1. A loop filter comprising: a register configures to store a result of arithmetic operation performed on a complex signal and outputs the stored complex signal; a first multiplier configures to multiply the complex signal output from the register and a predetermined coefficient; an absolute value judging unit configures to output a multiplier coefficient used to control such that the amplitude of the complex signal output from the register is held in a predetermined range; a multiplier configures to multiply an output from the first multiplier and the multiplier coefficient; a second multiplier configures to multiply an input signal and a value (1−the predetermined coefficient); and an adder configures to add an output from the multiplier to an output from the second multiplier and inputs a result of addition into the register.