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About the Author: 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.

Since we used a cosine function as a continuous sinusoid in the previous section, shouldn't we use a sampled version of the same signal as a "sampled sinusoid" ? Thus we should get a +ve and a -ve frequency term here as well.

That's fair - I should be saying "complex sinusoid" in this section, to be more precise. Fixed in the master. - jos