A communication system includes a carrier generator configured to generate a first carrier signal and a demodulator configured to demodulate a modulated signal responsive to the first carrier signal. The demodulator includes a filter and a gain adjusting circuit. The filter is configured to filter a first signal. The first signal is a product of the first carrier signal and the modulated signal. The filter has a first cutoff frequency and a gain. The gain of the filter is controlled by a set of control signals. The gain adjusting circuit is configured to adjust the gain of the filter based on a voltage of the filtered first signal or a voltage of a second signal. The adjustable gain circuit is configured to generate the set of control signals.