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278                                             Chapter 7 DSP System Design

            In this chapter, we will first discuss a highly structured design approach
        based on a direct mapping technique. We stress that the scheduling, resource allo-
        cation, and assignment steps are crucial to a successful design. We will discuss dif-
        ferent formulations of the scheduling problem as well as some common
        optimization techniques. We will also demonstrate the shortcomings of conven-
        tional scheduling techniques and present a formulation of the scheduling problem
        that facilitates optimal scheduling.



        7.2 A DIRECT MAPPING TECHNIQUE

        Generally, an algorithm can be mapped to a software-hardware architecture
        either by direct mapping or by first mapping the algorithm to an intermediate, vir-
        tual machine followed by mapping to a programmable hardware structure. The
        first approach typically aims at high-performance, fixed-function systems whereas
        the second method sacrifices performance in an attempt to reduce both the design
        effort and cost by using standard digital signal processors.
            Next, we outline the direct mapping tech-
        nique that is suitable for design of fixed-function
        systems. The main steps in the direct mapping
        technique are shown in Figure 7.2. We will follow
        this approach in the case studies.

             1. Ideally, the specification of the system
                contain a complete specification of the
                system and its components. In reality,
                however, the specifications of the
                components from which the system is
                built must be derived from the system
                specification. In a top-down design
                approach component specification at a
                given system level will depend on the
                results of the synthesis done at the
                higher levels. Hence, the component
                specifications will evolve as the design
                progresses.
             2. A good DSP algorithm is selected and
                tuned to the application. Usually, a high-
                level language is used to develop and
                validate the correctness of the DSP
                algorithm. Note that a software
                implementation of the DSP algorithm
                can serve as specification for the next
                design phase.
             3. In the next phase, the algorithm is
                successively partitioned into a hierarchy
                                                      Figure 7.2 The main steps ir
                of processes. We refer to the tasks in the       the DSP system
                algorithm as processes, for example,             design phase—
                storage of data is considered as a               idealistic view
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