thanks for your response.
maybe the minimum frequency must pass through the filter is 3-5Hz. I'm not sure now. I forget to say that the input frequency is 48kHz, so is it hard to use the iir or fir filter to do it? maybe you are right. the coupled capacitor is a better choice. I just used the equiripple method to design a highpass filter in matlab. I attach the figure below. It is so hard to implement in hardware because the FIR needs 11418 taps, the attenuation is too small either.