Application of Complexity of Computations to Signal Processing

Algebraic Complexity of Computations is concerned with determining the smallest number of arithmetic operations which are needed to perform a computation. In addition to this primary concern, this area is also concerned with the systematic development of minimal algorithms. In these lectures we will emphasize the results in Complexity of Computations which are applicable to those computations which are performed in digital signal processing. In particular we will discuss the applications to finite impulse response (FIR) filtering and to computing the discrete Fourier transform (DFT).