Multiplicative Complexity, Convolution, and the DFT

the long version

This book introduces multiplicative complexity theory and applies it to the computation of discrete convolutions and the discrete Fourier transform. A mathematical framework is established that enables the multiplicative complexity of many common bilinear systems to be determined. Semilinear systems are introduced as a means of determining the multiplicative complexity of the discrete Fourier transform. Complexity results are derived for other discrete transforms such as the cosine and Hartley transforms. Complete proofs of all the major results are included - the book is essentially self-contained. Many examples are provided to demonstrate the application of the theory.