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A novel system formed by a Microwave Superconducting Quantum Interference Device (SQUID) Multiplexer (MUX) and a room temperature electronics employs frequency division multiplexing (FDM) technique to read out multiple cryogenic detectors. Since the detector signal is embedded in the phase of the SQUID signal, a Digital Quadrature Demodulator (DQD) is widely implemented to recover it. However, the DQD also generates a signal that aliases into the first Nyquist zone affecting the demodulated detector signal. In this work, we demonstrate how this spurious signal is generated and a mathematical model of it is derived and validated. In addition, we discuss different proposals to improve the attenuation of this undesired signal. Lastly, we implement one of the proposals in our readout system. Our measurements show an enhancement in the spurious signal attenuation of more than 35 dB. As a result, this …