In receiving apparatus for a double-sideband amplitude-modulated wave, a synchronous detector which samples the modulated wave for short periods centered on instants of peaks of the carrier at regularly-occurring intervals, with a sampling frequency greater than the Nyquist frequency for the modulating wave, equal to the carrier frequency divided by an integer, and reconstructs the modulating wave from the sequence of samples in a reconstruction filter. This detector has a high output signal-to-noise ratio and produces a distortionless output with positive or negative overmodulation, and with reduced or suppressed carrier.