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, having a simple dual port, capable of reading and writing signals simultaneously for 2M samples from and on different addresses, 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, wherein: the signal conversion section includes two pairs of the memory and the 2M registers; and the switching control section switches a connection state (i) between the 2M registers in one of the two pairs and the M butterfly operation sections and (ii) between the 2M registers in the other of the two pairs and the M butterfly operation sections, such that a role of the memory is switched between a memory for output and a memory for input for each stage of the fast Fourier transform and the inverse fast Fourier transform.