/* calculates the inverse fast Fourier transform of a complex packed array, and stores
* it into fft_results. Storage conventions as for complex_fft */
int complex_inverse_fft (size_t N, double *data, double *fft_results) {
size_t i;
int retcode;
/* initialize the data for fft */
for (i=0; i<2*N; i++) fft_results [i] = data [i];
/* use the corresponding routine if N is power of 2 */
if (is_power_of_n (N,2)) {
/* perform the fft */
retcode = gsl_fft_complex_radix2_inverse (fft_results, 1, N);
}
else {
/* alloc memory for wavetable and workspace */
gsl_fft_complex_wavetable * wavetable = gsl_fft_complex_wavetable_alloc (N);
gsl_fft_complex_workspace * workspace = gsl_fft_complex_workspace_alloc (N);
/* perform the fft */
retcode = gsl_fft_complex_inverse (fft_results, 1, N, wavetable, workspace);
/* free memory */
gsl_fft_complex_wavetable_free (wavetable);
gsl_fft_complex_workspace_free (workspace);
}
return retcode;
}
QuantityType fftgtof(const QuantityType& g, double rstep, double rmin)
{
if (g.empty()) return g;
int padrmin = int(round(rmin / rstep));
int Npad1 = padrmin + g.size();
// pad to the next power of 2 for fast Fourier transformation
int Npad2 = (1 << int(ceil(log2(Npad1))));
// sine transformations needs an odd extension
// gpadc array has to be doubled for complex coefficients
int Npad4 = 4 * Npad2;
valarray<double> gpadc(0.0, Npad4);
QuantityType::const_iterator gi;
// copy the original g signal
int ilo = padrmin;
for (gi = g.begin(); gi != g.end(); ++gi, ++ilo)
{
gpadc[2 * ilo] = *gi;
}
// copy the odd part of g skipping the first point,
// because it is periodic image of gpadc[0]
int ihi = 2 * Npad2 - 1;
for (ilo = 1; ilo < Npad2; ++ilo, --ihi)
{
gpadc[2 * ihi] = -1 * gpadc[2 * ilo];
}
int status;
status = gsl_fft_complex_radix2_inverse(&(gpadc[0]), 1, 2 * Npad2);
if (status != GSL_SUCCESS) throw invalid_argument(EMSGFFT);
QuantityType f(Npad2);
for (int i = 0; i < Npad2; ++i)
{
f[i] = gpadc[2 * i + 1] * Npad2 * rstep;
}
// real components should be all close to zero
assert(fabs(valarray<double>(gpadc[slice(0, 2 * Npad2, 2)]).min()) <=
SQRT_DOUBLE_EPS * gpadc.max());
assert(fabs(valarray<double>(gpadc[slice(0, 2 * Npad2, 2)]).max()) <=
SQRT_DOUBLE_EPS * gpadc.max());
return f;
}
/*
* Extracting information from a noisy signal
*/
void extract_noisy_signal(int count, double *values) {
plot_t p;
p.outfile = "output5.png";
p.title = "Noisy signal";
p.xlabel = "t [s]";
p.ylabel = "u(t) [m]";
p.xmin = 0;
p.xmax = 0;
init_gnuplot(&p);
gsl_complex_packed_array data = calloc(2*count, sizeof(double));
// Noisy signal
BEGIN_SCATTER(p, "u(t)");
double t = 0;
for (int i = 0; i < count; i++) {
PLOT(p, t, values[i]);
data[2*i] = values[i];
t += 1.0/count;
}
END_PLOT(p);
p.outfile = "output6.png";
p.title = "FFT of noisy signal";
p.xlabel = "f [Hz]";
p.ylabel = "U(f) [m]";
p.xmin = -1500;
p.xmax = 1500;
init_gnuplot(&p);
gsl_fft_complex_radix2_forward(data, 1, count);
// FFT of noisy signal
BEGIN_SCATTER(p, "U(f)");
double f = -count/2;
for (int i = count; i < 2*count; i += 2) {
double y = data[i];
data[i] = H(f) * data[i];
data[i+1] = H(f) * data[i+1];
PLOT(p, f, y);
f += 1.0;
}
for (int i = 0; i < count; i += 2) {
double y = data[i];
data[i] = H(f) * data[i];
data[i+1] = H(f) * data[i+1];
PLOT(p, f, y);
f += 1.0;
}
END_PLOT(p);
gsl_fft_complex_radix2_inverse(data, 1, count);
p.outfile = "output7.png";
p.title = "Inverse FFT of data";
p.xlabel = "t [s]";
p.ylabel = "u(t) [m]";
p.xmin = 0;
p.xmax = 1;
init_gnuplot(&p);
// Filtered signal
BEGIN_PLOT(p, "u(t)");
t = 0;
double umax = 0;
int periods = 0;
char letter = 0;
int bits = 0;
const double plen = 0.0078;
for (int i = 0; i < 2*count; i += 2) {
if (t >= plen * (double)periods && t < plen * ((double)periods + 1.0)) {
if (data[i] > umax) umax = data[i];
} else {
if (umax < 1) letter *= 2;
else letter = letter*2 + 1;
bits++;
if (bits % 8 == 0) {
printf("%c", letter);
bits = 0;
letter = 0;
}
umax = 0;
periods++;
}
PLOT(p, t, (data[i]));
t += 1.0/count;
}
if (umax < 1) letter *= 2;
else letter = letter*2 + 1;
printf("%c\n", letter);
END_PLOT(p);
}
