Tech Topic | February 2022 Hearing Review

By Laura Winther Balling, PhD, Lars Dalskov Mosgaard, PhD, and Dana Helmink, AuD

Hearing aid signal processing is central to the sound that surrounds the user every day. This article lays out different possible signal-processing strategies, focusing on the choice of filter bank and sampling rate, and how these relate to sound quality. Although both time- and frequency-domain filter banks have their advantages, the sound-quality benefits of a time-domain filter bank outweigh other considerations.

Many elements are important for a successful hearing aid—including ones that are not directly hearing-related, including as efficient batteries, reliable connectivity, and user-friendly design. However, signal processing remains at the heart of it all. 

The signal-processing choices in a hearing aid profoundly influence the hearing loss treatment, just like the sound in the hearing aids profoundly influences the person wearing them. Although basic hearing aids with connectivity and rechargeable batteries can be bought over the internet, the best, most appropriate sound requires the right signal-processing choices and an individualized fitting by a knowledgeable hearing care professional.

This article shows how sound quality and signal processing are related, with a focus on filter banks and sampling rates, and outlines the pros and cons of different possible choices. Ultimately, we argue for a choice of filter bank and sampling rate that preserves the signal and matches the human auditory system as closely as possible.

A Basic Processing Pathway

A common processing pathway in digital hearing aids starts with the signal being picked up by a microphone and converted from analog to digital. An analysis filter bank splits the signal up into multiple frequency bands, or channels, ready for further digital signal processing—processes such as compression and noise reduction. After processing, the signal is put back together by a synthesis filter bank and played out through the receiver in the hearing aid. This common approach to hearing aid design illustrates the important role of filter banks in digital signal processing.

Another important concept is sampling, which is the process of converting the continuous analog sound signal into discrete parts, the so-called samples, to be ready for further processing. This is done at different audio sampling rates (ie, with a different number of samples per second). CDs and many music streaming services use 44.1kHz or 44,100 samples per second. For hearing aids, audio sampling rates typically range between 20kHz and 33.1kHz.

The sampling rate is related to the frequency that can be represented in the signal, so that the highest frequency that can be represented is half the sampling rate. This frequency is known as the Nyquist frequency. This means that a 20kHz sampling rate has a Nyquist frequency of 10 kHz, allowing frequencies up to 10 kHz. Likewise, a 33kHz sampling rate allows frequencies up to 16.5 kHz. These numbers are sampling rates at the input stage; later in the processing pathway, the signal may be down-sampled to save processing capacity, before being up-sampled again. 

Although other factors, such as receiver roll-off, may limit the frequency range of the output, higher fidelity in the high frequencies remains relevant for certain hearing losses. A high sampling rate also has other sound quality benefits, including lower processing delay and more gently sloping filters.

Time- and Frequency-Domain Filter Banks

Although the basic processing pathway is the same across many hearing aids, a fundamental difference is the choice of filter bank. So-called frequency-domain, or uniform, filter banks are used by most hearing aid manufacturers, while Widex hearing aids rely on time-domain, or non-uniform, filter banks, a choice made in pursuit of natural sound.

The difference between the two types has to do with a fundamental trade-off in processing between time and frequency resolution. In any filter bank, the time resolution of each frequency band is proportional to the width of that frequency band. Broadly speaking, this means that a bandwidth that is 5 times wider has a time resolution that is 5 times higher. Conversely, a narrower bandwidth means poorer time resolution.

Frequency-domain filter banks limit the system to frequency bands of the same width across the entire frequency range. In practice, this means that all bands are relatively narrow, because bandwidth is set based on the bandwidth needed for the lowest frequencies, where the ear’s frequency sensitivity is the highest, and the bands therefore have to be narrow. Because of the trade-off between time and frequency described above, this also means that all bands—in both high and low frequencies—operate with the same, relatively poor, time resolution.

In contrast, non-uniform filter banks, including time-domain filter banks, offer the flexibility to operate with filters that may vary in bandwidth. This means that the hearing aid designers are free to set the bandwidths, in principle, any way they like. So, while for a uniform or frequency-domain filter bank all bands have the same width and time resolution, in a time-domain filter bank the bands vary in width, and therefore also in time resolution.

The Widex time-domain filter bank is designed with narrower bands at the lower frequencies and broader bands at the higher frequencies, thus keeping the same trade-off between time and frequency in the filter bank as humans have in their auditory systems. This filter bank design mimics the logarithmic way the ear works, with higher frequency sensitivity at lower frequencies and lower sensitivity at higher frequencies. In the human ear, the difference is physiologically manifested by larger areas of the cochlea being dedicated to detecting lower frequencies and smaller areas for higher frequencies. It is also heard in the fact that a doubling of frequency is always a difference of one octave, whether it is the difference between 125 and 250 Hz or between 4 and 8 kHz. This will be familiar to anyone doing pure-tone audiometry, which has increasing widths between test frequencies.

Frequency-domain filter banks may also attempt to mimic the logarithmic way the ear works, collapsing bands at the higher frequencies and reducing, for instance, from 64 processing bands to 16 fitting bands. However, the original relatively poor time resolution remains a problem. 

The importance of this can be illustrated with a spectrogram (Figure 1). The consonant that is highlighted is short in duration (the horizontal axis) but high and wide in frequency (the vertical axis), while the crucial information highlighted for the vowel is of longer duration but lower and narrower in frequency. This means that the signal is best represented by filters where the high frequencies have high time resolution, while the low frequencies need better frequency resolution (ie, exactly the way the Widex time-domain filter banks are set up).


