// Compute relative out-of-band energy // // _h : filter coefficients [size: _h_len x 1] // _h_len : filter length // _fc : analysis cut-off frequency // _nfft : fft size float liquid_filter_energy(float * _h, unsigned int _h_len, float _fc, unsigned int _nfft) { // validate input if (_fc < 0.0f || _fc > 0.5f) { fprintf(stderr,"error: liquid_filter_energy(), cut-off frequency must be in [0,0.5]\n"); exit(1); } else if (_h_len == 0) { fprintf(stderr,"error: liquid_filter_energy(), filter length must be greater than zero\n"); exit(1); } else if (_nfft == 0) { fprintf(stderr,"error: liquid_filter_energy(), fft size must be greater than zero\n"); exit(1); } // allocate memory for complex phasor float complex expjwt[_h_len]; // initialize accumulators float e_total = 0.0f; // total energy float e_stopband = 0.0f; // stop-band energy // create dotprod object dotprod_crcf dp = dotprod_crcf_create(_h,_h_len); unsigned int i; unsigned int k; for (i=0; i<_nfft; i++) { float f = 0.5f * (float)i / (float)(_nfft); // initialize complex phasor for (k=0; k<_h_len; k++) expjwt[k] = cexpf(_Complex_I*2*M_PI*f*k); // compute vector dot product float complex v; dotprod_crcf_execute(dp, expjwt, &v); // accumulate output float e2 = crealf( v*conjf(v) ); e_total += e2; e_stopband += (f >= _fc) ? e2 : 0.0f; } // destroy dotprod object dotprod_crcf_destroy(dp); // return energy ratio return e_stopband / e_total; }
// Helper function to keep code base small void dotprod_crcf_bench(struct rusage *_start, struct rusage *_finish, unsigned long int *_num_iterations, unsigned int _n) { // normalize number of iterations *_num_iterations *= 100; *_num_iterations /= _n; if (*_num_iterations < 1) *_num_iterations = 1; float complex x[_n]; float h[_n]; float complex y[8]; unsigned int i; for (i=0; i<_n; i++) { x[i] = randnf() + _Complex_I*randnf(); h[i] = randnf(); } // create dotprod structure; dotprod_crcf dp = dotprod_crcf_create(h,_n); // start trials getrusage(RUSAGE_SELF, _start); for (i=0; i<(*_num_iterations); i++) { dotprod_crcf_execute(dp, x, &y[0]); dotprod_crcf_execute(dp, x, &y[1]); dotprod_crcf_execute(dp, x, &y[2]); dotprod_crcf_execute(dp, x, &y[3]); dotprod_crcf_execute(dp, x, &y[4]); dotprod_crcf_execute(dp, x, &y[5]); dotprod_crcf_execute(dp, x, &y[6]); dotprod_crcf_execute(dp, x, &y[7]); } getrusage(RUSAGE_SELF, _finish); *_num_iterations *= 8; // clean up objects dotprod_crcf_destroy(dp); }
int main() { // options unsigned int num_channels=4; // number of channels unsigned int m=5; // filter delay unsigned int num_symbols=12; // number of symbols // derived values unsigned int num_samples = num_channels * num_symbols; unsigned int i; unsigned int j; // generate filter // NOTE : these coefficients can be random; the purpose of this // exercise is to demonstrate mathematical equivalence unsigned int h_len = 2*m*num_channels; float h[h_len]; for (i=0; i<h_len; i++) h[i] = randnf(); //for (i=0; i<h_len; i++) h[i] = 0.1f*i; //for (i=0; i<h_len; i++) h[i] = (i<=m) ? 