How to make harmonic analysis use C++ ?

Harmonic analysis is a mathematical tool used to analyze periodic functions by decomposing them into a sum of sinusoidal functions with different frequencies, amplitudes, and phases. In order to perform harmonic analysis using C programming language, the following steps can be followed:

1. Define the periodic function to be analyzed as a series of discrete values. This can be done by either inputting the values manually or by reading them from a file.

2. Calculate the discrete Fourier transform (DFT) of the input signal using the Fast Fourier Transform (FFT) algorithm. This can be implemented using the FFTW library or by writing your own FFT algorithm.

3. Extract the frequency spectrum of the input signal by calculating the magnitude and phase of each frequency component in the DFT output.

4. Use the frequency spectrum to analyze the harmonic content of the input signal by identifying the dominant frequencies and their corresponding amplitudes and phases.

5. Visualize the harmonic analysis results using plots and graphs to better understand the periodic nature of the input signal.

Here is an example code snippet in C that performs harmonic analysis on a given periodic function using FFT:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <fftw3.h>

#define N 256 // number of discrete samples
#define Fs 1000.0 // sampling frequency
#define f1 50.0 // fundamental frequency
#define f2 100.0 // second harmonic frequency

int main()
{
    double x[N], y[N], freq[N], mag[N], phase[N];
    int i;

    // generate a test signal with two harmonics
    for (i = 0; i < N; i++) {
        x[i] = sin(2.0 * M_PI * f1 * i / Fs) +
               0.5 * sin(2.0 * M_PI * f2 * i / Fs);
    }

    // perform FFT on the input signal
    fftw_complex *in, *out;
    fftw_plan p;
    in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
    out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
    for (i = 0; i < N; i++) {
        in[i][0] = x[i];
        in[i][1] = 0.0;
    }
    p = fftw_plan_dft_1d(N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
    fftw_execute(p);

    // extract frequency spectrum from the FFT output
    for (i = 0; i < N; i++) {
        freq[i] = i * Fs / N;
        mag[i] = sqrt(out[i][0] * out[i][0] + out[i][1] * out[i][1]) / N;
        phase[i] = atan2(out[i][1], out[i][0]);
    }

    // print out the harmonic content of the input signal
    printf("Frequency\tMagnitude\tPhase\n");
    for (i = 0; i < N/2; i++) {
        printf("%f\t%f\t%f\n", freq[i], mag[i], phase[i]);
    }

    // clean up resources
    fftw_destroy_plan(p);
    fftw_free(in);
    fftw_free(out);

    return 0;
}