The tensor product: a mathematical programming language for FFTs and other fast DSP operations

The use of the tensor product as a tool for modeling and developing digital signal processing algorithms is discussed. A precise mathematical definition of the tensor product is established along with several important properties. Special tensor matrices suited for implementation on various computer architectures are then identified. The notion of the stride permutation matrix is introduced as a method of modeling operand addressing. An important connection between tensor matrices and stride permutations is made explicit. By identifying particular tensor matrices suited for implementation on a given machine the tensor product has been transformed from a mathematical convenience into an extremely useful tool for matching algorithms to computer architectures. Several design examples in which a tensor matrix multiplication is implemented on several radically different types of computer architectures are presented.<>