A frequency synthesizer for RF pulses for RF coils used in MRI apparatuses, includes: a D/A converter which converts digital values of the waveform of a fundamental wave whose frequency is lower than a Nyquist frequency, which is half the sampling frequency, into an analog waveform; and a band-pass filter which passes only a prescribed alias out of an alias group whose frequency is higher than the Nyquist frequency, contained in said analog waveform, wherein: said prescribed alias having passed said band-pass filter is transmitted from said RF coil as an RF pulse.