Electrochemical impedance spectroscopy (EIS) is a non-invasive tool capable of characterizing batteries' states based on impedance over a specific frequency range. Considering that the use of lithium-ion batteries with large capacity in many electric vehicles imposes an extremely high impedance measurement accuracy in a range of sub-mΩ, EIS systems widely use a digital lock-in amplifier (DLIA) that allows ultra-precision impedance measurement at the cost of a long settling time. This work presents an onboard EIS system with further reduced measurement time. In the proposed EIS system, the DLIA embedding of a pair of quasi-linear-phase band-pass filters is utilized to shorten the settling time by widening the bandwidth of the noise suppression low-pass filter with minimum accuracy degradation. Compared to the EIS systems using the conventional DLIA, this work achieves a 45% and 57% reduction in the estimated settling time over the frequency range of 1-to-1000 Hz and at the lower bound (1 Hz), respectively.