(1.4) together with (1.5), it is readily observed that the maximum penalty (inferred above) is V2 (1.5 dB). Thus, the required SIN falls on the average, between that given by (1.4) and (1.40). (3) Wideband Detector with a Continuous Integration Post-Detection RC Filter Perhaps the simplest alternative of all consists of a square-law (envelope) detector followed by an RC filter which acts as a continuous integrator, as shown in Figure 1.12. (SQUARE-LAW) THRESHOLD ENVELOPE FILTER DETECTOR Figure 1.12. Continuous integration detector. Interception Detectors A similar configuration using digital integration is considered in [6]. When noise only is present, the RC filter output is a random process whose instantaneous mean and variance are theoretically constant (independent of time). Furthermore, the instantaneous signal-to-noise ratio (mean-to- standard deviation ratio) is only a function of the ratio of the rpe-detection filter bandwidth W ss to the RC filter 3 dB cutoff frequency fc. When signal-plus-noise is present, the RC filter output mean and variance become functions of time over the message duration. Furthermore, the mean-to-standard deviation ratio is again a function of WssIf, plus, now, the pre-detection bandwidth signal-to-noise power. If the noise bandwidth BN of the RC filter is chosen equal to that of the integrate-and-dump with integration interval equal to the message duration, namely, (1.41) or, equivalently, (1.42) then, for large WSSTM, the RC filter output mean-to-standard deviation ratio becomes (noise only) WssTM (1.43) (signal-plus-noise). In (1.43) the parameter t1 represents the time epoch of the single message duration TM. If any threshold crossing by the RC filter output z(t) constitutes an alarm, then for large WssIf (or, equivalently, large WSSTM), it may be assumed that z(t) is a Gaussian process and the false alarm and detection probabilities are From a practical standpoint, it is necessary only to assume that the RC filter has been inte- grating on noise for a period of time which is