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A spectrum analyzer for use with a real-time sampled-data detection system is described. At regular time intervals, it provides the detection system with an updated spectrum of the whole frequency band of the sampled data plus one or more narrower bandwidth, higher resolution (NBHR) spectra at selected frequencies. The number of NBHR spectra, their positions, bandwidths, and resolutions are input parameters that can be changed quickly. This analyzer is very simple in design. Computation and storage requirements are rather low. Hardware implementation, if wanted, requires an FFT processor only. In this case, almost all computations take place inside the FFT processor.