Abstract: An improvement in a digital frequency synthesizer comprising a voltage-controlled oscillator (VCO) for producing a signal S.sub.VCO having a frequency f.sub.VCO, a first signal generator for generating a plurality of signals S.sub.AS having a spectrum of frequencies f.sub.AS, all exceeding a given minimum frequency f.sub.M, a mixer responsive to S.sub.VCO and to S.sub.AS to produce an output signal having a frequency (f.sub.VCO .+-.f.sub.AS), a divide-by-N divider responsive to (f.sub.VCO .+-.f.sub.AS) to produce a signal S.sub.N having a frequency f.sub.N, a second signal generator for generating a first reference signal S.sub.R1 having a frequency f.sub.R1, a phase detector responsive to S.sub.N and S.sub.R1 to produce a d.c. control signal E.sub.c whose amplitude varies with the phase relation of S.sub.N and S.sub.R1, and a filter for supplying E.sub.c back to said VCO, the VCO being responsive to E.sub.c to produce an output signal S.sub.VCO of frequency f.sub.VCO where (f.sub.VCO .+-.f.sub.AS )=Nf.sub.