Negative Exponents

What should be? Multiplying it by gives, using property (1),

Dividing through by then gives

Similarly, we obtain

for all integer values of , i.e., .

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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.

Do you need a caveat about the case a=0?

In the beginning of this section, at
http://www.dsprelated.com/dspbooks/mdft/Positive_Integer_Exponents.html,
a is defined as real and positive. There is a tradeof between continuity of flow and being self-contained on every page.