scholarly journals The Role of the Bandwidth-Duration Product WT in the Detectability of Diotic Signals

2021 ◽  
Author(s):  
◽  
Judi Lapsley Miller
Keyword(s):  
Gaussian Noise ◽  
Critical Band ◽  
Ideal Observer ◽  
Fundamental Parameter ◽  
Band Pass Filter ◽  
Individual Values ◽  
Pass Filter ◽  
Time Frequency ◽  
Linear Detector ◽  
Temporal Integrator

<p>The bandwidth-duration product, WT , is a fundamental parameter in most theories of aural amplitude discrimination of Gaussian noise. These theories predict that detectability is dependent on WT , but not on the individual values of bandwidth and duration. Due to the acoustical uncertainty principle, it is impossible to completely specify an acoustic waveform with both finite duration and finite bandwidth. An observer must decide how best to trade-off information in the time domain with information in the frequency domain. As Licklider (1963) states, "The nature of [the ear's] solution to the time-frequency problem is, in fact, one of the central problems in the psychology of hearing."This problem is still unresolved, primarily due to observer inconsistency in experiments, which degrades performance making it difficult to compare models. The aim was to compare human observers' ability to trade bandwidth and duration, with simulated and theoretical observers. Human observers participated in a parametric study where the bandwidth and duration of 500 Hz noise waveforms was systematically varied for the same bandwidth-duration products (WT = 1, 2, and 4, where W varied over 2.5-160 Hz, and T varied over 400-6.25 ms, in octave steps). If observers can trade bandwidth and duration, detectability should be constant for the same WT . The observers replicated the experiments six times so that group operating characteristic (GOC) analysis could be used to reduce the effects of their inconsistent decision making. Asymptotic errorless performance was estimated by extrapolating results from the GOC analysis, as a function of replications added. Three simulated ideal observers: the energy, envelope, and full-linear (band-pass filter, full-wave rectifier, and true integrator) detectors were compared with each other, with mathematical theory and with human observers. Asymptotic detectability relative to the full-linear detector indicates that human observers best detect signals with a bandwidth of 40-80 Hz and a duration of 50-100 ms, and that other values are traded off in approximately concentric ellipses of equal detectability. Human detectability of Gaussian noise was best modelled by the full-linear detector using a non-optimal filter. Comparing psychometric functions for this detector with human data shows many striking similarities, indicating that human observers can sometimes perform as well as an ideal observer, once their inconsistency is minimised. These results indicate that the human hearing system can trade bandwidth and duration of signals, but not optimally. This accounts for many of the disparate estimates of the critical band, rectifier, and temporal integrator, found in the literature, because (a) the critical band is adjustable, but has a minimum of 40-50 Hz, (b) the rectifier is linear, rather than square-law, and (c) the temporal integrator is either true or leaky with a very long time constant.</p>

scholarly journals The Role of the Bandwidth-Duration Product WT in the Detectability of Diotic Signals

2021 ◽  
Author(s):  
◽  
Judi Lapsley Miller
Keyword(s):  
Gaussian Noise ◽  
Critical Band ◽  
Ideal Observer ◽  
Fundamental Parameter ◽  
Band Pass Filter ◽  
Individual Values ◽  
Pass Filter ◽  
Time Frequency ◽  
Linear Detector ◽  
Temporal Integrator

<p>The bandwidth-duration product, WT , is a fundamental parameter in most theories of aural amplitude discrimination of Gaussian noise. These theories predict that detectability is dependent on WT , but not on the individual values of bandwidth and duration. Due to the acoustical uncertainty principle, it is impossible to completely specify an acoustic waveform with both finite duration and finite bandwidth. An observer must decide how best to trade-off information in the time domain with information in the frequency domain. As Licklider (1963) states, "The nature of [the ear's] solution to the time-frequency problem is, in fact, one of the central problems in the psychology of hearing."This problem is still unresolved, primarily due to observer inconsistency in experiments, which degrades performance making it difficult to compare models. The aim was to compare human observers' ability to trade bandwidth and duration, with simulated and theoretical observers. Human observers participated in a parametric study where the bandwidth and duration of 500 Hz noise waveforms was systematically varied for the same bandwidth-duration products (WT = 1, 2, and 4, where W varied over 2.5-160 Hz, and T varied over 400-6.25 ms, in octave steps). If observers can trade bandwidth and duration, detectability should be constant for the same WT . The observers replicated the experiments six times so that group operating characteristic (GOC) analysis could be used to reduce the effects of their inconsistent decision making. Asymptotic errorless performance was estimated by extrapolating results from the GOC analysis, as a function of replications added. Three simulated ideal observers: the energy, envelope, and full-linear (band-pass filter, full-wave rectifier, and true integrator) detectors were compared with each other, with mathematical theory and with human observers. Asymptotic detectability relative to the full-linear detector indicates that human observers best detect signals with a bandwidth of 40-80 Hz and a duration of 50-100 ms, and that other values are traded off in approximately concentric ellipses of equal detectability. Human detectability of Gaussian noise was best modelled by the full-linear detector using a non-optimal filter. Comparing psychometric functions for this detector with human data shows many striking similarities, indicating that human observers can sometimes perform as well as an ideal observer, once their inconsistency is minimised. These results indicate that the human hearing system can trade bandwidth and duration of signals, but not optimally. This accounts for many of the disparate estimates of the critical band, rectifier, and temporal integrator, found in the literature, because (a) the critical band is adjustable, but has a minimum of 40-50 Hz, (b) the rectifier is linear, rather than square-law, and (c) the temporal integrator is either true or leaky with a very long time constant.</p>

