In a signal generator based on Direct Frequency Synthesis, a first reference frequency generator generates a signal of a reference frequency. A plurality of second reference frequency generators, respectively, generates K signals with different frequencies Asin(.omega..sub.1 t+.psi.), Asin(.omega..sub.2 t+.psi.) . . . Asin(.omega..sub.K t+.psi.), which are in phase at time point (t=0), in response to the output signal of the first reference frequency generator. A switching circuit selectively switches the output signals from the plurality of said second reference frequency generators. A timing pulse generator generates timing pulses to operate said switching circuit at time T as given by .vertline..omega..sub.i+1 T-.omega..sub.i T.vertline.=2l.pi. (l:integer) where i=1, 2 . . . K-1.