Short-Period Noise Envelope Statistics: A Basis for Envelope Detector Design
Technical rept. no. 17
TEXAS INSTRUMENTS INC DALLAS EQUIPMENT GROUP
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This report focuses on the use of certain detection statistics, in particular the instantaneous amplitude or envelope, and the instantaneous power, in the design of a controlled false alarm rate detector. To achieve false alarm rate control, the detection statistic must be stationary, but need not be Gaussian. Parameters of a Gaussian process can be conveniently transformed into a stationary, normalized detection statistic. For an envelope detector the normalization consists of dividing the envelope by a long-term 1 to 2 minutes estimate of the RMS noise level the instantaneous power is normalized by dividing it by the long-term average power. The stationarity of the normalized envelope is demonstrated with one hour of uninterrupted, Korean Seismic Research Station single-site, short-period noise, by compiling distributions of the base- ten logarithm of the normalized envelope. The envelopes closely follow the Rayleigh distribution which is the theoretical distribution for envelopes of a Gaussian process. Retaining this model at the 5 significance level establishes adequate control of the false alarm rate.
- Seismic Detection and Detectors