Figure 1. Speech spectrogram illustrating a vowel (lower box) that requires higher frequency resolution (ie, more fine-grained frequency information for a narrower frequency range), and a consonant (upper box) that requires higher time resolution (ie, more fine-grained temporal information for a narrower time range).

Down-sampling

An important characteristic of a frequency-domain filter bank with narrow filters is that it makes down-sampling of the signal straightforward. This increased possibility for down-sampling is a major advantage of choosing a frequency-domain filter bank, because the reduction of samples also means a reduction in power consumption. For a time-domain filter bank, the benefits of down-sampling are minor and do not outweigh the risks of artifacts that are inherent to non-linear processes such as down- and up-sampling. This means that the choice of a time-domain filter bank entails other more difficult mechanisms to keep power consumption sufficiently low. However, avoiding down-sampling and preserving the original input signal means higher fidelity, reduced risk of artifacts, and improved sound quality. In addition, the hearing aid delay is kept much lower in a time-domain filter bank, which also contributes to improved sound quality.

Hearing Aid Delay

Hearing aid delay refers to the time it takes from the point when the sound is picked up by the microphone to the point when the amplified sound reaches the ear drum. Several different elements contribute to delay, including both hardware and signal-processing delay. Delay matters in this context because it is shaped by the choice of filter bank and sampling rate. More importantly for the hearing aid user, delay is a major determinant of sound quality (for more on this subject, see Balling et al1 and Schepker et al2).

Choosing a frequency-domain filter bank means that all filters have the same, relatively long, delay. In addition, a frequency-domain filter bank is generally chosen for the purpose of being able to down-sample the signal, which in turn also contributes to the total delay, because down-sampling and the subsequent reconstruction of the signal take time. This means that digital hearing aids that operate in this way generally have relatively long delays in the range of 5-8 ms, as shown for Manufacturers 1 and 2 in Figure 2. Although this sounds negligible, it still leads to audible artifacts for open and vented fittings, where the direct sound coming through the venting interacts with the delayed hearing aid sound to create an artifact called comb filtering.


Figure 2. Delays of leading digital hearing aids.

In contrast, the time-domain filter bank and high sampling rate in Widex hearing aids keep delay short—around 2.5 ms on average in the Universal program—for two reasons: 

  1. The delay is much shorter for the broader filters in the higher frequencies; this is also the reason for the sloping delay over frequency seen in Figure 2. 
  2. The signal is not down-sampled, and this contributor to delay is thus avoided. 

This reduction in delay is seen for all Widex hearing aids. It is advanced even further with ZeroDelay in the Widex MOMENT hearing aids, which is a separate processing pathway that allows delay as low as 0.5 ms. This pathway is used in PureSound, a program intended for mild-to-moderate hearing losses with open and vented fittings, which virtually eliminates the comb-filter effect.3,4

An Evolutionary Perspective

In addition to advantages in signal preservation and delay, the varying width of the filters in the Widex filter bank also mirrors the human ear, and with that the likely evolution of the speech signal. The evolution of speech is obviously not something that can be studied directly, but it stands to reason that the speech signal would have evolved to maximize the information that can be conveyed and to make that conveyance of information as robust as possible, given the properties of the human ear. In other words, we assume that the speech signal is optimized for the human auditory system.

Looking at the ear canal, this evolutionary perspective explains why the frequency range where the signal is most amplified by the ear canal resonances—typically between 2 and 4 kHz for adults—is also a crucial range for speech comprehension. And considering the cochlea, the way the different frequencies are processed, with larger areas and thus higher sensitivity for lower frequencies, corresponds to the fact that speech sounds are clustered towards the lower end of the audible range. Wanting to match this system as closely as possible is a key motivation for the Widex filter bank choice. 

Conclusion

As we have seen, there are plausible reasons for choosing either a frequency-domain or a time-domain filter bank. The choice of a frequency-domain filter bank makes life easier for the manufacturer, but it is not necessarily better for the hearing aid wearer. The better options for down-sampling with frequency-domain filter banks allow better power efficiency, but this also increases delay and decreases sound quality.  For a hearing aid manufacturer like Widex, which makes all design choices to produce the best, most natural, sound quality, this means that the only reasonable choice is a time-domain filter bank, with the accompanying high sampling rate. Although this does make it more challenging to optimize power consumption, Widex has worked over generations of hearing aids to overcome that challenge, because we believe that the key to a good life with hearing aids is the best, most natural, sound quality provided in collaboration with the HCP. The underlying philosophy is that nothing can be better for the hearing aid user than processing that matches the ear as closely as possible and preserves the signal as completely as possible.

Correspondence can be addressed to Dr Balling at: [email protected]

Citation for this article: Balling LW, Mosgaard LD, Helmink D. Signal processing and sound quality. Hearing Review. 2022;29(2):20-23.

References

  1. Balling LW, Townend O, Stiefenhofer G, Switalski W. Reducing hearing aid delay for optimal sound quality: A new paradigm in processing. Hearing Review. 2020;27(4):20-26. 
  2. Schepker H, Denk F, Kollmeier B, Doclo S. Subjective sound quality evaluation of an acoustically transparent hearing device. Paper presented at: 2019 AES International Conference on Headphone Technology; August 27-29, 2019; San Francisco, CA. 
  3. Kuk F, Slugocki C. Quantifying acoustic distortions from hearing aid group delays. WidExpress. 2021;44:1-5.
  4. Balling LW, Townend O, Helmink D. Sound quality for all: The benefits of ultra-fast signal processing in hearing aids. Hearing Review. 2021;28(9):32-35.