MATLAB Project – Modelling an Auditory System

This project aims to familiarise with MATLAB by working on a real-world model, specifically an auditory system that simulates the components associated with hearing. Note that this project is an individual task.

An auditory system mimics the behaviour of a biological cochlea found in humans and other mammals. The system converts a 1D discrete-time audio signal to a 2D time-frequency signal called an auditory spectrogram. From this spectrogram, audio information can be extracted, as shown in Table 1. Its application includes hearing aids, speech and musical information retrieval, audio multimedia systems, and brain modelling.

To convert a one-dimensional (1D) sound signal into a two-dimensional (2D) time-frequency representation, a cochlear filterbank is used. A cochlear filterbank comprises multiple gammatone filters either in parallel or cascaded form. The bandwidth of each gammatone filter increases with increasing frequency so that a high centre frequency filter has a higher bandwidth than a filter with low centre frequency, as shown in Figure 1(a).

A gammatone filter generally behaves like a bandpass filter but has differences associated to the behaviour of the cochlea mechanics. Each gammatone filter is tuned to a specific centre frequency. It only responds to a specific frequency that corresponds to the mechanics of one specific location on the cochlea. So, when the input signal resonates close to the centre frequency of the filter, the filter will output a resonating signal at its centre frequency. Hence, to model an entire cochlea, a gammatone filterbank is used. A filterbank will have a number of gammatone filters whose centre frequencies are tuned from low to high for the entire spectrum of a sound signal.

Figure 1: Increasing bandwidth with increasing centre frequency in the gain response of gammatone filters. (a) x-axis is linearly scaled where intervals between frequencies are the same; (b) x-axis is logarithmically-scaled where intervals between frequencies are nonlinear.

Ideally, the varying filters tuned differently will react to the different frequencies in the input signal and will output multiple signals. These signals are then half-wave rectified, where all negative values are set to 0 and only positive values are maintained. They can be visualised as a 2D image known as an auditory spectrogram, as shown in Figure 2.

An alternative method of showing a spectrogram is by calculating the short-time Fourier transform (STFT) of a sound signal.

Progress Report (25%)

You are expected to complete up to task 4 from the MATLAB model section. Prepare a 2000- word progress report on the tasks – follow the guidelines given in the learning guide where relevant. Describe what you have done to complete the tasks. If you are unable to complete any task, explain what you are experiencing. Use any online English grammar and vocabulary checking application to ensure that your report is coherent and clear, e.g. Grammarly – marks will be given if you are able to convey your ideas clearly and concisely.

Submit your progress report and your MATLAB script files that you have modified using the Turnitin link in vUWS under “Assessment 1”.

Final Report (50%)

Prepare a 4000-word final report with the structure outlined below. The final report should include the images as well as the correlation coefficient results and the gammatone filter impulse response (screen capture – do not use your phone to capture any images). Use any online English grammar and vocabulary checking application to ensure that your report is coherent and clear, e.g. Grammarly – marks will be given if you are able to convey your ideas clearly and concisely.

The sections to be included in the final report are:

1. Objectives – alternatively, you can include a motivation statement on why this project is important.
2. Components of the auditory
3. Modelling the auditory model using MATLAB using the specification from Table 2 clearly Also, mention about the filter order from Table 2 required to show

the gammatone impulse response. Also, address the following questions in your report for additional marks:

4. The inner hair cell response has all its negative values set to 0. How can these values be converted from negative to positive? Suggest a computational method to differentiate the current positive values with the positive values converted from the negative values.
5. If individual samples in a spectrogram each have values larger than one, the temporal and spectral profile will have varying dynamic ranges (y-axis range) for different sound loudness. This effect makes it difficult to compare the two profiles of different dynamic One method is to lock the dynamic range of the signals to be analysed between 0 and 1. Suggest a computational method to attain temporal and spectral profiles with their amplitudes between 0 to 1.
6. Results and discussion (screen capture of all the; screen capture of MATLAB command window showing correlation coefficients (CC) and the symbolic equation). Discuss on the CC results to indicate the degree of difference between pairs of vectors and matrices in task 12.
   1. Address which CC result is highest and thus, most
   2. Conversely, address which CC result is lowest and thus, least
   3. How is the temporal profile signal related to the original sound signal? Use your observation and any key terminologies to describe their
7. Conclusion (discuss your experience in using MATLAB for modelling of the auditory model, its usefulness, and difficulties).
8. Either Harvard-style or IEEE-style referencing is acceptable – See the last slide in Auditory Signal Processing.pdf as an example.

Submit your final report and your MATLAB script files that you have modified using the Turnitin link in vUWS under “Assessment 3”.