Sound Source Mapping Thesis

The research question

How can a system determine where a sound comes from, rather than simply detect that a sound occurred?

This completed undergraduate Electronics Engineering thesis brought together dynamic microphones, a hardware interface, and personal-computer software for sound-source mapping. The objective was to locate a source producing sound above a threshold, with potential examples including noisy equipment or other identifiable sound sources.

The original thesis title was Designing and Developing a Hardware Interface and Software for Sound Mapping of a Sound Source above Threshold via Dynamic Microphones and Personal Computer.

Thesis adviser: Engr. Ronnie Yu

My contribution

This was a group project. My responsibilities covered both engineering work and team coordination:

Interface CAD design: preparing the CAD design for the hardware interface.
Mathematical foundations: contributing to the mathematics behind the sound-mapping approach and how it relates to locating the sound source.
Results analysis: tabulating and interpreting the software’s results.
Team coordination: distributing tasks among group members and coordinating regularly with the thesis adviser.

How the team approached it

The team researched microphone selection to support signal acquisition, investigated the placement of the hardware, and used triangulation as the preferred approach for locating the sound source. Troubleshooting was part of integrating and operating the system.

The conceptual flow was sound source → dynamic microphones → hardware interface → PC software → mapped location. Sensor placement and the interpretation of the resulting signals connected the physical setup to the software output.

System design

The work connected three parts of an engineering system:

Part	Role in the project
Dynamic microphones	Acquire the sound signals used for mapping.
Hardware interface	Connect the sensing hardware with the personal computer; my contribution included its CAD design.
PC software and mathematics	Support interpretation of the signals and source-location mapping; I contributed to the mathematical foundations and analysis of the results.

The threshold defines which sounds are of interest. Locating a sound is a separate task: it requires relating the observations to the physical arrangement of the microphones. The team investigated hardware placement and selected triangulation as the preferred approach.

Mathematics behind sound mapping

My contribution included the mathematics connecting sound observations with a source’s location. The following mathematical background explains that relationship; it is an explanatory model rather than a transcription of the thesis’s implementation equations.

From physical positions to distances

In a two-dimensional model, let the source position be $\mathbf{s} = (x, y)$ and microphone $i$ be at $\mathbf{m}_i = (x_i, y_i)$ . Their separation is:

d_i = \sqrt{(x - x_i)^2 + (y - y_i)^2}

This connects the unknown source coordinates to the known sensor positions. Localization uses measured information to constrain where the source can be. An above-threshold observation alone does not uniquely determine those coordinates.

Connecting sound propagation with geometry

One common acoustic-localization model uses arrival-time differences. For propagation speed $c$ and a shared emission time $t_0$ , the ideal arrival time is:

t_i = t_0 + \frac{d_i}{c}

Subtracting two arrival times removes the unknown emission time:

c\left(t_i - t_j\right) = d_i - d_j

A time difference therefore constrains a difference in distances. Several such constraints can support a position estimate. This is time-difference-of-arrival localization, distinct from triangulation based on measured bearings; it is included here as general background, not a claim that the thesis implemented this particular method. MathWorks explains the model and its geometric constraints.

Interpreting the output

The mathematical model provides a way to reason about the software’s answer: whether a mapped position is consistent with the observations and the sensor arrangement. My work included tabulating and interpreting the software results, connecting the numerical output back to the physical system.

Completed work and engineering outcomes

The thesis covered microphone-selection research, hardware-placement investigation, interface design, software-result interpretation, and system troubleshooting. The placement investigation favored triangulation for the mapping approach.

My contributions joined CAD design, mathematical reasoning, and results analysis, alongside coordinating with the adviser and distributing the team’s tasks. Together, these activities addressed the full engineering problem: acquiring a physical signal, relating it to a spatial model, and interpreting the resulting location information.

Connection to my engineering work

Sound mapping brings together the questions that still interest me: how a physical signal becomes data, how geometry helps interpret that data, and how an engineer checks whether the output makes sense. My work on the mathematical foundations, interface design, and results interpretation connected electronics, mathematics, and software.

For a separate, interactive exploration of signals and mathematical rules, visit the signals and anomalies Lab. That experiment uses synthetic data and is not a reproduction of this thesis.

Sound Source Mapping with Dynamic Microphones