A complexity-based timing analysis of fast real transforms

Within the past decade, real-valued trigonometric transforms have gained increased awareness in real-time or computationally-intensive applications characterized by voluminous real data sets. The computational savings of real-valued transforms over their complex-valued counterparts have led to proliferation of fast real transforms wherein each author claims the lowest theoretical complexity (i.e., the number of additions and multiplications) than any other real-valued FFT algorithm. However, the performance of an algorithm not only depends on its additive and multiplicative complexities, but also on the number of machine cycles attributed to data-transfer operations-for example, load and store instructions. In this paper, a performance analysis of four real-valued trigonometric transforms based on a timing study is presented. An improved fast Hartley transform algorithm is developed which is computationally more efficient than the algorithms studied herein when computed on a SPARC-based computing platform