# Audio Frequency Amplitudes | C++

### August 26th, 2021 11:40:29 PM

```					//From https://create.arduino.cc/projecthub/abhilashpatel121/easyfft-fast-fourier-transform-fft-for-arduino-9d2677
#include <cmath>
#include <iostream>
const unsigned char sine_data[] = {	//Quarter a sine wave
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 sine(int i){	//Inefficient sine
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){	//Inefficient cosine
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);
}

//Example data:

//-----------------------------FFT Function----------------------------------------------//
float* FFT(int in[],unsigned int N,float Frequency){	//Result is highest frequencies in order of loudness. Needs to be deleted.
/*
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: [email protected]
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 sampleRates[13]={1,2,4,8,16,32,64,128,256,512,1024,2048};
int a = N;
int o;
for(int i=0;i<12;i++){		//Snapping N to a sample rate in sampleRates
if(sampleRates[i]<=a){
o = i;
}
}

int in_ps[sampleRates[o]] = {};     //input for sequencing
float out_r[sampleRates[o]] = {};   //real part of transform
float out_im[sampleRates[o]] = {};  //imaginory part of transform
int x = 0;
int c1;
int f;
for(int b=0;b<o;b++){                     // bit reversal
c1 = sampleRates[b];
f = sampleRates[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<sampleRates[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 = sampleRates[i];              // overall values of sine/cosine  :
i11 = sampleRates[o] / sampleRates[i+1];    // loop with similar sine cosine:
e = 360 / sampleRates[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<sampleRates[o];i++)
{
std::cout << (out_r[i]);
std::cout << ("\t");                                     // un comment to print RAW o/p
std::cout << (out_im[i]); std::cout << ("i");
std::cout << std::endl;
}
*/

//---> here onward out_r contains amplitude and our_in conntains frequency (Hz)
for(int i=0;i<sampleRates[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;
std::cout << (out_im[i]); std::cout << ("Hz");
std::cout << ("\t");	// un comment to print freuency bin
std::cout << (out_r[i]);
std::cout << std::endl;
}

x = 0;       // peak detection
for(int i=1;i<sampleRates[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;
}
float* f_peaks = new float[sampleRates[o]];
for(int i=0;i<5;i++){     // updating f_peak array (global variable)with descending order
f_peaks[i]=out_im[in_ps[i]];
}
return f_peaks;
}

//------------------------------------------------------------------------------------//
//main.cpp
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
};

int main(){
const unsigned int SAMPLE_RATE = 48*1000;	//48khz
auto result = FFT(data,64,SAMPLE_RATE);
std::cout << result[0] << " " << result[1] << " " << result[2] << " " << result[3] << std::endl;
delete[] result;
return 0;
}
```