Design of FIR filters with magnitude specifications

Abstract

In this paper, we present a method for the design of an FIR filter that minimizes the Chebyshev error in the magnitude frequency domain. The method exhibits desirable properties similar to those characterizing the Parks-McClellan algorithm and requires less than seven iterations to solve the nonlinear filter design problem. The O ( N 2 ) iterative method yields filters that are 40% better than those designed using conventional techniques and results in filters that are 30% shorter.

A model of the cochlear apex and structure for study of mechanism and response characteristics

“…The model is appropriate for developing the estimation methods towards understandings how the cochlea works. This is the case because the aforementioned model properties enable us to derive expressions to compute model constant values from values of response characteristics such as bandwidths and maximum group delays of pressure or velocity [1,3,4] as will be elaborated upon later in this paper. Building on these expressions, we may further develop methods to estimate values of model constants (and from them, mechanistic variables) from characteristics of noninvasive responses (such as psychophysical tuning curves and otoacoustic emissions).…”

“…With the method introduced above for determining model constant values from noninvasive response characteristics, we can now (2) determine the wavenumber and impedance from human noninvasive response characteristics, and also (3) differentiate between their profiles in the human base and apex (which provides us with information regarding how these two regions of the cochlea function differently). We do so by first plotting (in figure 2) the wavenumber and impedance of two points along the length of the cochlea -one from the apex with a low CF, 1 kHz, and another from the base with a higher CF, 10 kHz.…”

“…In addition to comparative analysis built on estimating values of model constants from characteristics, we can study the model expressions for wavenumber and impedance more deeply (without specifying model constant values) as they provides us with a general understanding of how the cochlea functions across mammalian species. In addition to their use for studying auditory physics, the model and estimation methods are also useful for developing easily tunable auditory filters for engineering applications and perceptual studies [3].…”