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We describe a simple method for the wavelength measurement of optical signals that is easily capable of measuring a 1-nW average power optical signal with a wavelength resolution of 0.1 pm/Hz12/ while maintaining a large measurement range in excess of 12 nm. The system uses an erbium-doped fiber amplifier to increase the signal level before being measured with a wide-band edge filter. This technique is well suited to the measurement of low duty cycle time-multiplexed signals such as those in multiplexed fiber sensor systems. We show that the measurement of the amplified signal is improved despite the broadband nature of the amplified spontaneous emission noise. We show for the first time that the addition of an amplifier can increase the detection capabilities of the edge filter method beyond the shot noise limit of an unamplified measurement.