Lecture 6: A Family of Divide and Conquer Algorithms for Computing the Walsh-Hadamard Transform

Background Material

• Elementary matrix operations and linear algebra

Reading

• WHT Paper (wht.ps,wht.pdf)
  
• Programming Schemata for Tensor Products (schema.ps, schema.pdf) - provides tensor product factorizations and programs resulting from these factorizations.
• FFT paper (fft.ps, fft.pdf) - contains info on programming with the tensor product and the WHT.

Topics

• Tensor product (also known as the Kronecker product) and its properties
• Tensor product factorizations
• The Walsh-Hadamard Transform (WHT)
• Factorizations of the WHT and partition trees (a family of WHT algorithms)
• A program to compute the WHT
• Dataflow patterns of different WHT algorithms

Lecture notes

• WHT Lecture (wht.ppt,wht.pdf)

Programs

1. wht.txt (WHT program)
2. wht_prog.mws (Maple worksheet)
3. wht_prog.html (HTML view of Maple worksheet)

Related Links

• wht package