scholarly journals Band pass filter design against interrupted‐sampling repeater jamming based on time‐frequency analysis

2019 ◽  
Vol 13 (10) ◽  
pp. 1646-1654 ◽  
Author(s):  
Jian Chen ◽  
Wenzhen Wu ◽  
Shiyou Xu ◽  
Zengping Chen ◽  
Jiangwei Zou
Keyword(s):  
Frequency Analysis ◽  
Filter Design ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Band Pass

scholarly journals A Spectrum Detection Approach for Bearing Fault Signal Based on Spectral Kurtosis

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yunfeng Li ◽  
Liqin Wang ◽  
Jian Guan
Keyword(s):  
Wavelet Spectrum ◽  
Rolling Element Bearing ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Time Frequency ◽  
Bearing Fault ◽  
Spectral Kurtosis ◽  
Spectrum Detection ◽  
Detection Approach ◽  
The Impact

According to the similarity between Morlet wavelet and fault signal and the sensitive characteristics of spectral kurtosis for the impact signal, a new wavelet spectrum detection approach based on spectral kurtosis for bearing fault signal is proposed. This method decreased the band-pass filter range and reduced the wavelet window width significantly. As a consequence, the bearing fault signal was detected adaptively, and time-frequency characteristics of the fault signal can be extracted accurately. The validity of this method was verified by the identifications of simulated shock signal and test bearing fault signal. The method provides a new understanding of wavelet spectrum detection based on spectral kurtosis for rolling element bearing fault signal.

One Abstraction Method for Displacement Response in the Sweep-Frequency Testing of Rotating Spindle

2016 ◽  
Vol 693 ◽  
pp. 1377-1384
Author(s):  
Yu Zhu Guo ◽  
Tian Ning Chen ◽  
Xiao Peng Wang ◽  
Yan Fei Xu
Keyword(s):  
Frequency Domain ◽  
High Speed ◽  
Measured Signal ◽  
Band Pass Filter ◽  
Shape Error ◽  
Cnc Milling ◽  
Sweep Frequency ◽  
Pass Filter ◽  
Time Frequency ◽  
Displacement Response

ion Method for Displacement Response in the Sweep-Frequency Testing of Rotating Spindle Guo Yuzhu1,a*, Chen Tianning1,b, Wang Xiaopeng1,c and Xu Yanfei11 State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, 710049 Xi’an, China [email protected], [email protected], [email protected] Keywords: Rotating spindle; Sweep-frequency measurement; Error separation. Abstract. In the measurement of motorized spindle dynamic performance, the non-contact sweep-frequency excitation is adopted to obtain the displacement response of spindle rotor under high speed rotating. Due to the shape error at measurement section, eccentric error and random vibration, the illusory signals is introduced to the practical measured signal, which makes it difficult to analyze the displacement response. To effectively separate the error, a new method combining template signal and slip filtering is presented. After analyzing the characteristics of displacement response and illusory signals in time-frequency domain, the template signal constructed by the non-superposing portions between response and error is employed to eliminate the error in superposing portions. And a band-pass filter which can slip in time-frequency domain is employed to eliminate the other error. A spindle of CNC milling machine is tested at 7000 r/min, and the analysis result shows that the displacement response can be abstracted successfully from the original signal measured by rotating spindle.

