Complex signal processing is not - complex

Wireless systems often make use of the quadrature relationship between pairs of signals to effectively cancel out-of-band and interfering in-band signal components. The understanding of these systems is often simplified by considering both the signals and system transfer-functions as ´complex´ quantities. The complex approach is especially useful in highly-integrated multi-standard receivers where the use of narrow-band fixed-coefficient filters at the RF and high IF frequencies must be minimized. A tutorial review of complex signal processing for wireless applications emphasizing a graphical and pictorial description rather than an equation-based approach is first presented. Next, a number of classical modulation architectures are described using this formulation. Finally, more recent developments such as complex filters, image-reject mixers, low-IF receivers, and over-sampling A/D converters are discussed.