We evaluate the group delay and the maximum matching error with respect to different stretch factor k as reported in Table 3-1. With the increasing stretch factor k, the transition
bandwidth increase gradually and the group delay decreases from 27.3 ms to 9.4 ms. Notice that when the stretch factor goes from 1.2 to 1.4, the group delay is unchanged. This is because when the stretch factor is larger then 1.2, the stop-band frequency of the lowest-frequency band intersects the zero point. We only can stretch the transition bandwidth when the stop-band frequency is a positive value. Besides, the maximum matching error of prescribed targets increases from 0.8 dB to 7.1 dB. But after applying the matching-error optimization method, matching error only increase from 0dB to 2dB. Note that a feasible solution is found for stretch factor k larger than 0.8. The filter bank satisfy the group delay (smaller then 10 ms) and maximum error (smaller then 3dB) constraint.
Table 3-1 Group delay & matching error with respect to k
original with error reduction
0.0 27.3 0.8 0.0
0.2 21.6 1.1 0.0
0.4 17.0 1.5 0.8
0.6 13.4 2.4 1.4
0.8 10.0 3.3 1.5
1.0 9.8 4.2 1.5
1.2 9.4 5.7 1.9
1.4 9.4 7.1 2.0
Group delay (ms) Stretch factor k
Matching error (dB)
The magnitude response of the quasi-ANSI S1.11 1/3-octave filter bank is depicted in Figure 3-6 and Figure 3-7. The bands in lower frequencies have a wider transition bandwidth to reduce the group delay. Besides, only the nine lowest-frequency bands have been modified, the other bands which are located at the frequencies larger then 1000Hz still satisfy the ANSI S1.11 1/3-octave standard.
2000 4000 6000 8000 10000 12000 -60
-40 -20 0
Frequency (Hz)
Magnitude (dB)
Figure 3-6 Magnitude response of quasi-ANSI S1.11 1/3-octave filter bank
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-60 -40 -20 0
Frequency (Hz)
Magnitude (dB)
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Frequency (Hz)
Magnitude (dB)
(a)
(b)
Figure 3-7 Magnitude response comparison between (a) ANSI S1.11 1/3-octave filter bank (b) quasi-ANSI S1.11 1/3-octave filter bank
We use the quasi-ANSI S1.11 1/3-octave filter bank to match the prescriptions from NAL-NL1 of three different type of hearing loss as shown in Figure 3-8 ~ Figure 3-10. Firstly, the audiogram in Figure 3-8 is the most common type of hearing loss called presbycusis type
which is the hearing loss due to aging. The hearing loss will increase with the frequency. The maximum matching error of the 18 prescribed amplification target is 0.4dB. Secondly, the hearing loss in Figure 3-9 increases with the frequency decreases which is contrary to presbycusis type. Moreover, the hearing loss in Figure 3-10 is a severe hearing loss and is almost flat across all the frequencies. Because the difference of the adjacent prescribed gains is larger then the two cases before, this case is more difficult to match. The matching error is 1.5dB in this case and is still small then 3dB.
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0
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Figure 3-8 Matching result for hearing loss due to aging
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0
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Figure 3-9 Matching result for rising hearing loss
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Figure 3-10 Matching result for severe flat hearing loss
In order to evaluate the matching capability of the proposed filter bank, we are going to examine it using various hearing loss audiograms. The results are illustrated in Figure 3-11 ~ Figure 3-16. These audiograms are downloaded from the Independent Hearing Aid Information which is a public service by Hearing Alliance of America. [23] These audiograms are also adopted in [18] to verify the matching capability. But the work in [18] is trying to match the audiograms itself not the prescriptions. We think that we can compensate the hearing loss more properly by matching the prescriptions to the hearing loss. If we fitting our hearing aid to match the audiograms, it may have the amplification exceed actually what hearing loss people need. Moreover, matching the audiograms is easier due to less amplification targets. Even through it is more difficult to match the prescriptions, the matching results show that the proposed filter bank can have a much smaller matching error compared to the filter bank design in [18].
In the following, the hearing loss levels are defined as described in Figure 2-2 and summarized as follows.
Normal hearing: 0 ~ 19 dB
Mild hearing loss: 20 ~ 39 dB
Moderate hearing loss: 40 ~ 59 dB
Severe hearing loss: 60 ~ 89 dB
Profound hearing loss: 90 + dB
Figure 3-11 shows an audiogram with mild hearing loss around frequency 4 KHz. Such kind of hearing loss results probably from diseases or career injury. People can not hear most consonants and will have severe trouble in noisy environments. The maximum matching error is 0.2 dB, while that in [18] is about 8 dB after optimization. Therefore the maximum matching error is considerably reduced.
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Figure 3-11 Matching result for mild hearing loss at 4 KHz
Figure 3-12 shows an audiogram with mild hearing loss in the whole frequencies.
People with such kind of hearing loss have difficulties in hearing most vowels and consonants and will have more trouble in noisy conditions. The maximum matching error is 0.2 dB, whereas that in [18] is about 3.5 dB after gain optimization. The matching accuracy is higher than that in [18].
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Figure 3-12 Matching result for mild hearing loss in whole frequencies
Figure 3-13 shows an audiogram with mild to moderate hearing loss at low frequencies and mild hearing loss at high frequencies. The primary effect will be a loss of overall loudness because most vowels cannot be heard. Very close distance conversations may be necessary.
The maximum matching error is 0.1 dB, whereas that in [18] is about 2.5 dB after gain optimization.
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125 250 500 1,000 2,000 4,000 8,000 0
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Figure 3-13 Matching result for mild to moderate hearing loss in low frequencies
Figure 3-14 again shows a most common type of hearing loss which is due to aging and
has moderate to profound hearing loss at middle to high frequencies. As the frequency becomes higher, the hearing impaired has higher hearing loss. The sensitivity at low frequencies is relatively good to get some vowel information and know that someone is talking. However, the loss of too many consonants will make one unable to distinguish one word from another. The maximum error is 0.3 dB, whereas that in [18] is about 8 dB after optimization. The matching error is significantly reduced.
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Figure 3-14 Matching result for hearing loss due to aging
Figure 3-15 shows a type of hearing loss which is common seen in older workers in noisy industries and has severe hearing loss in middle to high frequencies. It is generally due to the effects of too much noise for too many years on the inner ear and related structures.
Note that in the lower frequencies, the hearing sensitivity is good enough to give some vowel information. However, the high hearing loss in high frequency leads to miss so many consonants and may have a large problem distinguishing one word from another. The maximum error is 0.6 dB, whereas that in [18] is about 8 dB after optimization. The matching error is significantly reduced.
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Figure 3-15 Matching result for hearing loss
Figure 3-16 shows an audiogram with severe to profound hearing loss at all frequencies, where almost all hearing thresholds are around 90 dB. Because the hearing loss is severe to profound, the prescribed gains are very large and change largely between two gains. It is difficult to match all of the amplification targets. The maximum error is 2.5 dB. It is well known that people are not sensitive to a matching error below 3 dB, so the matching result is satisfactory.
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Figure 3-16 Matching result for hearing loss
4 I MPLEMENTATION R ESULTS
We exploit the natural property of 1/3-octave filter bank to design a complexity-effective architecture by the use of multirate & interpolated finite-impulse response (IFIR) techniques.
We fold our filter bank into an architecture using only one filter to reduce the complexity. To avoid the computation conflicts or stalls, the scheduling method is also provided to minimize the required storage elements. Besides, we apply some low-power techniques to reduce the power consumption.