Complex Amplitude

Note that the amplitude and phase can be viewed as the magnitude and angle of a single complex number

which is naturally thought of as the complex amplitude of the complex sinusoid defined by the left-hand side of either Eq.(1.9) or Eq.(1.10). The complex amplitude is the same whether we are talking about the continuous-time sinusoid or the discrete-time sinusoid .

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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.