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Repeatability problems, usually accompanied by low accuracy, are often experienced in power measurements, especially in those concerning spread spectrum signals, peculiar to digital wireless communication systems, and involving a specified frequency range. For this concern, a new method for power measurements is presented. The method applies original and straightforward digital signal-processing algorithms to the input signal power spectrum, preliminarily provided by optimized versions of well-known estimators, such as those based on weighted overlapped segment averaging and multitaper approaches. The outcomes of many experiments, conducted on spread spectrum signals of third-generation telecommunication systems, confirm the efficacy of the proposed method in assuring reliable and accurate results in various types of power measurement.