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 bandwidth 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 bandwidth. The bandwidth of the filter is controlled by a set of control signals. The bandwidth adjusting circuit is configured to adjust the bandwidth of the filter based on a frequency of the filtered first signal and a frequency of the first signal, or a phase of the filtered first signal and a phase of the first signal. The bandwidth adjusting circuit is configured to generate the set of control signals.