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Abstract: The paper presents the synthesis of FIR filters with the magnitude characteristic that matches an arbitrary human audiogram, by using two of the toolkits provided by Matlab: the levinson function, that implements the Levinson-Durbin algorithm, and the standard routine fir2, based on the frequency sampling method. The performances of the filters synthesized with the two Matlab toolkits are evaluated by comparing their magnitude characteristics against the given audiogram, for the same length of the filters. Moreover, for each of the two implemented filters having the optimal length, for the same maximum approximation error, the impulse response and phase characteristic are also discussed.
Keywords: FIR filter, Levinson-Durbin algorithm, human audiogram.
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I. INTRODUCTION
The sensitivity of the human ear varies with frequency, being less sensitive at very low and very high frequencies, and most sensitive to sounds in the range of frequencies used by human spoken language (500 Hz - 4 kHz). When hearing loss of a person is suspected, an audiometry is performed. The audiologists measure the threshold intensity of the human hearing in the range of 125-8000 Hz, generally in octave steps and often including the half-octave frequencies; hence standardized frequencies include: 125, 250, 500, 750, 1000, 1500, 2000, 3000, 4000, 6000 and 8000 Hz.
The audiogram is the graphical representation of the sound level required for a person to just detect specific sounds across the frequencies that it can hear. The audiogram charts the hearing level relative to a standardized curve representing normal hearing. Therefore, the units of the y-axis are decibels hearing level (dB HL). Normal hearing is classified as being between -10 dB HL and 15 dB HL [1].
Hearing loss is usually accompanied by a reduction in the loudness range of sound that a person can process. This range is different across the frequency spectrum of hearing. A deteriorated hearing of a person can be improved by fitting an electro-acoustic device, called hearing aid, which selectively amplify the sounds based on these two factors: the frequency of the sound and the loudness of the sound source.
The field of research of this paper is the synthesis of a digital FIR filter that models the human hearing response, based on the data recorded in an...