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Cheap and Effective Hearing Tests and Hearing

Biplov Ale1,3, Dr. Ruchi Sharma (Au.D)2, Andrew Long1, and Steven Wilkinson1

  1. Department of Mathematics and Statistics, Northern Kentucky University, Highland Heights, KY 41099
  2. TriHealth, 625 Eden Park Drive, Cincinnati OH 45206
  3. Department of Physics, Geology, and Engineering Technology, Northern Kentucky University, Highland Heights, KY 41099


Many older adults need glasses as their vision fails, and frequently those glasses are provided by insurance (at least in United States). Hearing may also start to fail, and hearing aids would provide a measure of improved hearing; however, and in stark contrast, hearing aids are usually not provided by insurance, and are often out of financial reach for many. This problem is even worse in third world countries where only a few can afford hearing assistance. Furthermore, the technology for hearing tests has advanced little over the fifty years that one author has had his hearing tested: one is still ushered into a sound-proof booth, where tones of various frequencies are played into one’s ears. The patient signals whenever a tone is heard, and a certain amount of second guessing occurs (sometimes based upon perceived patterns of sound input from the tester). This imparts an odd psychological match of wits between the tester and the testee, which likely has nothing to do with the patient's hearing.

We propose to develop a simple and inexpensive program that will allow one to test one’s own hearing, and then a simple hearing aid based on the profile generated by the hearing test.


Our objective in this project is two-fold:

  1. To create a simple Mathematica-driven hearing profiler (“Tester”), to identify those frequencies at which one needs correction.
  2. To create an inexpensive noise-cancelling device (either headphones or earbuds) to provide that correction, which is possible in one of two ways:
    • Volume enhancement of frequencies not heard well by the patient
    • Frequency shifting; remapping sounds to frequencies at which one still hears well


The project has two main phases: “Prototyping” and “Device Development and Miniaturizing”. In prototyping, we decided to go with simple yet versatile approach of using Arduino UNO board. Signal processing, hearing profiling, and frequency shifting codes will be written in Mathematica and will be run on a laptop, which connects to the Arduino board. The Arduino acts as the interface for the digital components such as speakers, potentiometers, contact sensors, and microphones. The initial schematic for the prototyping has been illustrated below:

Prototypical testing system schematic

The next step of “Device Development and Testing” involves initially designing a hearing aid device structure and scaling down the size of the components. It also might be necessary to convert the Mathematica code into another language more suitable for the hardware -- something public domain, such as python or R. The code will be uploaded to the components and the device performance will be tested along with any bug resolution handling.



We began by considering some of the currently available options for hearing testing apps and devices, to see if our objectives were already being met by existing technologies. While we found some interesting options, nothing was doing exactly what we intended to do. We might mention, in particular, a few of the better options:

  1. Hearing Test: Audiometry, Tone: This one essentially attempts to reproduce the results of a standard hearing test (see the figures above).

Biplov: please fill in the back ground here

Hearing Testing

The Audiogram

Audiograms are visual representations of a patient's state of hearing ability (we will call this a hearing "profile").

An example audiogram of a hearing-impaired 60+ Male (patient A)
Normal hearing for a 60+ Male (patient B)
Changes from year to year (patient A)
2021 results (patient A)

Unfortunately, changes are usually in the wrong direction. As one can see the patient's curves are "descending", meaning that it takes more decibels for a particular frequency to be heard. The 2021 results for patient A show severe hearing loss at the highest frequencies.

Notice that there is a profile for each ear, left and right. Sometimes hearing loss is symmetric, but it needn't be; each ear should be tested individually.

The Profile Function

For each individual there is a left ear and right ear profile function, and , which the audiogram seeks to capture. Let's assume that the hearing loss is symmetric, i.e. . We argue that traditionally we have done a poor job of modeling this function : replacing (what we might imagine is generally) a smooth continuous function with a linear spline built on only a few data points:

where by we mean the linear spline (line segment) joining two adjacent data points obtained from the hearing test, e.g. and .

A pure tone sound can be represented by two parts: the frequency and the amplitude :

The loudness is a function of the amplitude, and proportional to the square of the amplitude:


  • How does Mathematica turn "loudness" into decibels, especially since we're passing through speakers, which allow us to also adjust loudness?
  • How do loudness levels translate into decibels?

Hearing Correction

There are several different approaches to "correcting" hearing. The traditional idea is to reinstate the sounds that a patient is missing, by augmenting volume. This is a somewhat crude approach: we have all been witnesses to the sad spectacle of some hearing-impaired person being shouted at by a friend or loved one.

Our approach is to retain a sound signal's uniqueness. In particular, we wanted to avoid aliasing -- two distinctly different sounds having the same profile to a patient. In effect deafness is the most dramatic example of this problem: all sounds sound the same (they are all unheard equally; equally silent); and so no information can be conveyed aurally (athough information may be conveyed by lip reading, digital speech translators, or other means).

Future Work

It would be wonderful if one's hearing aid could determine the precise location of the desired sound, and then focus on sounds emitted from that location, in particular. In order to achieve this, one might monitor the eyes, and the point upon which they're focousing. This suggests that a helmet might be the better model for the future, albeit one which is as discreet as possible. While we're at it, we might envision an app for lip-reading, to help facilitate the collection of speech, which might even be fed back through Mathematica and then read aloud using more distinguishable speech (e.g. speech in frequencies easier for the listener to hear).

We have jokingly referred to a case where a colleague's spouse can no longer hear his daughter's voice, because it's pitched in frequencies which he can't hear; so why not turn her voice down an octive or two, thus making it more accessible (even if your daughter ends up sounding like Darth Vadar).


Everyone should have access to cheap and readily available hearing tests and hearing aids. Hearing is no less important than vision, and the loss of hearing has a profound impact on one’s ability to socialize and remain an engaged member of one’s society. This research should help to overcome that by providing a simple diagnostic audiogram, which can then be integrated with a relatively cheap, accessible, and effective hearing aid.


This work was partially funded by a 2022 Summer Greaves Research Award (Ale).

Thanks to Department of Mathematics and Statistics Chair Brooke Buckley for departmental support.


  • Hochberg, Julian E. Perception. 1978. 2nd Edition. Prentice-Hall Foundations of Modern Psychology Series Richard S. Lazarus, Editor.
  • Freeman, Ira M. Sound and Ultrasonics. 1968. Illustrated by George T. Resch. Random House Science Library, New York.
  • Simple wav sound files for analysis
  • How to Read an Audiogram
    • Audiograms are used to diagnose and monitor hearing loss.
    • Audiograms are created by plotting the thresholds at which a patient can hear various frequencies.
    • Details from that page, including a somewhat disparaged formula for computing hearing loss
  • Presbycusis, or age-related hearing loss:
    • "The low and mid frequencies of human speech carry the majority of energy of the sound wave. This includes most of the vowel information of words (figure 4). It is the high frequencies, however, that carry the consonant sounds, and therefore the majority of speech information. These consonant sounds tend to be not only high pitched, but also soft, which makes them particularly difficult for patients with presbycusis to hear. As a result of their hearing loss pattern, patients with high-frequency hearing loss will often report being able to hear when someone is speaking (from the louder, low-frequency vowels) but not being able to understand what is being said (due to the loss of consonant information)."