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//
// firhilb_example.c
//
// Hilbert transform example. This example demonstrates the
// functionality of firhilbf (finite impulse response Hilbert transform)
// which converts a complex time series into a real one and then back.
//
// SEE ALSO: firhilb_interp_example.c
// firhilb_example.c
//
#include <stdio.h>
#include <complex.h>
#include <math.h>
#include "liquid.h"
#define OUTPUT_FILENAME "firhilb_example.m"
int main() {
unsigned int m = 7; // Hilbert filter semi-length
float As = 60.0f; // stop-band attenuation [dB]
float fc = 0.123456; // signal center frequency
unsigned int num_input_samples=128; // number of samples
// derived values
unsigned int h_len = 4*m+1; // filter length
unsigned int num_total_samples = num_input_samples + h_len;
// create Hilbert transform object
firhilbf qi = firhilbf_create(m,As); // interpolator
firhilbf qd = firhilbf_create(m,As); // decimator
firhilbf_print(qi);
// data arrays
float complex x[ num_total_samples]; // complex input
float y[2*num_total_samples]; // real output
float complex z[ num_total_samples]; // complex output
// initialize input array
unsigned int i;
for (i=0; i<num_total_samples; i++) {
x[i] = cexpf(_Complex_I*2*M_PI*fc*i);
x[i] *= (i < num_input_samples) ? 1.855f*hamming(i,num_input_samples) : 0.0f;
}
// execute interpolator (complex to real conversion)
firhilbf_interp_execute_block(qi, x, num_total_samples, y);
// execute decimator (real to complex conversion)
firhilbf_decim_execute_block(qd, y, num_total_samples, z);
// destroy Hilbert transform object
firhilbf_destroy(qi);
firhilbf_destroy(qd);
//
// export results to file
//
FILE*fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"h_len=%u;\n", 4*m+1);
fprintf(fid,"num_input_samples=%u;\n", num_input_samples);
fprintf(fid,"num_total_samples=%u;\n", num_total_samples);
fprintf(fid,"tx = 0:(num_total_samples-1);\n");
fprintf(fid,"ty = [0:(2*num_total_samples-1)]/2;\n");
fprintf(fid,"tz = tx;\n");
for (i=0; i<num_total_samples; i++) {
// print results
fprintf(fid,"x(%3u) = %12.4e + %12.4ej;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%3u) = %12.4e;\n", 2*i+1, y[2*i+0]);
fprintf(fid,"y(%3u) = %12.4e;\n", 2*i+2, y[2*i+1]);
fprintf(fid,"z(%3u) = %12.4e + %12.4ej;\n", i+1, crealf(z[i]), cimagf(z[i]));
}
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(3,1,1);\n");
fprintf(fid," plot(tx,real(x),'Color',[0.00 0.25 0.50],'LineWidth',1.3,...\n");
fprintf(fid," tx,imag(x),'Color',[0.00 0.50 0.25],'LineWidth',1.3);\n");
fprintf(fid," legend('real','imag','location','northeast');\n");
fprintf(fid," ylabel('transformed/complex');\n");
fprintf(fid," axis([0 num_total_samples -2 2]);\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,1,2);\n");
fprintf(fid," plot(ty,y,'Color',[0.00 0.25 0.50],'LineWidth',1.3);\n");
fprintf(fid," ylabel('original/real');\n");
fprintf(fid," axis([0 num_total_samples -2 2]);\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,1,3);\n");
fprintf(fid," plot(tz,real(z),'Color',[0.00 0.25 0.50],'LineWidth',1.3,...\n");
fprintf(fid," tz,imag(z),'Color',[0.00 0.50 0.25],'LineWidth',1.3);\n");
fprintf(fid," legend('real','imag','location','northeast');\n");
fprintf(fid," ylabel('transformed/complex');\n");
fprintf(fid," axis([0 num_total_samples -2 2]);\n");
fprintf(fid," grid on;\n");
// plot results
fprintf(fid,"nfft=4096;\n");
fprintf(fid,"%% compute normalized windowing functions\n");
fprintf(fid,"X=20*log10(abs(fftshift(fft(x/num_input_samples,nfft))));\n");
fprintf(fid,"Y=20*log10(abs(fftshift(fft(y/num_input_samples,nfft))));\n");
fprintf(fid,"Z=20*log10(abs(fftshift(fft(z/num_input_samples,nfft))));\n");
fprintf(fid,"f =[0:(nfft-1)]/nfft-0.5;\n");
fprintf(fid,"figure; plot(f, X,'LineWidth',1,'Color',[0.50 0.50 0.50],...\n");
fprintf(fid," f*2,Y,'LineWidth',2,'Color',[0.00 0.50 0.25],...\n");
fprintf(fid," f, Z,'LineWidth',1,'Color',[0.00 0.25 0.50]);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-1.0 1.0 -80 20]);\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD [dB]');\n");
fprintf(fid,"legend('original/cplx','transformed/real','regenerated/cplx','location','northeast');");
fclose(fid);
printf("results written to %s\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
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