Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Calculation Scheme Based on a Weighted Primitive: Application to Image Processing Transforms | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2007 Article ID 45321 17 pages doi 2007 45321 Research Article Calculation Scheme Based on a Weighted Primitive Application to Image Processing Transforms Maria Teresa Signes Pont Juan Manuel García Chamizo Higinio Mora Mora and Gregorio de Miguel Casado Departamento de Tecnologia Informatica y Computation Universidad de Alicante 03690 San Vicente del Raspeig 03071 Alicante Spain Received 29 September 2006 Accepted 6 March 2007 Recommended by Nicola Mastronardi This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level the method shows suitable for developing a processor which achieves a satisfying trade-off between time delay area costs and stability. The method is particularly suitable for the mathematical transforms used in signal processing applications. A generic calculation scheme is developed for the discrete fast Fourier transform DFT and then applied to other integral transforms such as the discrete Hartley transform DHT the discrete cosine transform DCT and the discrete sine transform DST . Some comparisons with other well-known proposals are also provided. Copyright 2007 Maria Teresa Signes Pont et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION Mathematical notation aside the motivation behind integral transforms is easy to understand. There are many classes of problems that are extremely difficult to solve or at least quite unwieldy from the algebraic standpoint in their original domains. An integral transform maps an equation from
