A demodulator is configured to demodulate a modulated signal responsive to a 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 bandwidth adjusted based on a set of control signals. The bandwidth adjusting circuit is coupled to the filter, and configured to generate the set of control signals based on at least a frequency of the filtered first signal and a frequency of the first signal. The bandwidth adjusting circuit includes a frequency detector configured to generate a second signal based on a frequency relationship between the frequency of the filtered first signal and the frequency of the first signal.