Daily Blog Entry 1

Today was the first day of my second week of research. Last week I devoted much of the week to background research in order to understand the material needed tackle this research project. I mainly researched the mathematical meanings and derivations of Fourier transformations slowly working my way towards understanding discrete Fourier transformations (DFTs) and fast Fourier transformations (FFTs). I discovered an FFT is the one and the same with a DFT; the only difference between the two are the way they are derived. In computing, calculating a DFT is nearly impossible as it is a function of magnitude O(N²). FFTs, in comparison, are functions of magnitude O(NlogN).

I began this week by continuing where I left off last week with my research regarding the mathematical origins of digital signal processing (DSP). I started the day by looking at Spectral Tools, a music analysis program implementing Java and Max Runtime. I was unable to install Max Runtime on the lab computer but plan to run the program on my personal computer.

I also discovered a MIT Press publication entitled Computer Music Journal which can be accessed online through the MIT Press Journal website. While searching their database, I discovered a textbook I thought would be helpful, The Computer Music Tutorial by Curtis Roads, which I subsequently requested at the library.

Through my research on this site I discovered a two-part article, An Introduction to the Mathematics of Digital Signal Processing, by F. R. Moore which was published in Computer Music Journal which can be accessed through the JSTOR archive. These articles proved to be very enlightening regarding the mathematical aspects of DSP. The first article was a useful tool to recall the main themes of algebra and trigonometry that are imperative to the understanding of DSP. This article was written as an attempt to explain the math without explaining it through calculus, making it easier to understand.

The second article delves into sampling and transforms. Tomorrow I plan on finishing this article and will (hopefully) fully understand the math behind the transforms. I also plan to start programming a FFT from scratch.