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abhilash_patel
Published © GPL3+

EasyFFT: Fast Fourier Transform (FFT) for Arduino

This code performs FFT with good accuracy.

IntermediateFull instructions provided84,265
EasyFFT: Fast Fourier Transform (FFT) for Arduino

Things used in this project

Hardware components

Arduino Nano R3
Arduino Nano R3
×1

Software apps and online services

Arduino IDE
Arduino IDE

Story

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Schematics

Example connections for Audio analysis

Code

EasyFFT

Arduino
This code performs FFT and updates the F_peasks array with top 5 most dominent frequencies.
/*
//Example data:
int data[64]={14, 30, 35, 34, 34, 40, 46, 45, 30, 4,  -26,  -48,  -55,  -49,  -37,
-28,  -24,  -22,  -13,  6,  32, 55, 65, 57, 38, 17, 1,  -6, -11,  -19,  -34, 
-51,  -61,  -56,  -35,  -7, 18, 32, 35, 34, 35, 41, 46, 43, 26, -2, -31,  -50,
-55,  -47,  -35,  -27,  -24,  -21,  -10,  11, 37, 58, 64, 55, 34, 13, -1, -7};
*/


//---------------------------------------------------------------------------//
byte sine_data [91]=
 {
0,  
4,    9,    13,   18,   22,   27,   31,   35,   40,   44, 
49,   53,   57,   62,   66,   70,   75,   79,   83,   87, 
91,   96,   100,  104,  108,  112,  116,  120,  124,  127,  
131,  135,  139,  143,  146,  150,  153,  157,  160,  164,  
167,  171,  174,  177,  180,  183,  186,  189,  192,  195,       //Paste this at top of program
198,  201,  204,  206,  209,  211,  214,  216,  219,  221,  
223,  225,  227,  229,  231,  233,  235,  236,  238,  240,  
241,  243,  244,  245,  246,  247,  248,  249,  250,  251,  
252,  253,  253,  254,  254,  254,  255,  255,  255,  255
  };
float f_peaks[5]; // top 5 frequencies peaks in descending order
//---------------------------------------------------------------------------//


void setup() 
        {
        Serial.begin(250000);           
        }

        
void loop() {

/*
//example
FFT(data,64,100);        //to get top five value of frequencies of X having 64 sample at 100Hz sampling
Serial.println(f_peaks[0]);
Serial.println(f_peaks[1]);
delay(99999);
*/


/* 
after ruing above FFT(), frequencies available at f_peaks[0],f_peaks[1],f_peaks[2],f_peaks[3],f_peaks[4],
*/           
            }



//-----------------------------FFT Function----------------------------------------------//

float FFT(int in[],int N,float Frequency)
{
/*
Code to perform FFT on arduino,
setup:
paste sine_data [91] at top of program [global variable], paste FFT function at end of program
Term:
1. in[]     : Data array, 
2. N        : Number of sample (recommended sample size 2,4,8,16,32,64,128...)
3. Frequency: sampling frequency required as input (Hz)

If sample size is not in power of 2 it will be clipped to lower side of number. 
i.e, for 150 number of samples, code will consider first 128 sample, remaining sample  will be omitted.
For Arduino nano, FFT of more than 128 sample not possible due to mamory limitation (64 recomended)
For higher Number of sample may arise Mamory related issue,
Code by ABHILASH
Contact: abhilashpatel121@gmail.com 
Documentation:https://www.instructables.com/member/abhilash_patel/instructables/
2/3/2021: change data type of N from float to int for >=256 samples
*/

unsigned int data[13]={1,2,4,8,16,32,64,128,256,512,1024,2048};
int a,c1,f,o,x;
a=N;  
                                 
      for(int i=0;i<12;i++)                 //calculating the levels
         { if(data[i]<=a){o=i;} }
      
int in_ps[data[o]]={};     //input for sequencing
float out_r[data[o]]={};   //real part of transform
float out_im[data[o]]={};  //imaginory part of transform
           
