A programmable amplifier includes an amplifier, an input capacitor, a feedback circuit, and a high-pass filter circuit. The amplifier has an input coupled to the input capacitor for receiving an input signal. The feedback circuit includes multiple feedback capacitors of differing capacitance values that are each selectively coupled between the output of the amplifier and the input of the amplifier using multiple first switches. The high-pass filter circuit includes multiple switched capacitors of differing capacitance values that are each selectively coupled between the amplifier output and a ground node using multiple second switches. The first switches are configured to be selectively switched on for activating at least one feedback capacitor to adjust a gain of the amplifier, while the second switches are configured to be selectively switched at a first and second phase of a clock signal to adjust a high-pass cutoff frequency of the amplifier independently of how the gain is adjusted.