为apache commons快速傅立叶变换算法构建样本数据 [英] Build sample data for apache commons Fast Fourier Transform algorithm

问题描述

我想使用针对FFT（ FastFourierTransformer 类）的Apache数学公共实现来处理一些虚拟数据，其中8个数据样本对一个完整的正弦波有贡献。最大振幅230.我尝试过的代码片段如下：

I wanted to use Apache math commons implementation for FFT (FastFourierTransformer class) to process some dummy data whose 8 data samples are contributing to one complete sinusoidal wave. The maximum being amplitude 230. The code snippet that I tried is below :

private double[] transform() 
{   
    double [] input = new double[8];
    input[0] = 0.0;
    input[1] = 162.6345596729059;
    input[2] = 230.0;
    input[3] = 162.63455967290594;
    input[4] = 2.8166876380389125E-14;
    input[5] = -162.6345596729059;
    input[6] = -230.0;
    input[7] = -162.63455967290597;

    double[] tempConversion = new double[input.length];

    FastFourierTransformer transformer = new FastFourierTransformer();
    try {           
        Complex[] complx = transformer.transform(input);

        for (int i = 0; i < complx.length; i++) {               
            double rr = (complx[i].getReal());
            double ri = (complx[i].getImaginary());

            tempConversion[i] = Math.sqrt((rr * rr) + (ri * ri));
        }

    } catch (IllegalArgumentException e) {
        System.out.println(e);
    }

    return tempConversion;
}

1）现在方法转换返回的数据是一个复数的数组。该数组是否包含有关输入数据的频率组件信息？或者我创建的tempConversion数组将包含频率信息？ tempConversion数组中的值为：

1) Now the data returned by method transform is an array of complex number. Does that array contains the frequency component information about input data? or the tempConversion array that I created will contain the frequency information? The values in tempConversion array is :

 2.5483305001488234E-16
 920.0
 4.0014578493024757E-14
 2.2914314707516465E-13
 5.658858581079313E-14
 2.2914314707516465E-13
 4.0014578493024757E-14
 920.0

2）我搜索了很多但是在大多数地方都没有明确的文档说明数据算法的格式是什么（在样本代码方面要更好地理解）以及如何使用结果数组来计算信号中包含的频率？

2) I searched a lot but at most of the places there is no clear documentation on what format of data algorithm expects (in terms of sample code to understand better) and how do I use the array of results to calculate the frequencies contained in the signal?

推荐答案

您的输出数据看起来是正确的。您已计算出每个频率仓的复数FFT输出的幅度，该频率对应于该仓的相应频率的输入信号中的能量。由于您的输入纯粹是实数，输出是复共轭对称的，最后3个输出值是多余的。

Your output data looks correct. You've calculated the magnitude of the complex FFT output at each frequency bin which corresponds to the energy in the input signal at the corresponding frequency for that bin. Since your input is purely real, the output is complex conjugate symmetric, and the last 3 output values are redundant.

所以你有：

Bin     Freq        Magnitude
  0     0 (DC)        2.5483305001488234E-16
  1     Fs/8        920.0
  2     Fs/4          4.0014578493024757E-14
  3     3Fs/8         2.2914314707516465E-13
  4     Fs/2 (Nyq)    5.658858581079313E-14
  5     3Fs/8         2.2914314707516465E-13  # redundant - mirror image of bin 3
  6     Fs/4          4.0014578493024757E-14  # redundant - mirror image of bin 2
  7     Fs/8        920.0                     # redundant - mirror image of bin 1

除了bin 1（和bin 6）之外，所有值实际为0，对应的频率为 Fs / 8 如预期的那样。

All the values are effectively 0 apart from bin 1 (and bin 6) which corresponds to a frequency of Fs/8 as expected.

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