An algorithm is presented for the estimation of the fundamental frequency (F0) of speech or musical sounds. It is based on the well-known autocorrelation method with a number of modifications that combine to prevent errors. The algorithm has several desirable features. Error rates are about three times lower than the best competing methods, as evaluated over a database of speech recorded together with a laryngograph signal. There is no upper limit on the frequency search range, so the algorithm is suited for high-pitched voices and music. The algorithm is relatively simple and may be implemented efficiently and with low latency, and it involves few parameters that must be tuned. It is based on a signal model (periodic signal) that may be extended in several ways to handle various forms of aperiodicity that occur in particular applications. Finally, interesting parallels may be drawn with models of auditory processing.

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YIN, a fundamental frequency estimator for speech and music

In mammals, environmental sounds stimulate the auditory receptor, the cochlea, via vibrations of the stapes, the innermost of the middle ear ossicles. These vibrations produce displacement waves that travel on the elongated and spirally wound basilar membrane (BM). As they travel, waves grow in amplitude, reaching a maximum and then dying out. The location of maximum BM motion is a function of stimulus frequency, with high-frequency waves being localized to the “base” of the cochlea (near the stapes) and low-frequency waves approaching the “apex” of the cochlea. Thus each cochlear site has a characteristic frequency (CF), to which it responds maximally. BM vibrations produce motion of hair cell stereocilia, which gates stereociliar transduction channels leading to the generation of hair cell receptor potentials and the excitation of afferent auditory nerve fibers. At the base of the cochlea, BM motion exhibits a CF-specific and level-dependent compressive nonlinearity such that responses to low-level, near-CF stimuli are sensitive and sharply frequency-tuned and responses to intense stimuli are insensitive and poorly tuned. The high sensitivity and sharp-frequency tuning, as well as compression and other nonlinearities (two-tone suppression and intermodulation distortion), are highly labile, indicating the presence in normal cochleae of a positive feedback from the organ of Corti, the “cochlear amplifier.” This mechanism involves forces generated by the outer hair cells and controlled, directly or indirectly, by their transduction currents. At the apex of the cochlea, nonlinearities appear to be less prominent than at the base, perhaps implying that the cochlear amplifier plays a lesser role in determining apical mechanical responses to sound. Whether at the base or the apex, the properties of BM vibration adequately account for most frequency-specific properties of the responses to sound of auditory nerve fibers.

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Mechanics of the Mammalian Cochlea

Vol. 1 1. Neural Basis of Vision. 2. Color Vision. 3. Depth Perception. 4. Perception of Visual Motion. 5. Perceptual Organization in Vision. 6. Attention. 7. Visual Object Recognition. 8. Motor Control. 9. Neural Basis of Audition. 10. Auditory Perception and Cognition. 11. Music Perception and Cognition. 12. Speech Perception. 13. Neural Basis of Haptic Perception. 14. Touch and Haptics. 15. Perception of Pain and Temperature. 16. Taste. 17. Olfaction. Vol. 2 1. Kinds of Memory. 2. Models of Memory. 3. Cognitive Neuroscience. 4. Spatial Cognition. 5. Knowledge Representation. 6. Psycholinguistics. 7. Language Processing. 8. Problem Solving. 9. Reasoning. 10. Decision Making. 11. Concepts & Categorization. 12. Cognitive Development. 13. Culture & Cognition. Vol. 3 1. Associative Structures in Pavlovian and Instrumental Conditioning. 2. Learning: Laws and Models of Basic Conditioning. 3. Reinforcement Learning. 4. Neural Analysis of Learning in Simple Systems. 5. Learning Mutants. 6. Learning Instincts. 7. Perceptual Learning. 8. Spatial Learning. 9. Temporal Learning. 10. Role of Learning in Cognitive Development. 11. Language Acquisition. 12. Role of Learning in the Operation of Motivational Systems. 13. Emotional Plasticity. 14. Anatomy of Motivation. 15. Hunger Energy Homeostasis. 16. Thirst and Water-Salt Appetite. 17. Reproductive Motivation. 18. Social Behavior. 19. Addiction. Vol. 4 1. Representational Measurement Theory. 2. Signal Detection Theory. 3. Psychophysical Scaling. 4. Cognitive Neuropsychology. 5. Functional Brain Imaging. 6. Neural Network Modeling. 7. Parallel and Serial Processing. 8. Methodology and Statistics in Single-Subject Experiments. 9. Analysis, Interpretation, and Visual Presentation of Experimental Data. 10. Meta-Analysis. 11. Mathematical Modeling. 12. Analysis of Response Time Distributions. 13. Testing and Measurement. 14. Personality and Individual Differences. 15. Electrophysiology of Attention. 16. Single vs. Multiple Systems of Memory and Learning. 17. Infant Cognition. 18. Aging and Cognition.

Stevens' handbook of experimental psychology

The yield of alkenols and cycloalkenols is substantially improved by carrying out the reaction of olefins with formaldehyde in the presence of selected catalysts. In accordance with one embodiment, alk-3-en-1-ols are produced in good yields from isobutylene and formaldehyde in the presence of organic carboxylic acid salts of Group IB metals.