1.0f : 0.0f; //for (i=0; i<h_len; i++) h[i] = 1.0f; // create filterbank manually dotprod_crcf dp[num_channels]; // vector dot products windowcf w[num_channels]; // window buffers #if DEBUG // print coefficients printf("h_prototype:\n"); for (i=0; i<h_len; i++) printf(" h[%3u] = %12.8f\n", i, h[i]); #endif // create objects unsigned int h_sub_len = 2*m; float h_sub[h_sub_len]; for (i=0; i<num_channels; i++) { // sub-sample prototype filter, loading coefficients in // reverse order #if 0 for (j=0; j<h_sub_len; j++) h_sub[j] = h[j*num_channels+i]; #else for (j=0; j<h_sub_len; j++) h_sub[h_sub_len-j-1] = h[j*num_channels+i]; #endif // create window buffer and dotprod objects dp[i] = dotprod_crcf_create(h_sub, h_sub_len); w[i] = windowcf_create(h_sub_len); #if DEBUG printf("h_sub[%u] : \n", i); for (j=0; j<h_sub_len; j++) printf(" h[%3u] = %12.8f\n", j, h_sub[j]); #endif } // generate DFT object float complex x[num_channels]; // time-domain buffer float complex X[num_channels]; // freq-domain buffer #if 0 fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_BACKWARD, 0); #else fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_FORWARD, 0); #endif // generate filter object firfilt_crcf f = firfilt_crcf_create(h, h_len); float complex y[num_samples]; // time-domain input float complex Y0[num_symbols][num_channels]; // channelized output float complex Y1[num_symbols][num_channels]; // channelized output // generate input sequence (complex noise) for (i=0; i<num_samples; i++) y[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI); // // run analysis filter bank // #if 0 unsigned int filter_index = 0; #else unsigned int filter_index = num_channels-1; #endif float complex y_hat; // input sample float complex * r; // read pointer for (i=0; i<num_symbols; i++) { // load buffers for (j=0; j<num_channels; j++) { // grab sample y_hat = y[i*num_channels + j]; // push sample into buffer at filter index windowcf_push(w[filter_index], y_hat); // decrement filter index filter_index = (filter_index + num_channels - 1) % num_channels; //filter_index = (filter_index + 1) % num_channels; } // execute filter outputs, reversing order of output (not // sure why this is necessary) for (j=0; j<num_channels; j++) { windowcf_read(w[j], &r); dotprod_crcf_execute(dp[j], r, &X[num_channels-j-1]); } // execute DFT, store result in buffer 'x' fft_execute(fft); // move to output array for (j=0; j<num_channels; j++) Y0[i][j] = x[j]; } // // run traditional down-converter (inefficient) // float dphi; // carrier frequency unsigned int n=0; for (i=0; i<num_channels; i++) { // reset filter firfilt_crcf_reset(f); // set center frequency dphi = 2.0f * M_PI * (float)i / (float)num_channels; // reset symbol counter n=0; for (j=0; j<num_samples; j++) { // push down-converted sample into filter firfilt_crcf_push(f, y[j]*cexpf(-_Complex_I*j*dphi)); // compute output at the appropriate sample time assert(n<num_symbols); if ( ((j+1)%num_channels)==0 ) { firfilt_crcf_execute(f, &Y1[n][i]); n++; } } assert(n==num_symbols); } // destroy objects for (i=0; i<num_channels; i++) { dotprod_crcf_destroy(dp[i]); windowcf_destroy(w[i]); } fft_destroy_plan(fft); firfilt_crcf_destroy(f); // print filterbank channelizer printf("\n"); printf("filterbank channelizer:\n"); for (i=0; i<num_symbols; i++) { printf("%3u: ", i); for (j=0; j<num_channels; j++) { printf(" %8.5f+j%8.5f, ", crealf(Y0[i][j]), cimagf(Y0[i][j])); } printf("\n"); } // print traditional channelizer printf("\n"); printf("traditional channelizer:\n"); for (i=0; i<num_symbols; i++) { printf("%3u: ", i); for (j=0; j<num_channels; j++) { printf(" %8.5f+j%8.5f, ", crealf(Y1[i][j]), cimagf(Y1[i][j])); } printf("\n"); } // // compare results // float mse[num_channels]; float complex d; for (i=0; i<num_channels; i++) { mse[i] = 0.0f; for (j=0; j<num_symbols; j++) { d = Y0[j][i] - Y1[j][i]; mse[i] += crealf(d*conjf(d)); } mse[i] /= num_symbols; } printf("\n"); printf("rmse: "); for (i=0; i<num_channels; i++) printf("%12.4e ", sqrt(mse[i])); printf("\n"); printf("done.\n"); return 0; }
