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

Abstract

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. Index Terms—discrete Fourier transforms, error analysis, FIR filter, interpolation and non-uniform sampling.