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With the advance of hardware and software technology, modern phased array radars are now built with commercial-off-the-shelf (COTS) components, and it opens up a new era in real-time resource scheduling of digital signal processing. This paper targets the essential issues in building a component-oriented signal processor (SP), which is one of the two major modules in modern phased array radars. We propose a simple but effective task allocation policy and a real-time scheduling algorithm to address the design objectives of SPs. We are able to bound the number of processing units needed for a component-oriented SP in the design time, while everything was done empirically in the past. A series of experiments was done to demonstrate the strength of our methodology.