Fundamental Relations Between The Adaptive LMS Algorithm And The DFRFT

The Fractional Fourier transform (FRFT) is a generalized Fourier transform. It is the time-frequency plane of the signal processing, especially for the handling of non-stationary signal. It adds a degree of freedom parameter-rotation angle to increased flexibility. It has very broad prospects in the project, with the rapid development applications of the digital signal processing in engineering of discrete fractional Fourier transform (DFRFT); Rapid algorithm has become a critical issue. In this paper, based on the research of a variety of discrete fractional Fourier transform algorithm, it proposed the fractional Fourier transform algorithm which is based on least mean square error algorithm(LMS), the following elements:1. A detailed analysis of the existing variety of discrete fractional Fourier transform algorithm, it focuses on the Closed-form algorithm that proposed by Pie, etc., this algorithm is the basis of this study, the algorithm has been improved to be their nuclear transformation of the mobile algorithm.2. Based on the LMS-based analyzer model of Windrow and so on, which is used to achieve DFT. it proposed a calculation of fractional Fourier transform of the new methods. The algorithm is given a detailed model structure, algorithm derivation, proof, and conclusions, and finally examples of simulation of the algorithm are correct. This algorithm is mainly aimed at updating the data sampling points one by one, for the block of updated data sampling points, just after the last data entry, through an iterative algorithm of the LMS, it can be calculated the DFRFT of N point pre. This algorithm is faster than the monolithic terms, and compared with existing algorithms. It further improves the computational efficiency, more suitable for real-time demanding applications. 3. Correct the verification of the algorithm. Study the application for the linear FM Mobile (LFM) signal detection and parameter estimation and fractional domain adaptive filtering, describes the relevant theory, the simulation results. The experimental results verify the effectiveness of the algorithm, the algorithm has a wider range of practical application value.