1. A transmitter executing a distortion compensation process for compensating for a distortion in an output of an amplifier in advance by applying a reverse characteristic to a transmission signal before being amplified by the amplifier, the transmitter comprising: a distortion compensation coefficient storage unit that stores therein a value of power of a transmission signal and a distortion compensation coefficient that is used in the distortion compensation process in an associated manner; a power meter that measures power of the transmission signal before application of the distortion compensation process; a gain adjusting unit that adjusts a gain for the transmission signal before application of the distortion compensation process, when power of a transmission signal changes at certain timing based on an average of the power measured by the power meter, correspondingly to amplitude of the transmission signal at the certain timing; a distortion compensation processing unit that obtains a distortion compensation coefficient corresponding to the value of power of the transmission signal after being adjusted by the gain adjusting unit from the distortion compensation coefficient storage unit, and performs the distortion compensation process to the transmission signal using the distortion compensation coefficient thus obtained; and a distortion compensation coefficient updating unit that calculates an update for the distortion compensation coefficient stored in the distortion compensation coefficient storage unit and corresponding to the distortion compensation coefficient obtained by the distortion compensation processing unit based on an error between power of the transmission signal amplified by the amplifier and power of the transmission signal before the application of the distortion compensation process, and updates the distortion compensation coefficient stored in the distortion compensation coefficient storage unit using the update thus calculated.