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An optimum tuned correlation method is presented for the measurement of the amplitude and time constant of exponentially decaying pulses embedded in noise, with application specifically to transient studies on semiconductor junctions (d.l.t.s. technique and similar). It yields a peaked spectral type output which is only 3 dB inferior in S/N to an ideal least squares estimator. Alternatively, a discriminator type output may be obtained. The result should be of general application and results for other pulse shapes may be derived.