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A new method of generation of a single-sideband signal has been developed which provides distortionless reception with a square-law envelope detector. This performance is achieved through a new system design rather than a less subtle method, such as carrier reinsertion. It is well known that a single-sideband signal can be represented as a combination of amplitude and phase-modulated signals. Most methods of single-sideband generation do not allow separate control of the amplitude and phase modulation. However, in the system described in this paper the amplitude and phase-modulation components are generated separately and have a specific functional relationship with each other. The amplitude-modulation envelope is the square root of the waveform to be transmitted and the phase modulation is the Hilbert transform of the logarithm of the envelope. A signal generated in this manner will occupy a bandwidth equal to the bandwidth of the original modulating signal and may be received without distortion with a square-law envelope detector. Tests on the system have shown that it is possible to obtain  an average of 25-db sideband rejection using band-limited white noise as the modulating signal, and  an average of 2 per cent harmonic distortion and 9 per cent intermodulation distortion using a square-law detector.