TABLE OF CONTENTS Most analog signals are either sinusoids, or a combination of sinusoids (or can be approximated as a combination of sinusoids). This makes combinations of sinusoids especially interesting. It is easy to add sinusoids together; pressing keys on a piano or strumming a guitar adds several sinusoids together (though they do decay, unlike the sinusoids we usually study). In this chapter, we will investigate sinusoids and see how they can be added together to model signals. The goal is to gain a better understanding of sinusoids and get ready for the Fourier transform.
Greek letters are nothing to be afraid of. Mathematics uses variables, much like we do in computer programming. These variables are one letter, which allows things to be described concisely. Greek letters are often used simply because we tend to run out of our alphabetic letters. Also, there are letters that are good to avoid, like l, and o, since they look too much like the numbers 1 and 0.
Consider a right triangle (see Figure 4.1). We know, thanks to Pythagoras (or at least his school [15]) that a 2 + b 2 = c 2, so if we happen to know only two sides, we can calculate the third [1]. Also, with this information, we can figure out the angles ? 1 and ? 2. Since it is a right triangle, the third angle is 90 degrees by definition.
