The auditory compensation, especially the filter bank, is an important function in hearing aids because it makes the sound audible for the hearing-impaired people. Famous prescriptive formula like NAL-NL1 or HSE give the amplification targets on 1/3-octave frequencies from 125Hz to 8000Hz. The filter bank should be designed to well match the prescriptions, so that the hearing loss can be compensated accurately and maximize the speech intelligibility.
Furthermore, the overall signal processing delay and the power consumption is a critical issue for hearing aids as well as for the filter bank design. To the best of our knowledge, designing the filter bank for the digital hearing aids in the literature can be classified into two categories:
uniform filter banks [13] ~ [16] and non-uniform filter banks [17] ~ [20].
The uniform filter bank means that the bands are equally divided the frequencies from 0 to . A 16-band discrete Fourier transform (DFT) filter bank is designed in [13], while an 8-band filter bank with equal-spaced finite-impulse response (FIR) filters is implemented in [14]. [15] and [16] exploit the interpolation finite-impulse response (IFIR) techniques to realize a 7-band and a 8-band uniform filter bank respectively. The drawback of uniform filter
banks is that they do not match the non-uniform frequency characteristics in human auditory system. As a result, the uniform filter bank may face difficulties at matching the prescriptions for various types of hearing loss. Consequently, the using of non-uniform filter banks is more suitable.
As depicted in Figure 2-6, the common-used non-uniform filter banks can go a step further to classify into critical-band [17], symmetric-band [18][19], and 1/3-octave-band [20]
filter banks.
Frequency (Hz) Magnitude (dB)
Frequency (Hz) Magnitude (dB)
Frequency (Hz) Magnitude (dB)
Frequency (Hz) Magnitude (dB)
Uniform
Critical-like
Symmetric
1/3-octave
Figure 2-6 Different types of filter banks
In order to provide the frequency characteristics similar to that of the human auditory system, a critical-band filter bank is designed in [17]. The critical bands are divided according to psychoacoustics and have good match to human perception. However, the irregular property of the critical bands makes the implementation difficult. The design in [17], for
example, implements 16-band critical-like filter bank with rather high-order (110-tap) FIR filters, which has significant computation complexity. On the other hand, Lian and Wei proposed an 8-band and 16-band symmetric filter bank [18][19]. The symmetric filter bank is symmetric at /2 and has higher frequency resolution at both high and low frequencies. With the IFIR and frequency-response masking (FRM) techniques, the computational complexity is largely reduced. However, these symmetric banks have relatively small number of bands at middle frequencies and may not have sufficient resolutions for hearing loss compensation.
The preliminary results of matching capability for four types of filter bank are reported in Figure 2-7. Each type of filter bank is normalized to have 18 bands and designed at the sampling rate of 24 KHz. Then we evaluate the maximum matching error between the hearing aid’s frequency response and the 18 amplification targets prescribed by NAL-NL1. The uniform filter bank has equal-space bands from 0 to π. It has a lower frequency resolution in low frequencies so the matching error is large there. The maximum matching error is up to 8.4dB. The symmetric filter bank has a lower frequency resolution at middle frequencies. So, it has maximum matching error of 6.2dB at middle frequencies. The critical-like filter bank has a good match to the human hearing characteristics and the spacing is close to 1/3-octave filter bank at the middle and high frequencies. The bands are equally spaced at low frequencies, so it will have a larger error there. The maximum matching error is 3dB. Finally, by the use of 1/3-octave filter bank the hearing aid response can perfectly match the prescribed targets because the prescription formula calculates the prescriptions on 1/3-octave frequencies.
2000 4000 6000 8000
● 18 prescriptive targets from NAL-NL1 Matching curve of hearing aid system
Uniform filter bank Symmetric filter bank
Critical-like filter bank 1/3-octave filter bank
max error = 8.4 dB max error = 6.2 dB
max error = 3.0 dB max error = 0.0 dB
Figure 2-7 Matching capability comparison for four types of filter bank
An 18-band 1/3-octave filter bank has been designed and implemented in [20]. This work adopts the ANSI S1.11 standard base on the fact that the mostly used fitting formula NAL-NL1 prescribes the target gains on each 1/3-octave frequencies defined in the ANSI S1.11 standard. As a result, the hearing aid’s magnitude response can have the best capability to match any type of prescriptions by the use of ANSI S1.11 1/3-octave filter bank. The work also makes use of the multistage IFIR and multi-rate techniques to largely reduce the computational complexity (in terms of number of the multiplications per input sample). The complexity-effective architecture saves about 96% of multiplications comparing that with a straightforward FIR filter bank. However, the price this work pay is the long group delay which is up to 78ms and will largely limit the usage of this design. We observe that the unacceptable long group delay is due to the very sharp transition in lower frequency part of ANSI S1.11 1/3-octave bands. Even using the straightforward FIR or IIR to implement the filter bank, there still have group delay up to 27 ms and this can not be shortening further.
3 L OW -D ELAY F ILTER B ANK D ESIGN
In this chapter, we propose a design method of 18-band 1/3-octave filter bank. The input sampling rate is 24 KHz to cover the whole frequency range that have prescribed amplification targets from NAL-NL1 fitting formula. Firstly, a quasi-ANSI S1.11 1/3-octave specification is developed to reduce the group delay. Secondly, we present a systematic design flow to design and optimize the FIR filter coefficients such that filter use minimized orders to meet the specification. Thirdly, a matching-error optimization method is proposed. Finally, the filter bank exploration results and verifications on various types of hearing loss will be demonstrated.