Bioimpedance measurement is a non-invasive, radiation-free, and inexpensive method for measuring the electrical properties of biological tissues. In applications where transients occur, the commonly used swept sinewave is replaced with broadband signals such as multisine. This makes the signal generation and the extraction of the real and imaginary parts of the impedance challenging. In this brief, an alternative to traditional fast Fourier transform (FFT) or coherent demodulation is presented. Based on the Goertzel filter, this alternative is simpler and requires very few digital resources. Its robustness to the harmonic fold back phenomenon, enables simple ternary current pulses to be used for excitation. The developed digital architecture is capable of simultaneous demodulation of 16 frequencies with an accuracy of 97% and 96% on the magnitude and phase measurement respectively. Employing a ternary sequence allows the use of a low power H-bridge current driver. The analog front-end and demodulation algorithm were implemented in an ASIC using a 180-nm CMOS technology. The system was tested on an isolated pig heart distinguishing edema from non-edema tissue by impedance changes.