The Organization of the Cochlear Receptor

Basilar-membrane responses to single tones were measured, using laser velocimetry, at a site of the chinchilla cochlea located 3.5 mm from its basal end. Responses to low-level ( 80 dB the largest responses are elicited by tones with frequency about 0.4–0.5 octave below CF. For stimulus frequencies well above CF, responses stop decreasing with increasing frequency: A plateau is reached. The compressive growth of responses to tones with frequency near CF is accompanied by intensity-dependent phase shifts. Death abolishes all nonlinearities, reduces sensitivity at CF by as much as 60–81 dB, and causes a relative phase lead at CF.

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Basilar-membrane responses to tones at the base of the chinchilla cochlea

A comprehensive theory is formulated for the central formation of the pitch of complex tones, i.e., periodicity pitch [Schouten, Ritsma, and Cardozo, J. Acoust. Soc. Amer. 34, 1418–1424 (1962)]. This theory is a logical deduction from statistical estimation theory of the optimal estimate for fundamental frequency, when this estimate is constrained in ways inferred from empirical phenomena. The basic constraints are (i) the estimator receives noisy information on the frequencies, but not amplitudes and phases, of aurally resolvable simple tones from the stimulus and its aural combination tones, and (ii) the estimator presumes all stimuli are periodic with spectra comprising successive harmonics. The stochastic signals representing the frequencies of resolved tones are characterized by independent Gaussian distributions with mean equal to the frequency represented and a variance that serves as free parameter. The theory is applicable whether frequency is coded by place or time. Optimum estimates of fundamental frequency and harmonic numbers are calculated upon each stimulus presentation. Multimodal probability distributions for the estimated fundamental are predicted in consequence of variability in the estimated harmonic numbers. Quantification of the variance parameter from musical intelligibility data in Houtsma and Goldstein [J. Acoust. Soc. Amer. 51, 520–529 (1972)] shows it to be dependent upon the frequency represented and not upon other stimulus frequencies. The quantified optimum processor theory consolidates known data on pitch of complex tones.

An optimum processor theory for the central formation of the pitch of complex tones

A hearing aid device providing instantaneous gain compression for sound signals and adaptive control of nonlinear waveform distortion, the device comprising: (a) at least one bandpass nonlinearity (BPNL) amplifier comprising a first bandpass filter, a second bandpass filter, and a memoryless nonlinear (MNL) compressive audio amplifier configured to receive a sound signal from the first bandpass filter and provide an MNL compressive audio amplifier output to the second bandpass filter, wherein the MNL compressive audio amplifier is configured to produce the MNL compressive audio amplifier output by providing memoryless gain compression directly on a sound signal that is (1) received from the first bandpass filter and (2) exhibits instantaneous amplitudes greater than a compression threshold, the BPNL amplifier thereby producing a desired gain compression on the received sound signal at an output of the second bandpass filter, and (b) a controller in communication with the BPNL amplifier, the controller being configured to adjust the compression threshold of the MNL compressive audio amplifier. Adjustment of the compression threshold in each BPNL amplifier may be achieved at least partially in response to a user input and/or to sound signal changes. By adaptively controlling the compression threshold, performance of the device can by optimized to match its environment.

Hearing aids based on models of cochlear compression using adaptive compression thresholds

A model simulating cochlear spectrum analysis is disclosed which includes a pair of matched all pole lattices interconnected by a plurality of tip couplers providing non-linear distributed bilateral signal processing. One of the lattices along with the tip couplers corresponds to the organ of Corti found in the cochlea and the second lattice corresponds to the basilar membrane also found in the cochlea such that the model provides a striking resemblance in structure to the physical properties of the cochlea itself. With the cochlea model disclosed, distortion products and otoacoustic emissions are simulated. An intermediate model is also disclosed which provides bilateral signal processing but lacks distributed amplification.

Electronic simulator of non-linear and active cochlear spectrum analysis

Relations among compression, suppression, and combination tones in mechanical responses of the basilar membrane: data and MBPNL model.

Human psychophysical measurements of the cubic combination tone (2f1-f2) have shown that at low and moderate stimulus levels its phase decreases at 6 degrees-12 degrees per dB increase in stimulus level. This finding contrasts with physiological measurements in anaesthetized animals where the CT phase is insensitive to stimulus level. We have characterized quantitatively the difference in cochlear nonlinear response between humans and animals in terms of a cochlear nonlinear transmission line model having different nonlinear elements for human and animal. Following Hall [J. Acoust. Soc. Am. 56, 1818-1828 (1974)], a nonlinearity was introduced in the resistance of the cochlear partition (model A) for describing the animal cochlea. To model the human cochlea, we found that adding a nonlinear stiffness to the nonlinear mechanical loading of the basilar membrane gave the correct phase-amplitude dependence (model B). Simulation was used to solve the nonlinear models in the time domain. For high amplitude stimuli, both models predict similar results, mainly saturation in the response. The significant differences between the models occur at low and moderate stimulus intensities. According to model B the site of the resonant frequency along the basilar membrane depends on the stimulus level, while it is independent of stimulus level according to model A. As a result of the shift in the resonant site location in model B, the phase response profile is shifted as well, so that the phase response at the original resonant site depends on stimulus level. The psychophysical data on CT cancellation were predicted by model B, while physiological data on CT cancellation are predicted by model A.

Julius L. Goldstein

Papers

An optimum processor theory for the central formation of the pitch of complex tones

Hearing aids based on models of cochlear compression using adaptive compression thresholds

Electronic simulator of non-linear and active cochlear spectrum analysis

Relations among compression, suppression, and combination tones in mechanical responses of the basilar membrane: data and MBPNL model.

A cochlear nonlinear transmission‐line model compatible with combination tone psychophysics