x=0;  
      for(int b=0;b<o;b++)                     // bit reversal
         {
          c1=data[b];
          f=data[o]/(c1+c1);
                for(int j=0;j<c1;j++)
                    { 
                     x=x+1;
                     in_ps[x]=in_ps[j]+f;
                    }
         }

 
      for(int i=0;i<data[o];i++)            // update input array as per bit reverse order
         {
          if(in_ps[i]<a)
          {out_r[i]=in[in_ps[i]];}
          if(in_ps[i]>a)
          {out_r[i]=in[in_ps[i]-a];}      
         }


int i10,i11,n1;
float e,c,s,tr,ti;

    for(int i=0;i<o;i++)                                    //fft
    {
     i10=data[i];              // overall values of sine/cosine  :
     i11=data[o]/data[i+1];    // loop with similar sine cosine:
     e=360/data[i+1];
     e=0-e;
     n1=0;

          for(int j=0;j<i10;j++)
          {
          c=cosine(e*j);
          s=sine(e*j);    
          n1=j;
          
                for(int k=0;k<i11;k++)
                 {
                 tr=c*out_r[i10+n1]-s*out_im[i10+n1];
                 ti=s*out_r[i10+n1]+c*out_im[i10+n1];
          
                 out_r[n1+i10]=out_r[n1]-tr;
                 out_r[n1]=out_r[n1]+tr;
          
                 out_im[n1+i10]=out_im[n1]-ti;
                 out_im[n1]=out_im[n1]+ti;          
          
                 n1=n1+i10+i10;
                  }       
             }
     }

/*
for(int i=0;i<data[o];i++)
{
Serial.print(out_r[i]);
Serial.print("\t");                                     // un comment to print RAW o/p    
Serial.print(out_im[i]); Serial.println("i");      
}
*/


//---> here onward out_r contains amplitude and our_in conntains frequency (Hz)
    for(int i=0;i<data[o-1];i++)               // getting amplitude from compex number
        {
         out_r[i]=sqrt(out_r[i]*out_r[i]+out_im[i]*out_im[i]); // to  increase the speed delete sqrt
         out_im[i]=i*Frequency/N;
         /*
         Serial.print(out_im[i]); Serial.print("Hz");
         Serial.print("\t");                            // un comment to print freuency bin    
         Serial.println(out_r[i]); 
         */    
        }




x=0;       // peak detection
   for(int i=1;i<data[o-1]-1;i++)
      {
      if(out_r[i]>out_r[i-1] && out_r[i]>out_r[i+1]) 
      {in_ps[x]=i;    //in_ps array used for storage of peak number
      x=x+1;}    
      }


s=0;
c=0;
    for(int i=0;i<x;i++)             // re arraange as per magnitude
    {
        for(int j=c;j<x;j++)
        {
            if(out_r[in_ps[i]]<out_r[in_ps[j]]) 
                {s=in_ps[i];
                in_ps[i]=in_ps[j];
                in_ps[j]=s;}
        }
    c=c+1;
    }



    for(int i=0;i<5;i++)     // updating f_peak array (global variable)with descending order
    {
    f_peaks[i]=out_im[in_ps[i]];
    }



}
    

float sine(int i)
{
  int j=i;
  float out;
  while(j<0){j=j+360;}
  while(j>360){j=j-360;}
  if(j>-1   && j<91){out= sine_data[j];}
  else if(j>90  && j<181){out= sine_data[180-j];}
  else if(j>180 && j<271){out= -sine_data[j-180];}
  else if(j>270 && j<361){out= -sine_data[360-j];}
  return (out/255);
}

float cosine(int i)
{
  int j=i;
  float out;
  while(j<0){j=j+360;}
  while(j>360){j=j-360;}
  if(j>-1   && j<91){out= sine_data[90-j];}
  else if(j>90  && j<181){out= -sine_data[j-90];}
  else if(j>180 && j<271){out= -sine_data[270-j];}
  else if(j>270 && j<361){out= sine_data[j-270];}
  return (out/255);
}

//------------------------------------------------------------------------------------//

Credits

abhilash_patel
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