## Inspiration

We are a team of engineering science students with backgrounds in mathematics, physics and computer science. A common passion for the implementation of mathematical methods in innovative computing contexts and the application of these technologies to physical phenomena motivated us to create this project [Parallel Fourier Computing].

## What it does

Our project is a Discrete Fourier Transform [DFT] algorithm implemented in JavaScript for sinusoid spectral decomposition with explicit support for parallel computing task distribution. This algorithm is called by a web page front-end that allows a user to program the frequency/periodicity of a sum of three sinusoids, see this function on a graphical figure, and to calculate and display the resultant DFT for this sinusoid. The program successfully identifies the constituent fundamental frequencies of a sum of three sinusoids by use of this DFT.

## How We built it

This project was built in parallel, with some team members working on DCL integration, web page front ends and algorithm writing. The DFT algorithm used was initially prototyped in Python before being ported over to JavaScript for integration with the DCL network. We tested the function of our algorithm from a wide range of frequencies and sampling rates within the human spectrum of hearing. All team members contributed to component integration towards the end of the project, ensuring compliance with the DCL method of task distribution.

## Challenges We ran into

Though our team has an educational background in Fourier analysis, we were unfamiliar with the workflows and utilities of parallel computing systems. We were principly concerned with (1) how we can fundamentally divide the job of computing a Discrete Fourier Transform into a set of sequentially uncoupled tasks for parallel processing, and (2) how we implement such an algorithm design in the JavaScript foundation that DCL relies on. Initially, our team struggled to define clearly independent computing tasks that we could offload to parallel processing units to speed up our algorithm. We overcame this challenge when we realized that we could produce analytic functions for any partial sum term in our series and pass these exact functions off for processing in parallel. One challenge we faced when adapting our code to the task distribution method of the DCL system was writing a work function that was entirely self-contained without a dependence on external libraries or extraneously long procedural logic. To avoid library dependency, we wrote our own procedural logic to handle the complex number arithmetic that's needed for a Discrete Fourier Transform.

## Accomplishments that We're proud of

Our team successfully wrote a Discrete Fourier Transform algorithm designed for parallel computing uses. We encoded custom complex number arithmetic operations into a self-contained JavaScript function. We have integrated our algorithm with the DCL task scheduler and built a web page front end with interactive controls to program sinusoid functions and to graph these functions and their Discrete Fourier Transforms. Our algorithm can successfully decompose a sum of sinusoids into its constituent frequency components.

## What We learned

Our team learned about some of the constraints that task distribution in a parallel computing network can have on the procedural logic used in task definitions. Not having access to external JavaScript libraries, for example, required custom encoding of complex number arithmetic operations needed to compute DFT terms. Our team also learned more about how DFTs can be used to decompose musical chords into its fundamental pitches.

## What's next for Parallel Fourier Computing

Next steps for our project in the back-end are to optimize the algorithm to decrease the computation time. On the front-end we would like to increase the utility of the application by allowing the user to play a note and have the algorithm determine the pitches used in making the note.

#### Domain.com submission

Our domain name is http://parallelfouriercomputing.tech/

#### Team Information

Team 3: Jordan Curnew, Benjamin Beggs, Philip Basaric