Exploring FFT in C and C++: A Dive into FFTW

In the realm of signal processing, the Fast Fourier Transform (FFT) plays a crucial role, especially when comparing implementations in different programming languages. A recent analysis highlights the superiority of the C library FFTW over Python for FFT operations, showcasing a significant performance advantage in terms of processor load and memory usage. This is particularly relevant for users operating on resource-constrained devices, such as Raspberry Pi, where inefficient memory usage can lead to system crashes.

The FFTW library stands out for its efficiency, making it a preferred choice for developers looking to perform FFT calculations. The following code provides a practical example of how to implement FFT using FFTW in C, specifically utilizing data captured from an RTL-SDR (Software Defined Radio).

Implementation Steps

1. Include the FFTW Library

   #include <fftw3.h>
   

2. Define Constants

   #define CAPTURE 1000 // Size of the FFT
   

3. Declare Variables

   fftw_complex *in;
   fftw_complex *out;
   fftw_plan p;
   

4. Set Up the FFT

   void setFFT() {
       in = (fftw_complex *) fftw_malloc(sizeof(fftw_complex) * CAPTURE + 1);
       out = (fftw_complex *) fftw_malloc(sizeof(fftw_complex) * CAPTURE + 1);
       p = fftw_plan_dft_1d(CAPTURE, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
   }
   

5. FFT Function

   double *fft(uint8_t *data, int *count, double *power_spectrum) {
       double *power_spectrum_tmp = (double *) malloc(sizeof(double) * CAPTURE + 1);
       fftw_complex *cx_power_spectrum = (fftw_complex *) malloc(sizeof(fftw_complex) * CAPTURE + 1);
       int w = 0;
       int x = 0;
   
       // Transform to complex data, RTL-SDR receives 2 numbers for each iteration.
       for (int i = 0; i < CAPTURE * 2; i+=2) {
           in[x][0] = (data[i]/(255.0/2.0)) - 1.0;
           in[x][1] = (data[i+1]/(255.0/2.0)) - 1.0;
           x++;
       }
   
       fftw_execute(p);
   
       // Calculate power spectrum
       for (int i = 0; i < CAPTURE; i++) {
           double complex complex_tmp = out[i][0] + out[i][1]*I;
           complex_tmp = conj(complex_tmp) * complex_tmp;
           cx_power_spectrum[w][0] = creal(complex_tmp);
           cx_power_spectrum[w][1] = cimag(complex_tmp);
           w++;
       }
   
       // Convert complex to double
       for (int i = 0; i < CAPTURE; i++)
           power_spectrum_tmp[i] = cx_power_spectrum[i][0];
   
       // Reorganize data
       for (int i = 0; i < CAPTURE/2; i++)
           power_spectrum[i] = power_spectrum_tmp[i+(CAPTURE/2)];
       for (int i = 0; i < CAPTURE/2; i++)
           power_spectrum[i+(CAPTURE/2)] = power_spectrum_tmp[i];
   
       free(power_spectrum_tmp);
       free(cx_power_spectrum);
   
       return power_spectrum;
   }
   

This implementation showcases how to efficiently handle FFT calculations in C, leveraging the capabilities of the FFTW library to optimize performance. By using FFTW, developers can achieve faster processing times and better memory management, making it an essential tool for anyone working in the field of signal processing.