Have a look at Wikipedia's article on High-pass filters especially the section on algorithmic implementation of one .
Using an FFT would be a sledgehammer solution in this case. A simple FIR or IIR filter should suffice, but you need to decide on the design parameters for the filter first, i.e. Cut-off frequency (-3 dB point), pass-band ripple, stop-band gain, and whether you care about phase response or not.
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