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# The What, How and Why of Complex Sampling for SDR Transceivers

Software Defined Radio (SDR) transceivers are widely employed as powerful and low-cost platforms for classroom laboratory experimentation in the field of analog and digital communications. These SDR systems have also found application in student project work when significant signal processing horsepower is required for minimal cost. SDR systems typically utilize complex sampling, where instead of a single real-valued set of signal samples, a two-dimensional set of real and imaginary-valued samples are made available. Presenting the sampled data in this complex format has the benefit of allowing for unaliased signal processing right up to the sampling rate (instead of the usual Nyquist limit of half of the sampling rate). Hence, the constraints on the system sampling rate are somewhat lessened, and the requirements on the Analog to Digital Converter (ADC) are likewise lessened. While available in most SDRs, complex sampling is often mysterious, even to those with significant signal processing background. In this paper, the principle behind complex sampling and its benefits are derived, along with the associated cost. Next, the practical implementation of complex sampling for low-cost SDRs is described. Then, discussion of the processing of the complex data is presented. Finally, some examples utilizing complex sampling are given.