DFT

dft.cpp

// This is a function that performs the discrete fourier transform
// on an input array and returns a magnitude from 0-1 indicating
// detection strength (1 being prominent and 0 being silent)

// Additionally, it's also implemented here as an example

#include <iostream>
#include <math.h> 
#define _USE_MATH_DEFINES
using namespace std;

float DFT(float* input, float detFreq, int sampleRate){
    struct Coords{
        float x;
        float y;
        Coords(){};
        Coords(float newX, float newY){
            x = newX;
            y = newY;
        }
    };
    // Calculate DFT for freq = detFreq
    float waveLen = (float)sampleRate/detFreq;
    Coords coords[sampleRate];
    
    for(int i=0; i<sampleRate;i++){
        float x,y;
        // Get the angle
        float angle = (fmod((float)i,waveLen))/waveLen;
        // This is between 0 and 1
        // Convert to radians
        angle *= 2*M_PI;
        // Do trig to get x and y
        // sin is y, cos is x
        x = cos(angle)*input[i];
        y = sin(angle)*input[i];
        Coords newCoords(x,y);
        coords[i] = newCoords;
    }
    
    // Get average vector
    Coords avgVec(0,0);
    for(Coords i:coords){
        avgVec.x += i.x;
        avgVec.y += i.y;
    }
    
    // Get final magnitude
    // a^2 + b^2 = c^2
    // sqrt(x^2 + y^2) = c
    float mag = sqrt(pow(avgVec.x,2)+pow(avgVec.y,2))/sampleRate;
    // Make mag between 0 and 1
    mag *= 2;
    
    return mag;
}

int main() {
    float genFreq = 200; // Frequency to generate (to use as input for detection)
    float detFreq = 200; // Frequency to detect
    int sampleRate = 8000;
    float waveform[8000];

    // Create waveform
    for(int i=0;i<sampleRate;i++){
        waveform[i] = sin(genFreq * i * (1/(float)sampleRate) * (2 * M_PI));
    }
    // Run DFT
    float mag = DFT(waveform,detFreq,sampleRate);
    // Output Result
    cout << "The magnitude was: " << mag << endl;
    return 0;
}