and discrete cepstrum were examined, and also improvements of the discrete cepstrum method (regularization, stochastic (or probabilistic) smoothing, logarithmic frequency scaling, and adding control points). An evaluation with a large corpus of sound data showed the feasibility of discrete cepstrum spectral envelope estimation. After defining the requirements for the representation of spectral envelopes, filter coefficients, spectral representation, break-point functions, splines, formant representation, and high resolution matching pursuit were examined. A combined spectral representation with indication of the regions of formants (called fuzzy formants) was defined to allow for integration of spectral envelopes with precise formant descriptions. For file storage, new data types were defined for the Sound Description Interchange Format (SDIF) standard. Methods for manipulation were examined, especially interpolation between spectral envelopes, and between spectral envelopes and formants, and other manipulations, based on primitive operations on spectral envelopes. For sound synthesis, application of spectral envelopes to additive synthesis, and time-domain or frequency-domain filtering have been examined. For prototyping and testing of the algorithms, a spectral envelope viewing program was developed. Finally, the spectral envelope library, offering complete functionality of spectral envelope handling, was developed according to the principles of software engineering.
A linear and a nonlinear transmission line model of the basilar membrane is described. The motion of the basilar membrane model has been simulated by numerical methods and compared with physiological data for several types of sound stimuli. It is shown that a linear model exhibits a frequency modulation in its impulse response that is in accordance with physiological data. The nonlinear model displays a sharpened frequency response for lower sound intensities. Futhermore, a nonlinear model explains why hearing damage imposed by short, high-intensity, sounds is extended to the low-frequency regions of the cochlea.
The acoustic startle (ASR) is a transient motor response to an unexpected, intensive stimulus. The response is determined by stimulus parameters such as its intensity, rise time and duration. The dependence of the ASR on the stimulus duration is more complex than could be assumed from physical properties of acoustic pulse. This effect attracted the attention of few researchers. Some authors reported noticeable changes in the ASR amplitude only for very short (less than 4-6 ms) acoustic pulses. The systematic studies on the effect, however, have not been performed so far. The purpose of this study was to determine to what extent the ASR parameters are affected by the durations of the short stimulus. The amplitude of the acoustic startle reflex was assessed for a fixed tonal frequency (6.9 kHz), and for a variety of stimulus durations ranging between 2 and 10 ms. ASRs were studied in 11 adult, hooded rats exposed to a sequence of tone pulses (110 dB SPL) of different durations, presented in random order, with or without 70 dB white noise as a background. Statistical analysis revealed significant differences between ASR amplitudes for different durations. The startle amplitude increased with acoustic pulse duration and distinguishable differences were seen for stimulus duration between 2 and 8 ms. Further increase of pulse duration had no effect on ASR amplitude. The same pattern of changes was observed when the acoustic stimulus was presented with the white noise. In the tested range of stimulus duration no significant differences in the ASR latency were found. The observed differences may be attributed to changes of stimulus acoustic energy and to physiological characteristic of auditory system in the rat.
A special course in technical listening called timbre solfege has been developed and introduced in the Sound Engineering Department at the Chopin Academy of Music in Warsaw, Poland. Timbre solfege deals with various aspects of subjective evaluation of sound. The course program, which has been designed for training sound engineers, is described.
Atlas of Anatomy, Second Edition, is an essential resource for anyone studying gross anatomy. Containing over 2,400 full-color illustrations, this atlas guides you step-by-step through each region of the body, helping you master the details of anatomy.
Edited by Anne M. Gilroy, Brian R. MacPherson, Lawrence M. Ross ; based on the work of Michael Schuenke, Erik Schulte, Udo Schumacher ; illustrated by Markus Voll, Karl Wesker.
Citation: Gilroy, A. M., MacPherson, B. R., Ross, L. M., Schünke, M., Schulte, E., & Schumacher, U. (2012). Atlas of anatomy. New York: Thieme.
ISBN-10: 1604067454
ISBN-13: 978-1604067453
Partial preview available via Google Books.
The human hearing sense is an astonishingly effective signal processor. Recent experiments [1, 2, 3] suggest that it is even capable of overcoming limitations implied by the time-frequency uncertainty relation. The latter, mostly known from quantum mechanics, requires that the product of uncertainties in time and frequency, Δt∙Δf , cannot be smaller than the limiting value Δt∙Δf = (1/4π), which holds when the signal is a harmonically oscillating function with a Gaussian envelope.
