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Built-In Self-Test (BIST) offers a system the ability to test itself. Though it introduces inevitable extra cost for the added hardware, it also makes it possible to monitor, measure and calibrate the system on the fly as will shown. With BIST, the reliability of the overall system can be improved and the testing and maintenance cost be reduced. This dissertation discusses a proposed mixed-signal BIST architecture and the implementation of one of its key components — numerically controlled oscillator (NCO). The proposed BIST is composed of a NCO-based test pattern generator (TPG) and a selective spectrum analysis (SSA)-based output response analyzer (ORA). It utilizes the digital-to-analog converter (DAC) and analog-to-digital converter (ADC), which typically exist in a mixed-signal system, to interface the digital TPG and ORA with the analog device under test (DUT). Theoretically the SSA-based ORA is equivalent to fast Fourier transform (FFT), but it only utilizes two digital multiplier/accumulators (MACs) and thus requires much less area overhead than the latter. Because of its ability to perform spectrum estimation, the SSA-based ORA is able to conduct a suite of the analog functional measurements such a