Multirate Noble Identities

Figure 10.14 shows the two so-called ``noble identities'' for commuting downsamplers/upsamplers with ``sparse transfer functions'' which can be expressed a function of . Note that downsamplers and upsamplers are linear, time-varying operators. Therefore, operation order is very important. It is also important to note that adders or multipliers (any memoryless operators) can commute across downsamplers and upsamplers, as shown in Fig.10.15.

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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.