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The implementation of software for embedded digital signal processing (DSP) applications is an extremely complex process. The complexity arises from escalating functionality in the applications; intense time-to-market pressures; and stringent cost, power and speed constraints. To help cope with such complexity, DSP system designers have increasingly been employing high-level, graphical design environments in which system specification is based on hierarchical dataflow graphs. Consequently, a significant industry has emerged for the development of data-flow-based DSP design environments. Leading products in this industry include SPW from Cadence, COSSAP from Synopsys, ADS from Hewlett Packard, and DSP Station from Mentor Graphics. This paper reviews a set of algorithms for compiling dataflow programs for embedded DSP applications into efficient implementations on programmable digital signal processors. The algorithms focus primarily on the minimization of code size, and the minimization of the memory required for the buffers that implement the communication channels in the input dataflow graph. These are critical problems because programmable digital signal processors have very limited amounts of on-chip memory, and the speed, power, and cost penalties for using off-chip memory are often prohibitively high for embedded applications. Furthermore, memory demands of applications are increasing at a significantly higher rate than the rate of increase in on-chip memory capacity offered by improved integrated circuit technology.