Fractional Fourier Transform Of The Mobile Algorithm

As a new time-frequency analysis tool, fractional Fourier transform (FRFT) has attracted more and more researchers' interests. Therefore, the discretization of FRFT is becoming an important issue in the FRFT field. Least Mean Square (LMS) algorithm has enjoined wide practical application for its good performance and simplicity. This dissertation is focused on the calculation of discrete fractional Fourier transform (DFRFT) based on the adaptive LMS algorithm. The main contributions and innovations of it are:1. A new method which is called Running Algorithm for calculating discrete fractional Fourier transform based on the adaptive LMS algorithm is proposed. Then, the simulation of the algorithm is presented. As the transform matrix of DFRFT is orthogonal, conjugation of the matrix vector is inputted as the "input vector" of the LMS analyzer. The stream data which is updated with every new sample is inputted asthe "desired response" of the LMS analyzer. Choosing the adaptive speedμ=1/2,the weight vector which is adapted according adaptive LMS algorithm is proportional to the DFRFT of the stream data. According to the algorithm, 4(2N+1) complex multiplication and (4N+4) complex addition are demanded to compute the result of N points stream data when the last sample arrive, while other methods need at least o(NlogN) complex multiplication. The method that use adaptive LMS algorithm to calculate the DFRFT is useful for parallel computation applications and for Very Large Scale Integration(VLSI) implementation.2. Based on the proposed algorithm, a method for detecting feeble multi-component linear frequency modulation (LFM) signal is proposed. Applying adaptive linear enhancer (ALE) technology in the filtering of LFM signal in fractional Fourier transform domain, detection of the feeble multi-component is deserved at the cost of rapid increase of computation complex.