Text: book; for undergraduates and others studying sound and auditory perception. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
In der vorliegenden Arbeit werden zunchst exakte Definitionen der Worte: Ort, Geschwindigkeit, Energie usw. (z. B. des Elektrons) aufgestellt, die auch in der Quantenmechanik Gltigkeit behalten, und es wird gezeigt, da kanonisch konjugierte Gren simultan nur mit einer charakteristischen Ungenauigkeit bestimmt werden knnen ( 1). Diese Ungenauigkeit ist der eigentliche Grund fr das Auftreten statistischer Zusammenhnge in der Quantenmechanik. Ihre mathematische Formulierung gelingt mittels der Dirac-Jordanschen Theorie ( 2). Von den so gewonnenen Grundstzen ausgehend wird gezeigt, wie die makroskopischen Vorgnge aus der Quantenmechanik heraus verstanden werden knnen ( 3). Zur Erluterung der Theorie werden einige besondere Gedankenexperimente diskutiert ( 4).
Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: From harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.
Models which attempt to account for our ability to discriminate the pitch of pure tones are discussed. It is concluded that models based on a place (spectral) analysis should be subject to a limitation of the type Δf.d≥ constant, where Δf is the frequency difference limen (DL) for a tone pulse of duration d. The value of this constant will depend on the ability of the system to resolve small intensity differences. If a resolution of 1 dB is assumed, the value of the constant is about 0.24. In principle, a mechanism based on the measurement of time intervals could do considerably better than this. Frequency DLs were measured over a wide range of frequencies and durations. It was found that at short durations the product of Δf and d was about one order of magnitude smaller than the minimum predicted from the place model, except for frequencies above 5 kHz. A 'kink' in the obtained functions was also observed at about 5 kHz. It is concluded that the evidence is consistent with the operation of a time measuring mechanism for frequencies above this.
It has been suggested that at very short durations, frequency spread of the signal is what determines the frequency resolving power of the auditory system. The validity of this notion is examined by applying a version of the “uncertainty principle,” which says that the product of “effective bandwidth” and “effective duration” is a constant that depends on the signal envelope. This bandwidth‐duration constraint permits several different envelopes to be used for the carrier signal in a frequency‐discrimination experiment, while at the same time restricting all the signals to the same nominal bandwidth. Rectangular, exponential, Gaussian, and gamma functions were used as envelope functions for a 1000‐Hz carrier. Parameter values were selected to equate the signal bandwidths to the bandwidth of a rectangular envelope signal, which had a duration ranging from 2 to 32 msec. The frequency‐discrimination data indicate that equating signal bandwidth in this way does not serve to make the signals equally discriminable. A more accurate way to estimate the discriminability for the different envelope sinusoids is to measure how long each signal envelope provides an acceptable signal‐to‐noise ratio.
This report describes an implementation of a cochlear model proposed by Roy Patterson [Patterson1992]. Like a previous report [Slaney1988], this document is an electronic notebook written using a software package called Mathematica^TM [Wolfram 1988]. This report describes the filter bank and its implementation. The filter bank is designed as a set of parallel bandpass filters, each tuned to a different frequency. This report extends previous work by deriving an even more efficient implementation of the Gammatone filter bank, and by showing the MATLAB^TM code to design and implement an ERB filter bank based on Gammatone filters. 2.0 Ear Filters
Experiments in hearing
- G Békésy
- E G Wever
G. von Békésy and E. G. Wever, "Experiments in hearing", New York,
McGraw-Hill, 1960.
Weber-Fechner Law in Perception of Short Acoustic Pulses
- K Martinson
- M Majka
- M Senderecka
- T Kamisiński
- P Zieliski
K. Martinson, M. Majka, M. Senderecka, T. Kamisiński, and P. Zieliski,
"Weber-Fechner Law in Perception of Short Acoustic Pulses", unpublished.
Submillisecond Acoustic Pulses: Effective Pitch and Weber-Fechner Law in Discrimination of Duration Times
- M Majka
- P Sobieszczyk
- R Gebarowski
- P Zieliński
M. Majka, P. Sobieszczyk, R. Gebarowski, and P. Zieliński, "Submillisecond Acoustic Pulses: Effective Pitch and Weber-Fechner Law in
Discrimination of Duration Times", Cornell University Library, arXiv:
1404.6464, 2014.