A Method for Designing FIR Filters with Arbitrary Magnitude Characteristic Used for Modeling Human Audiogram

Abstract

This paper presents an iterative method for designing FIR filters that implement arbitrary magnitude characteristics, defined by the user through a set of frequency-magnitude points (frequency samples). The proposed method is based on the non-uniform frequency sampling algorithm. For each iteration a new set of frequency samples is generated, by processing the set used in the previous run; this implies changing the samples location around the previous frequency values and adjusting their magnitude through interpolation. If necessary, additional samples can be introduced, as well. After each iteration the magnitude characteristic of the resulting filter is determined by using the non-uniform DFT and compared with the required one; if the errors are larger than the acceptable levels (set by the user) a new iteration is run; the length of the resulting filter and the values of its coefficients are also taken into consideration when deciding a re-run. To demonstrate the efficiency of the proposed method a tool for designing FIR filters that match human audiograms was implemented in LabVIEW. It was shown that the resulting filters have smaller coefficients than the standard one, and can also have lower order, while the errors remain relatively small

IIR filter synthesis based on Real-Coded Genetic Algorithm for human audiogram emulation

“…The results yielded by our method were then compared against the 20 th order FIR filter (designed to match the same audiogram) synthesized by using the method previously reported in [4].…”

“…The values of the SSE, TSE and PME were measured for the IIR filter obtained with RCGA and compared to the FIR filter from [4]. The results are summarized in Table I: SSE in the 3 rd and 4 th columns, TSE and PME in the last two rows respectively.…”

“…3 (the values are in degrees). The IIR filter obtained with RCGA (the continuous-line plot) is nonlinear while the FIR filter from [4] (the dotted-line plot) is linear (excluding phase wraps at +/-180 degrees). In general, nonlinear phase characteristic is not considered important for hearing aids, although it could be an issue for application such as room response equalization.…”

“…Our previously work includes the development of a GA for designing FIR filters that implement arbitrary, user-defined, magnitude characteristics [4].…”

“…Phase responses of the matching filters (wrapped at +/-180 degrees) yielded by the proposed method and reported in[4].…”