Sinusoid Magnitude Spectra

A sinusoid's frequency content may be graphed in the frequency domain as shown in Fig.4.6.

An example of a particular sinusoid graphed in Fig.4.6 is given by

where

That is, this sinusoid has amplitude 1, frequency 100 Hz, and phase zero (or , if is defined as the zero-phase case).

Figure 4.6 can be viewed as a graph of the magnitude spectrum of , or its spectral magnitude representation [42]. Note that the spectrum consists of two components with amplitude , one at frequency Hz and the other at frequency Hz.

Phase is not shown in Fig.4.6 at all. The phase of the components could be written simply as labels next to the magnitude arrows, or the magnitude arrows can be rotated ``into or out of the page'' by the appropriate phase angle, as illustrated in Fig.4.16.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.