Various embodiments of the invention enable low-power accurate measurement of complex impedance at a range of frequencies of interest to determine a frequency response of a test sample. The system requires only a few external precision components that are not integrated into a microprocessor, thereby, providing a low-cost alternative to existing designs. In certain embodiments, low-power operation is accomplished by utilizing a simplified digital signal processing scheme that requires only a small number of ADC samples. Measurement accuracy is achieved by a digital conversion to baseband that does not suffer from channel matching issues and by utilizing a single analog path.