如何在 Arduino 中反转 FFT [英] How to Inverse FFT in Arduino

问题描述

我正在尝试使用 Arduino FFT 库根据以下代码过滤一些数据FFT(快速傅立叶变换)

I am trying to filter some data based on the the following code using Arduino FFT library for FFT (fast Fourier transform)

/*
fft_adc_serial.pde
guest openmusiclabs.com 7.7.14
example sketch for testing the fft library.
it takes in data on ADC0 (Analog0) and processes them
with the fft. the data is sent out over the serial
port at 115.2kb.
*/

#define LOG_OUT 1 // use the log output function
#define FFT_N 256 // set to 256 point fft

#include <FFT.h> // include the library

void setup() {
  Serial.begin(115200); // use the serial port
  TIMSK0 = 0; // turn off timer0 for lower jitter
  ADCSRA = 0xe5; // set the adc to free running mode
  ADMUX = 0x40; // use adc0
  DIDR0 = 0x01; // turn off the digital input for adc0
}

void loop() {
  while(1) { // reduces jitter
    cli();  // UDRE interrupt slows this way down on arduino1.0
    for (int i = 0 ; i < 512 ; i += 2) { // save 256 samples
      while(!(ADCSRA & 0x10)); // wait for adc to be ready
      ADCSRA = 0xf5; // restart adc
      byte m = ADCL; // fetch adc data
      byte j = ADCH;
      int k = (j << 8) | m; // form into an int

      k -= 0x0200; // form into a signed int
      k <<= 6; // form into a 16b signed int
      fft_input[i] = k; // put real data into even bins
     // Serial.print(millis());
     // Serial.print("input ");
     // Serial.print(i);
    //  Serial.print(" = ");
      Serial.println(k);
      fft_input[i+1] = 0; // set odd bins to 0
      delay(0.1);
    }
    fft_window(); // window the data for better frequency response
    fft_reorder(); // reorder the data before doing the fft
    fft_run(); // process the data in the fft
    fft_mag_log(); // take the output of the fft
    sei();
    Serial.println("start");

   for (byte i = 0; i < FFT_N/2; i++) {
     if(i<10 || i>20)
     {
       fft_log_out[i] = 0;
     }

     Serial.println(fft_log_out[i]);
   }    
  }
}

像这样应用过滤器后:

if(i<10 || i>20)
     {
       fft_log_out[i] = 0;
     }

然后我需要对 FFT 数据进行反演 fft_log_out[].

I then need to Inverse FFT data fft_log_out[].

我寻找了一个逆 FFT 函数(特别是在 http://wiki.openmusiclabs.com/wiki/FFTFunctions) 但在任何地方都找不到.

I looked for an Inverse FFT function (in particular in http://wiki.openmusiclabs.com/wiki/FFTFunctions) but can't find it anywhere.

那么如何在 Arduino 中获得逆 FFT?

So how can I get the Inverse FFT in Arduino?

推荐答案

利用前向变换可以得到逆FFT:

The inverse FFT can be obtained by making use of the forward transform:

for (int i = 0 ; i < 512 ; i += 2) {
  fft_input[i] =  (fft_input[i] >> 8);
  fft_input[i+1] = -(fft_input[i+1] >> 8);
}
fft_reorder();
fft_run();
// For complex data, you would then need to negate the imaginary part
// but we can skip this step since you have real data.

但是请注意，您的过滤代码存在一些问题.

Note however that your filtering code has a few issues.

首先，前向 FFT 的结果是带有幅度和相位信息的复数.使用fft_mag_log 仅获取幅度，仅靠幅度不足以恢复原始信号.因此，您应该使用 fft_input 数组中剩余的完整 FFT 输出作为过滤代码的输入.

First, the results of the forward FFT are complex numbers which carry both magnitude and phase information. Using fft_mag_log only takes the magnitude, which alone is not sufficient for recovery of the original signal. You should thus use the complete FFT output left in fft_input array as input to your filtering code.

其次，实值数据的 FFT 产生具有厄米对称性的频谱.要获得实值滤波输出，您必须保持对称性.因此，您不应将频谱上半部分的值完全归零:

Second, the FFT of real valued data results in a spectrum with Hermitian symmetry. To get a real valued filtered output, you must preserve that symmetry. So, you should not completely zero out the values in the upper half of the spectrum:

for (byte i = 0; i < FFT_N; i+=2) {
  if (! ((i>=20 && i<=40) || (i>=FFT_N-40 && i<=FFT_N-20)))
  {
    fft_input[i] = 0;
    fft_input[i+1] = 0;
  }
}

第三，过滤将彼此独立地应用于每个数据块，始终假设先前的输入为零.这通常会导致块边界处的不连续性.为避免这种情况，您应该考虑使用重叠添加方法.

Third, the filtering would be applied to each block of data independently of each other, always assuming that previous inputs were zeros. This typically results in discontinuities at the block boundaries. To avoid this, you should consider using the overlap-add method.

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