SPRACN4 August   2019 66AK2G12 , 66AK2H06 , 66AK2H12 , 66AK2H14 , OMAP-L132 , OMAP-L138 , TMS320C6452 , TMS320C6454 , TMS320C6455 , TMS320C6457 , TMS320C6652 , TMS320C6654 , TMS320C6655 , TMS320C6657 , TMS320C6672 , TMS320C6674 , TMS320C6678 , TMS320C6742 , TMS320C6743 , TMS320C6745 , TMS320C6746 , TMS320C6747 , TMS320C6748

 

  1.   Using DSPLIB FFT Implementation for Real Input and Without Data Scaling
    1.     Trademarks
    2. 1 Real Input Introduction
      1. 1.1 Prerequisites
      2. 1.2 Computing a Length N/2 Complex FFT From a Length N Real Input Sequence
      3. 1.3 Returning to a Length N Real Sequence Using a Length N/2 Complex IFFT
      4. 1.4 Benchmark of the Efficient Compute of FFT
    3. 2 Fixed Point FFT With No Data Scaling
      1. 2.1 Suggested Change
      2. 2.2 Example Application
    4. 3 Summary
    5. 4 References

1 Real Input Introduction

Algorithms to perform forward and Inverse Fast Fourier Transforms (FFT and IFFT) typically assume complex input and output data. However, many applications use only real-valued data in the time domain. A simple but inefficient solution to this problem is to pad N-length real input signals to N-length complex input signals with zero-valued imaginary components.

xreal = { 1, 2, 3, ... }
xcplx = { 1, 0, 2, 0, 3, 0, ...}

The complex FFT can then be applied to the double-length sequence. However, this method is obviously inefficient. This topic explains how to use the complex-valued FFT and IFFT algorithms to efficiently process real-valued sequences without padding those sequences. There are two key advantages to this approach:

  • Lower memory footprint - M bytes per sequence instead of 2M bytes
  • Fewer cycles - length N/2 FFT and IFFT computation instead of length N

For more information on the derivation of this method, see Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS320 DSP Platform.

Example C code for this method is also available for download.