Research On The Simulation And FPGA Realization Of Discrete Fractional Fourier Transform

With the further development of science and technology, signal processing technology has also been considerable progressed. In the field of signal processing, the conventional Fourier transform is an applied research focus today. But with the increasing complexity of application of signal form, the conventional Fourier transform is particularly inadequate to analysis and processing time-varying non-stationary signals. It is the main reason that the Fourier Transform key functions used by the decision. Fractional Fourier Transform (FrFT) as a generalized form of the Fourier Transform can not only deal with the signals of the general sense, but also resolved time-varying non-stationary signals. Compared to another time-frequency tools, its unique characteristics are well received by many researchers. This paper discussed design of hardware platform about the signal processing board based on FPGA chip, met discrete fractional Fourier transform (DFrFT) and the algorithm based on Running Algorithm hardware implementation and analyzed the result of the simulation. The main contributions of this dissertation are summarized as follow:1. The hardware design of signal processing board. Requirements in accordance with this topic, signal processing board system including processing board and the display control portion. The author's main task is to complete hardware design of the processing board, including the functional classification, the system components of each module selection and implementation details, PCB layout drawing and so on. Processing board main modules includes A/D acquisition, FPGA processing and D/A converter, RS232 serial communication. In addition to some of the PCB design considerations, such as power supply design, high-speed design, the article has a statement.2. DFrFT algorithm analysis and implementation. Paper a brief overview of the definition of fractional Fourier transform and its properties, and then comparing several discrete Fourier transform method used in engineering to achieve the advantages and disadvantages. Close-form algorithm is Pei made a direct discrete fractional Fourier transform algorithm, this method is followed most of the continuous FrFT transform the nature of the current discrete algorithm with the smallest computational complexity and easy engineering implementation. Therefore, this design is based on Close-form algorithm FPGA hardware implementation. Engineering tests show that the correctness of the experimental results and practical engineering applications superiority.3. Analysis and complement of the discrete Fourier transform algorithm base on Running Algorithm. It is an important consult by the complexity of an algorithm about the general nature of this algorithm. The paper discussed the Technology Toolbox aim at decrease complexity of the discrete Fourier transform algorithm base on Running Algorithm. The paper descried the application background and significance of the algorithm base on Running Algorithm. Combination of VHDL language and FPGA signal processing on-board mobile-based Simulation of Running Algorithm. Experimental data show that the algorithm based on Running Algorithm system to ensure accuracy of the calculation results under the premise of improved signal processing in real time.