A DDS (direct digital synthesizer) remarkably increased in the number of frequencies which can be output while maintaining the phase coherency, and an NMR instrument using such a DDS are provided. A DDS including phase accumulators and a phase-to-amplitude modulator is provided with a plurality of phase accumulators operating with fixed phase implements which are equal to powers of 2, a controller for outputting each bit of a frequency tuning word as control data, a plurality of switches for outputting an output of an associated one of the phase accumulators when an associated one of the control data supplied from the controller is 1 and outputting 0 when the associated one of the control data is 0, and an adder for adding up outputs of the switches.