Spectral flatness factor and ‘intermittency’ in turbulence and in non-linear noise

1961 ◽  
Vol 10 (3) ◽  
pp. 366-370 ◽  
Author(s):  
D. A. Kennedy ◽  
S. Corrsin
Keyword(s):  
Shear Layer ◽  
Gaussian Noise ◽  
Band Pass Filter ◽  
Noise Band ◽  
Free Shear Layer ◽  
Pass Filter ◽  
Centre Frequency ◽  
Non Linear ◽  
Band Pass ◽  
Flatness Factor

The flatness factor F of the signal transmitted through a band-pass filter has been measured for the turbulence in a free shear layer and for a squared Gaussian noise. They both show flatness factor increasing with centre frequency fc. In the turbulence, band-passed signals look intermittent and have larger F than the full signal, but in the squared noise, band-passed signals all have smaller F than the full signal although they look more intermittent.It is shown analytically that the derivative of a smoothed, squared Gaussian noise may have flatness factor either greater or less than the undifferentiated signal.

scholarly journals Fault Diagnosis of Oil Pumping Machine Retarder Based on Sound Texture-Vibration Entropy Characteristics and Gray Wolf Optimization-Support Vector Machine

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Shutao Zhao ◽  
Ke Chang ◽  
Erxu Wang ◽  
Bo Li ◽  
Kedeng Wang ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Contrast Ratio ◽  
Permutation Entropy ◽  
Support Vector ◽  
Box Dimension ◽  
Gray Wolf ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Time Frequency ◽  
The Impact

In order to diagnose the retarder faults of oil pumping machine accurately in complex environments and improve the generalization of the algorithm, a GWO-SVM fault diagnosis algorithm based on the combination of sound texture and vibration entropy characteristics was proposed. Firstly, the acquired sound signal was purified by band-pass filter, then generalized S-transform was developed to extract the box dimension, directivity, and contrast ratio, which reflect the characteristics of time-frequency spectrum, to construct three-dimensional texture eigenvectors. Secondly, the K parameter of variational mode decomposition (VMD) was reasonably selected by the energy method, and then the vibration signal was decomposed to get modal components, and the permutation entropy was obtained from modal components. Finally, joint eigenvectors were constructed and fed into SVM for learning. The gray wolf optimization (GWO) algorithm was used to optimize the parameters of the SVM model based on mixed kernel function, which reduces the impact of sensor frequency response, environmental noise, and load fluctuation disturbance on the accuracy of retarder fault diagnosis. The results showed that the GWO-SVM fault diagnosis method, which is based on the combination of sound texture and vibration entropy characteristics, makes full use of the complementary advantages of signal frequency band. And the overall diagnostic accuracy for the experimental samples reaches 100%, which has good generalization ability.

Time–Frequency Signal Processing for Integrity Assessment and Damage Localization of Concrete Piles

2019 ◽  
Vol 20 (02) ◽  
pp. 2050020 ◽  
Author(s):  
Jing-Liang Liu ◽  
Si-Fan Wang ◽  
Jin-Yang Zheng ◽  
Chia-Ming Chang ◽  
Xiao-Jun Wei ◽  
...  
Keyword(s):  
Damage Identification ◽  
Assessment Tool ◽  
Band Pass Filter ◽  
Damage Localization ◽  
Pass Filter ◽  
Time Frequency ◽  
Integrity Assessment ◽  
Mode Decomposition ◽  
Noisy Signals ◽  
Phase Angles

This paper presents a new integrity assessment and damage localization method for piles based on one-dimensional wave propagation theory by integrating the analytical mode decomposition (AMD), recursive Hilbert transform (RHT) and complex continuous wavelet transform (CCWT) into a single assessment tool. The AMD is first used as a band pass filter to extract the mono-component over a frequency band of interest from the response of a pile head, aimed at attenuating the interference from various noisy signals. Then, the mono-component signal is demodulated into a purely frequency-modulated signal by means of RHT, which greatly reduces the interferences from the amplitude-modulated function. Finally, the CCWT is utilized to process the frequency-modulated signal and to calculate phase angles; the latter are subsequently mapped into the time–frequency domain to localize pile damage. The methodology is verified by a numerical example, in which a concrete pile is modeled by the finite element method considering the soil-pile interaction, and by an experimental case study on an actual pile. The results from the numerical and experimental examples demonstrate that the proposed method improves the efficiency of damage identification when compared with other three methods ([Formula: see text], [Formula: see text] and CCWT). In addition, the proposed method enables the localization of damage in full-scale piles situated in soil with an acceptable engineering accuracy by mutual validation with other pile integrity assessment methods, e.g. the ultrasonic emission method.

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