A built-in-self-test (BIST) circuit is connected to a processor and a sigma-delta modulator (SDM) and includes an averaging circuit, a reference signal generator, and a comparator. The averaging circuit calculates an average of a sum of a set of bit signals of the SDM output signal over a period of time period, and generates an average SDM signal. The reference signal generator generates a reference SDM signal based on an SDM input signal. The comparator compares the voltage levels of the average SDM and reference SDM signals with a threshold value, and generates a test output signal based on the comparison.