int
main (void)
{
int i; double data[2*128];
for (i = 0; i < 128; i++)
{
REAL(data,i) = 0.0; IMAG(data,i) = 0.0;
}
REAL(data,0) = 1.0;
for (i = 1; i <= 10; i++)
{
REAL(data,i) = REAL(data,128-i) = 1.0;
}
for (i = 0; i < 128; i++)
{
printf ("%d %e %e\n", i,
REAL(data,i), IMAG(data,i));
}
printf ("\n");
gsl_fft_complex_radix2_forward (data, 1, 128);
for (i = 0; i < 128; i++)
{
printf ("%d %e %e\n", i,
REAL(data,i)/sqrt(128),
IMAG(data,i)/sqrt(128));
}
return 0;
}
int main(void)
{
int i; double data[2*N];
double freq;
FILE * indat = fopen("dat","r");
if (readfile(indat, data) != 0) {printf("Bad input file!\n"); return -1;}
// printf("file read...\n");
#if 0
for(i=0; i<N; i++){
printf("%d %e %e\n",i,REAL(data,i),IMAG(data,i));
}
#endif
gsl_fft_complex_radix2_forward(data,1,N);
for(i=0;i<N; i++){
if(i < N/2){
freq = ((double) i)/N ;//* 2.0 * M_PI;
}else{
freq = ((double)(i-N))/N;// * 2.0 * M_PI;
}
printf("%g %e %e\n",freq,
REAL(data,i)/sqrt(N*N),
IMAG(data,i)/sqrt(N*N));
}
return 0;
}
/* calculates the fast Fourier transform of a complex packed array, and stores
* it into fft_results. The length of the array is 2*N, and the storage
* convention is that the real and imaginary parts of the complex number are
* stored in consecutive locations */
int complex_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_forward (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_forward (fft_results, 1, N, wavetable, workspace);
/* free memory */
gsl_fft_complex_wavetable_free (wavetable);
gsl_fft_complex_workspace_free (workspace);
}
return retcode;
}
int
main (void)
{
// printf("EPS: %e\n", EPS);
size_t size = pow(2, SIZE);
size_t i; double data[2*size];
for (i = 0; i < size; i++)
{
REAL(data,i) = 0.0; IMAG(data,i) = 0.0;
}
REAL(data,0) = 1.0;
for (i = 1; i <= 10; i++)
{
REAL(data,i) = REAL(data,size - i) = 1.0;
}
/* for (i = 0; i < size; i++)
{
printf ("%d %e %e\n", i,
REAL(data,i), IMAG(data,i));
}
printf ("\n");
*/
# pragma adapt begin
gsl_fft_complex_radix2_forward (data, 1, size);
double norm = 0;
for (i = 0; i < size; i++)
{
// printf ("%d %e %e\n", i,
// REAL(data,i)/sqrt(128),
// IMAG(data,i)/sqrt(128));
norm += square(REAL(data, i)/sqrt(size)) + square(IMAG(data,i)/sqrt(size));
}
norm = sqrt(norm);
# pragma adapt output norm EPS
# pragma adapt end
// printf("norm: %.16f\n", norm);
double diff = (ANS-norm);
double error = ABS(diff);
if ((double)error < (double)EPS) {
printf("fft - SUCCESSFUL!\n");
}
else {
printf("fft - FAILED!\n");
}
return 0;
}
/*
* The spectrum of a simple AM wave
*/
void am_wave(void) {
plot_t p;
p.outfile = "output3.png";
p.title = "AM wave";
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*N, sizeof(double));
BEGIN_SCATTER(p, "u(t)");
double t = 0;
for (int i = 0; i < 2*N; i += 2) {
data[i] = u(t);
PLOT(p, t, data[i]);
t += dt;
}
END_PLOT(p);
p.outfile = "output4.png";
p.title = "FFT of AM wave";
p.xlabel = "f [Hz]";
p.ylabel = "S(f) = |U(f)|^2 [m^2]";
p.xmin = 0;
p.xmax = 40;
init_gnuplot(&p);
gsl_fft_complex_radix2_forward(data, 1, N);
BEGIN_PLOT(p, "S(f)");
double f = 0;
for (int i = 0; i < N; i += 2) {
PLOT(p, f, (data[i]*data[i] + data[i+1]*data[i+1])/(N*N));
f += 1.0;
}
END_PLOT(p);
free(data);
}
int
main (void)
{
int i;
for (i = 0; i < PULSE_SAMPLE_LEN; i++)
{
REAL(data,i) = 0.0; IMAG(data,i) = 0.0;
}
REAL(data,0) = 1.0;
for (i = 1; i <= PULSE_ACTUAL_LEN; i++)
{
REAL(data,i) = REAL(data,PULSE_SAMPLE_LEN-i) = 1.0;
}
#if PRINT_RES
for (i = 0; i < PULSE_SAMPLE_LEN; i++)
{
printf ("%d %e %e\n", i,
REAL(data,i), IMAG(data,i));
}
printf ("\n\n");
#endif
gsl_fft_complex_radix2_forward (data, 1, PULSE_SAMPLE_LEN);
#if PRINT_RES
for (i = 0; i < PULSE_SAMPLE_LEN; i++)
{
printf ("%d %e %e\n", i,
REAL(data,i)/sqrt(PULSE_SAMPLE_LEN),
IMAG(data,i)/sqrt(PULSE_SAMPLE_LEN));
}
#endif
return 0;
}
/*
* The Fourier transform of a Gaussian
*/
void gaussian(void) {
plot_t p;
p.outfile = "output1.png";
p.title = "Gaussian";
p.xlabel = "t [s]";
p.ylabel = "x(t) [m]";
p.xmin = -N/2*dt;
p.xmax = N/2*dt;
init_gnuplot(&p);
gsl_complex_packed_array data = calloc(2*N, sizeof(double));
BEGIN_SCATTER(p, "x(t)");
double t = -N/2 * dt;
for (int i = 0; i < 2*N; i += 2) {
data[i] = x(t);
PLOT(p, t, data[i]);
t += dt;
}
END_PLOT(p);
gsl_fft_complex_radix2_forward(data, 1, N);
p.outfile = "output2.png";
p.title = "FFT of a Gauissian";
p.xlabel = "f [Hz]";
p.ylabel = "X(f) [m]";
p.xmin = -512;
p.xmax = 512;
init_gnuplot(&p);
fprintf(p.fp, "plot '-' title 'Real',"
"'-' title 'Imag',"
"'-' with lines title 'Analytical'\n");
// Real part
double f = -1.0/(2.0*dt);
for (int i = N; i < 2*N; i += 2) {
PLOT(p, f, creal(shift(f))*(data[i]/(double) N));
f += 1.0;
}
for (int i = 0; i < N; i += 2) {
PLOT(p, f, creal(shift(f))*(data[i]/(double) N));
f += 1.0;
}
// Imag. part
NEW_PLOT(p);
f = -1.0/(2.0*dt);
for (int i = N+1; i <= 2*N; i += 2) {
PLOT(p, f, cimag(shift(f))*data[i]/(double) N);
f += 1.0;
}
for (int i = 1; i <= N; i += 2) {
PLOT(p, f, cimag(shift(f))*data[i]/(double) N);
f += 1.0;
}
// Analytical
NEW_PLOT(p);
f = -1.0/(2.0*dt);
for (int i = 1; i <= 2*N; i += 2) {
PLOT(p, f, X(f));
f += 1.0;
}
END_PLOT(p);
free(data);
}
/*
* 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);
}
