PROBLEM TO BE SOLVED: To provide a frequency synthesizer by which the uniformly distributed spurious radiation which is inherent in a DDS is improved, without increasing the circuit scale (ROM size) of the DDS. SOLUTION: Signals which has no phase requantization errors are obtained from ROM-A 13 and B 14 by phase data corresponding to 'j1' bit from the MSB side of frequency setting data ΔΦ, while spurious signals by phase requantization errors are obtained from ROM-C 18 and D 19 by phase data corresponding to the remaining 'j2' nit on the LSB side viewed from j1 of the phase data of 'j0' bit. The output of the ROM-C 18 and D 19 is converted into the same sampling rate with the 'j1' bit side by interpolation filters 20 and 21, and the spurious radiation is reduced by band limitation. The output of the ROM-A 13 and B 14 and the interpolation filters 20 and 21 is mixed by a complex mixer 57, and the signals of frequency corresponding to the frequency setting data ΔΦ are obtained.