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// Compute equivalent noise bandwidth of window functions
#include <stdio.h>
#include <string.h>
#include "liquid.h"
#define OUTPUT_FILENAME "window_enbw_example.m"
int main() {
// options
unsigned int m = 20; // window semi-length
float beta = 10.0f; // Kaiser beta factor
unsigned int nfft = 1200; // transform size
float th = 0.95f; // threshold for spectral energy
// derived values
unsigned int i;
unsigned int wlen = 2*m+1; // window length
float w[wlen];
float w2 = 0.0f;
for (i=0; i<wlen; i++) {
w[i] = liquid_kaiser(i,wlen,beta);
w2 += w[i]*w[i]; // window energy
}
// compute transform, ensuring symmetry
float complex buf_time[nfft];
float complex buf_freq[nfft];
memset(buf_time, 0x00, nfft*sizeof(float complex));
buf_time[0] = w[m];
for (i=1; i<=m; i++) {
buf_time[i] = w[m+i];
buf_time[nfft-i] = w[m-i];
}
fft_run(nfft, buf_time, buf_freq, LIQUID_FFT_FORWARD, 0);
// integrate spectral energy starting from DC and moving evenly outward
// in both directions
float energy_ratio[nfft];
float e2_sum = 0.0f;
unsigned int i_threshold = 0;
for (i=0; i<nfft; i++) {
unsigned int r = i % 2;
unsigned int L = (i-r)/2;
int k = (i==0) ? 0 : (r==0 ? -(int)(L+r) : (int)(L+r));
unsigned int j = (k+nfft) % nfft;
float e2 = cabsf(buf_freq[j])*cabsf(buf_freq[j]);
// normalize to transform size
energy_ratio[i] = e2_sum / (nfft * w2);
if (i_threshold == 0 && energy_ratio[i] > th)
i_threshold = i;
e2_sum += e2;
}
float enbw = (float)i_threshold / (float)nfft;
printf("equivalent noise bandwidth: %.6f Fs\n", enbw);
FILE*fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s: auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n\n");
fprintf(fid,"m=%u;\n",m);
fprintf(fid,"enbw=%f;\n",enbw);
fprintf(fid,"th=%f;\n",th);
fprintf(fid,"nfft=%u;\n",nfft);
for (i=0; i<wlen; i++)
fprintf(fid,"w(%4u) = %12.4e;\n", i+1, w[i]);
for (i=0; i<nfft; i++) {
fprintf(fid,"W(%4u) = %12.4e;\n", i+1, crealf(buf_freq[i]));
fprintf(fid,"R(%4u) = %12.4e;\n", i+1, energy_ratio[i]);
}
fprintf(fid,"f=[0:(nfft-1)]/nfft-0.5;\n");
fprintf(fid,"t=-m:m;\n");
fprintf(fid,"figure('position',[50 50 600 1200]);\n");
fprintf(fid,"subplot(3,1,1);\n");
fprintf(fid," plot(t,w,'Color',[0 0.25 0.5],'LineWidth',2);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('Sample Index');\n");
fprintf(fid," ylabel('Window Value');\n");
fprintf(fid," axis([-m m -0.1 1.1]);\n");
fprintf(fid," title(sprintf('Equivalent Noise Bandwidth: %%.6f Fs (%%.1f %%%% Energy)', enbw, th*100));\n");
fprintf(fid,"subplot(3,1,2);\n");
fprintf(fid," plot(f,20*log10(abs(fftshift(W/sum(w)))),'Color',[0 0.5 0.25],'LineWidth',2);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('normalized frequency');\n");
fprintf(fid," ylabel('PSD [dB]');\n");
fprintf(fid," axis([-0.5 0.5 -140 20]);\n");
fprintf(fid,"subplot(3,1,3);\n");
fprintf(fid," plot([0:(nfft-1)]/nfft, R, 'Color',[0.5 0.2 0], 'LineWidth',2,...\n");
fprintf(fid," enbw, th, 'ok', 'MarkerSize', 3, 'LineWidth',2);\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('Normalized Bandwidth');\n");
fprintf(fid," ylabel('Accumulated Energy Ratio');\n");
fprintf(fid," axis([0 0.1 -0.1 1.1]);\n");
fclose(fid);
printf("results written to %s\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
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