To suppress noise generation in a wide band and to suppress a clock speed from being increased in a sigma-delta modulation apparatus and a sigma-delta modulation power amplifier. A sigma-delta modulator creates a sigma-delta modulated signal for a digital output from a digital modulator, according to a clock given in advance. A threshold comparator indexes a portion in which the level of a digital output from the digital modulator is higher than a predetermined threshold and sends the resulting output. A replacing unit replaces the indexed portion with an output from a corresponding thinning unit. A filter unit performs band elimination filter processing on an output from the replacing unit and a digital-to-analog converter (D/A) performs digital-to-analog conversion on an output from the filter unit.