Methods and apparatus for a low energy accelerator processor architecture with short parallel instruction word. An integrated circuit includes a system bus having a data width N, where N is a positive integer; a central processor unit coupled to the system bus and configured to execute instructions retrieved from a memory coupled to the system bus; and a low energy accelerator processor coupled to the system bus and configured to execute instruction words retrieved from a low energy accelerator code memory, the low energy accelerator processor having a plurality of execution units including a load store unit, a load coefficient unit, a multiply unit, and a butterfly/adder ALU unit, each of the execution units configured to perform operations responsive to op-codes decoded from the retrieved instruction words, wherein the width of the instruction words is equal to the data width N. Additional methods and apparatus are disclosed.