1. An adaptive equalizer that performs adaptive equalization on a time-domain signal in a frequency domain, comprising a signal conversion section that performs at least one of a fast Fourier transform and an inverse fast Fourier transform, wherein the signal conversion section includes: a memory capable of reading and writing signals for 2M samples, where M is a natural number; 2M registers accessible to the memory; M butterfly operation sections; and a switching control section that switches a connection state between the 2M registers and the M butterfly operation sections.