We present a method for compilation of multi-dimensional stream processing programs from affine recurrence equations with unbounded domains into imperative code with statically allocated memory. The method involves a novel polyhedral schedule transformation called periodic tiling. It accommodates existing polyhedral optimizations to improve memory access patterns and expose parallelism. This enables efficient execution of programming languages with unbounded recurrence equations, as well as optimization of existing languages from which this form can be derived. The method is experimentally evaluated on 5 DSP algorithms with large problem sizes. Results show potential for improved throughput compared to hand-optimized C++ (speedups on a 6-core Intel Xeon CPU up to 10× with a geometric mean 3.3×). 1