Periodic Sequences that Facilitate Data Set Spectrum Measurements

The modulated pulse spectrum (MPS), defined below, of a data set's signal is a basic characteristic of the data set that is of interest, for example, in determining how much bandwidth the signal requires. One can usually calculate an MPS, but it is often necessary to confirm the calculation by experiment. The usual practice in such experiments is to apply a binary pseudorandom sequence (also called maximumlength sequence1) to the input of a data set and measure the resulting output signal with a spectrum analyzer. This technique usually leads to a picture that shows the MPS approximately, but not exactly and not in a repeatable manner; the reasons are given in Section II. The output of the spectrum analyzer is usually not constant at any one frequency setting, and the relative level at each frequency is not proportional to the MPS. An example is shown on Fig. 1. If a data set modulator is a member of the quadrature amplitude modulation (QAM) class, which includes the differential phase shift keyed modulators, then there exist easily generated periodic constellation point sequences whose resulting signals have line spectra with amplitudes that are proportional to the modulator's MPS, and thus facilitate accurate experimental measurement of the MPS. The derivation and application of these sequences are the subject of this paper. The next section establishes the properties required of the constel2089