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A method is presented for obtaining the output signal and noise from a linear detector, including the output signal wave form and both the signal and the noise spectra. The method is applicable to any type of amplitude-modulated input signal at any signal-to-noise ratio, provided only that the bandwidth is small compared with the center-band frequency, and requires that certain steps be performed graphically rather than analytically. A comparison is made with square-law detection for a few useful cases. It is demonstrated that the linear detector gives a higher output signal-to-noise ratio than the square-law detector for some types of signal.