trum analyzer. It may be easily shown that from a detection theoretic point of view, the outputs of a discrete frequency spectrum analyzer at the candidate hop fre- quencies are equivalent to an optimum non-coherent detection channelized receiver.¹¹ The spectral values may therefore be compared to appropriate thresholds and detection decisions made akin to the PB-FBC. Realization of the spectrum analyzer requires that a particular RF fre- quency band, fa to fb, be translated to a lowpass frequency region SO that fa 0 and fb fm, where fm = fb - fa The lowpass waveform (signal-plus-noise) is then sampled at a rate of 2fm samples/second and for a period of Th sec- onds to obtain a sample set of N = 2fmTh samples. A discrete Fourier trans- form is then calculated using the sample set for each of the candidate hop frequency locations. The magnitude of the Fourier transform at each fre- quency is compared with a threshold to determine if its spectral value is suf- ficiently large to indicate the presence of a signal (a hop pulse). This process is repeated for each hop pulse interval Figure 1.16 shows functionally the steps involved in the spectrum analyzer algorithm and the pertinent equations of operation. the translation of the bandpass sub-band into the lowpass range (0,fm) assumes that the candidate hop frequencies are at f1 = Wh,f2 = 2Wh, = 3W etc., with the total num- ber of frequencies (channels) being fm/Wh. Consider now a full-band or N--channel spectrum analyzer, with the probability of a correct hop pulse decision being 0.9. (For the sake of the following, a message is assumed to be present.) Since, for a full-band spec- trum analyzer Phit = 1, on a per-hop basis, the probability of correctly deter- mining the hop pulse frequency is therefore 0.9. Such a receiver would employ a maximum-likelihood decision process, and the required SIN for NT = 106 (plus the other example parameters previously cited) is (perfect time synchronization and no freuency error assumed) about the same as that required by a 500-chann