arXiv subjects

Samiya A Alkhairy

Publications and source records attributed to Samiya A Alkhairy.

6 recordsLinked to original sources

arXiv2026

Auditory Filter Behavior and Updated Estimated Constants

Filters from the Gammatone family are often used to model auditory signal processing, but the filter constant values used to mimic human hearing are largely set to values based on historical psychoacoustic data collected several decades ago. Here, we move away from this long-standing convention, and estimate filter constants using a range of more recent reported filter characteristics (such as quality factors and ratios between quality factors and peak group delay) within a characteristics-based framework that clarifies how filter behavior is related to the underlying constants. Using a sharp-filter approximation that captures shared peak-region behavior across certain classes of filters, we analyze the range of behaviors accessible when the full degrees of freedom of the filter are utilized rather than fixing the filter order or exponent to historically prescribed values. Filter behavior is characterized using magnitude-based and phase-based characteristics and their ratios, which reveal which characteristics are informative for constraining filter constants and which are only weakly constraining. We show that these insights and estimation methods extend to multiple realizable filter classes from the Gammatone family and apply them, together with recent physiological and psychoacoustic observations, to derive constraints on and estimates for filter constants for human auditory filters. More broadly, this framework supports the design of auditory filters with arbitrary characteristic-level specifications and enables systematic assessment of how variations in filter characteristics influence auditory models, perceptual findings, and technologies that rely on auditory filterbanks.

eess.AS↗

arXiv2025

Characteristics-Based Design of Generalized-Exponent Bandpass Filters

We develop characteristics-based filter design methods for a class of IIR bandpass filters, which we refer to as Generalized-Exponent Filters (GEFs) and that are represented as second-order filters raised to non-unitary exponents. GEFs have a peak, are effectively linear phase, and are useful for seismic signal phase-picking, cochlear implants, and equalizers. The native frequency-domain specifications for GEFs are not on given frequency responses but rather on filter characteristics such as peak frequency, bandwidth, and group delay. Our characteristics-based method for filter design accommodates direct specification of a trio of frequency-domain characteristics from amongst the peak frequency, convexity, ndB quality factors, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. We achieve this by deriving filter parameterizations with sets of filter characteristics which involves deriving closed-form analytic expressions mapping sets of filter characteristics to the original filter constants by making sharp-filter approximations. This results in parameterizations for GEFs including ones with simultaneous specification of magnitude-based and phase-based characteristics (e.g. bandwidths and group delays). This in turn enables designing sharply tuned filters without significant group delay, and simultaneous control over frequency selectivity and synchronization which is important in designing filterbanks. Our filter design methods with direct control over characteristics may also be utilized beyond static filter design for higher-order variable bandpass filter design and may be useful for characteristics-based adaptive filtering. Our methods are inherently stable, highly accurate in meeting strict specifications on desired characteristics, simple, and computationally efficient. The methods extend to the design of related bandpass and multiband filters.

eess.SP↗

arXiv2025

Rational-Exponent Filters with Applications to Generalized Exponent Filters

We present filters with rational exponents in order to provide a continuum of filter behavior not classically achievable. We discuss their stability, the flexibility they afford, and various representations useful for analysis, design and implementations. We do this for a generalization of second-order filters which we refer to as rational-exponent Generalized Exponent Filters (GEFs) that are useful for a diverse array of applications. We present equivalent representations for rational-exponent GEFs in the time and frequency domains: transfer functions, impulse responses, and integral expressions - the last of which allows for efficient real-time processing without preprocessing requirements. Rational-exponent filters enable filter characteristics to be on a continuum rather than limiting them to discrete values thereby resulting in greater flexibility in the behavior of these filters without additional complexity in causality and stability analyses compared with classical filters. In the case of GEFs, this allows for having arbitrary continuous rather than discrete values for filter characteristics such as (1) the ratio of 3dB quality factor to maximum group delay - particularly important for filterbanks which have simultaneous requirements on frequency selectivity and synchronization; and (2) the ratio of 3dB to 15dB quality factors that dictates the shape of the frequency response magnitude.

eess.SP↗

arXiv2024

Cochlear Wave Propagation and Dynamics in the Human Base and Apex: Model-Based Estimates from Noninvasive Measurements

Cochlear wavenumber and impedance are mechanistic variables that encode information regarding how the cochlea works - specifically wave propagation and Organ of Corti dynamics. These mechanistic variables underlie interesting features of cochlear signal processing such as its place-based wavelet analyzers, dispersivity and high-gain. Consequently, it is of interest to estimate these mechanistic variables in various species (particularly humans) and across various locations along the length of the cochlea. In this paper, we develop methods to estimate the mechanistic variables (wavenumber and impedance) from noninvasive response characteristics (such as the quality factors of psychophysical tuning curves) using an existing analytic shortwave single-partition model of the mammalian cochlea. We then apply these methods to estimate human mechanistic variables using reported values for quality factors from psychophysical tuning curves and a location-invariant ratio extrapolated from chinchilla. Our resultant estimates for human wavenumbers and impedances show that the minimum wavelength (which occurs at the peak of the traveling wave) is smaller in base than the apex. The Organ of Corti is stiffness dominated rather than mass dominated, and there is negative effective damping prior to the peak followed by positive effective damping. The effective stiffness, and positive and negative effective damping are greater in the base than the apex. The methods introduced here for estimating mechanistic variables from characteristics of invasive or noninvasive responses enable us to derive such estimates across various species and locations where the responses are describable by sharp filters. In addition to studying cochlear wave propagation and dynamics, the estimation methods developed here are also useful for auditory filter design.

q-bio.QM↗

arXiv2021

Analytic Methods for Differential Algebraic Equations

We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems as it is carried out by hand. Analytic solutions to the system and analytic characterization through governing equations provide insights into the behaviors of DAEs as well as the parametric regions of operation for each potential behavior. For each system (DAEs), and choice of dependent variable, there is a corresponding governing equation which is univariate ODE or PDE that is typically higher order than the constitutive equations of the system. We first introduce a direct formulation for representing systems of linear DAEs. Unlike state space formulations, our formulation follows very directly from the system of constitutive equations without the need for introducing state variables or singular matrices. Using this formulation for the system of constitutive equations (DAEs), we develop methods for deriving analytic expressions for the full solution (complementary and particular) for all dependent variables of systems that consist of constant coefficient ordinary-DAEs and special cases of partial-DAEs. We also develop methods for deriving the governing equation for a chosen dependent variable for the constant coefficient ordinary-DAEs and partial-DAEs as well as special cases of variable coefficient DAEs. The methods can be automated with symbolic coding environments thereby allowing for dealing with systems of any size while retaining analytic nature. This is relevant for interpretable modeling, analytic characterization and estimation, and engineering design in which the objective is to tune parameter values to achieve specific behavior. Such insights cannot directly be obtained using numerical simulations.

math.GM↗

arXiv2020

An analytic physically motivated model of the mammalian cochlea

We develop an analytic model of the mammalian cochlea. We use a mixed physical-phenomenological approach by utilizing existing work on the physics of classical box-representations of the cochlea, and behavior of recent data-derived wavenumber estimates. Spatial variation is incorporated through a single independent variable that combines space and frequency. We arrive at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. We perform model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank and filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.

q-bio.TO↗