Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS 320 DSP Platform
Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS 320 DSP Platform
复制标题
使用 TMS 320 DSP 平台实施实值序列的快速傅里叶变换算法
DOI：
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发表时间：
2002
期刊：
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通讯作者：
R. Matusiak
中科院分区：
文献类型：
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作者：
R. Matusiak
快速傅立叶变换（FFT）是离散傅立叶变换（DFT）的一种有效计算方法，是数字信号处理应用中最重要的工具之一。由于其结构良好的形式，FFT成为评估数字信号处理器（DSP）性能的基准。FFT算法的发展假设输入序列由复数组成。这是因为复杂的相位因子或旋转因子导致复杂的变量。因此，FFT算法被设计为执行复数乘法和加法。然而，在大量的真实的应用中，输入序列由真实的数组成。本应用报告讨论了用于有效计算实值序列DFT的两种算法的理论和用法，这些算法在Texas Instruments TMS320C6000 DSP上实现。第一种算法使用一个N点复DFT和额外的计算来执行两个N点实值序列的DFT。第二种算法使用一个N点复DFT和额外的计算来执行2N点实值序列的DFT。这些额外的计算，被称为分裂操作的实现，在C和C6000汇编语言。对于在C6000上的实现，涵盖了C语言和汇编语言中的优化技术。
The Fast Fourier Transform (FFT) is an efficient computation of the Discrete Fourier Transform (DFT) and one of the most important tools used in digital signal processing applications. Because of its well-structured form, the FFT is a benchmark in assessing digital signal processor (DSP) performance. The development of FFT algorithms has assumed an input sequence consisting of complex numbers. This is because complex phase factors, or twiddle factors, result in complex variables. Thus, FFT algorithms are designed to perform complex multiplications and additions. However, the input sequence consists of real numbers in a large number of real applications. This application report discusses the theory and usage of two algorithms used to efficiently compute the DFT of real-valued sequences as implemented on the Texas Instruments TMS320C6000 . The first algorithm performs the DFT of two N-point real-valued sequences using one N-point complex DFT and additional computations. The second algorithm performs the DFT of a 2N-point real-valued sequence using one N-point complex DFT and additional computations. Implementations of these additional computations, referred to as the split operation, are presented both in C and C6000 assembly language. For implementation on the C6000, optimization techniques in both C and assembly are covered.