Throughout this assignment, we will be analyzing and synthesizing musical notes....

In signal processing, two key concepts arise continuously: analysis and synthesis. Analysis is the

act of decomposing a signal into an alternative representation. Synthesis is the act of building a

signal from an alternative representation. We use signal representations to better understand,

manipulate, and generate data. In this lab assignment, we will focus on one very important

representation of signals: the Fourier (or frequency) representation. In fact, this representation

is the topic of most of ECE 3500.

Throughout this assignment, we will be analyzing and synthesizing musical notes. Musical notes

are arranged in groups of twelve, called octaves. The standard frequencies associated with the

twelve notes in an octave of frequencies range from 220 Hz to 440 Hz. We will be using a 12-tone

equal-temperament note scale (i.e., the standard, modern music scale). The frequency 220 Hz is

known as the note ‘A’. Each following note has a frequency of 220 × 2

n/12, where n is the number

of notes higher than ‘A’ (‘A’, ‘A#’, ‘B’, ‘C’, ‘C#’, ‘D’, ‘D#’, ‘E’, ‘F’, ‘F#’, ‘G’, ‘G#’). The next

‘A’ note then starts at a frequency of 440 Hz.

This lab assignment has three learning objectives:

1. To familiarize yourself with Fourier analysis in MATLAB

2. To analyze a simple music piece (in this case, Yankee Doodle) using Fourier analysis

3. To synthesize a musical piece (in this case, music from Beethoven)

4. To engineer solutions for analyzing and synthesizing a complex musical piece

Your experiment will be divided into three parts. In your lab report, you primarily address the

final part of the lab. See the lab report guidelines on the class website for more information.