int main(int argc, char*argv[]) { // options unsigned int num_channels=6; // number of channels (must be even) unsigned int m=4; // filter delay unsigned int num_symbols=4*m; // number of symbols // validate input if (num_channels%2) { fprintf(stderr,"error: %s, number of channels must be even\n", argv[0]); exit(1); } // derived values unsigned int num_samples = num_channels * num_symbols; unsigned int i; unsigned int j; // generate filter // NOTE : these coefficients can be random; the purpose of this // exercise is to demonstrate mathematical equivalence #if 0 unsigned int h_len = 2*m*num_channels; float h[h_len]; for (i=0; i<h_len; i++) h[i] = randnf(); #else unsigned int h_len = 2*m*num_channels+1; float h[h_len]; // NOTE: 81.29528 dB > beta = 8.00000 (6 channels, m=4) liquid_firdes_kaiser(h_len, 1.0f/(float)num_channels, 81.29528f, 0.0f, h); #endif // normalize float hsum = 0.0f; for (i=0; i<h_len; i++) hsum += h[i]; for (i=0; i<h_len; i++) h[i] = h[i] * num_channels / hsum; // sub-sampled filters for M=6 channels, m=4, beta=8.0 // -3.2069e-19 -6.7542e-04 -1.3201e-03 2.2878e-18 3.7613e-03 5.8033e-03 // -7.2899e-18 -1.2305e-02 -1.7147e-02 1.6510e-17 3.1187e-02 4.0974e-02 // -3.0032e-17 -6.8026e-02 -8.6399e-02 4.6273e-17 1.3732e-01 1.7307e-01 // -6.2097e-17 -2.8265e-01 -3.7403e-01 7.3699e-17 8.0663e-01 1.6438e+00 // 2.0001e+00 1.6438e+00 8.0663e-01 7.3699e-17 -3.7403e-01 -2.8265e-01 // -6.2097e-17 1.7307e-01 1.3732e-01 4.6273e-17 -8.6399e-02 -6.8026e-02 // -3.0032e-17 4.0974e-02 3.1187e-02 1.6510e-17 -1.7147e-02 -1.2305e-02 // -7.2899e-18 5.8033e-03 3.7613e-03 2.2878e-18 -1.3201e-03 -6.7542e-04 // create filterbank manually dotprod_crcf dp[num_channels]; // vector dot products windowcf w[num_channels]; // window buffers #if DEBUG // print coefficients printf("h_prototype:\n"); for (i=0; i<h_len; i++) printf(" h[%3u] = %12.8f\n", i, h[i]); #endif // create objects unsigned int h_sub_len = 2*m; float h_sub[h_sub_len]; for (i=0; i<num_channels; i++) { // sub-sample prototype filter #if 0 for (j=0; j<h_sub_len; j++) h_sub[j] = h[j*num_channels+i]; #else // load coefficients in reverse order for (j=0; j<h_sub_len; j++) h_sub[h_sub_len-j-1] = h[j*num_channels+i]; #endif // create window buffer and dotprod objects dp[i] = dotprod_crcf_create(h_sub, h_sub_len); w[i] = windowcf_create(h_sub_len); #if DEBUG printf("h_sub[%u] : \n", i); for (j=0; j<h_sub_len; j++) printf(" h[%3u] = %12.8f\n", j, h_sub[j]); #endif } // generate DFT object float complex x[num_channels]; // time-domain buffer float complex X[num_channels]; // freq-domain buffer #if 1 fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_BACKWARD, 0); #else fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_FORWARD, 0); #endif float complex y[num_samples]; // time-domain input float complex Y0[2*num_symbols][num_channels]; // channelizer output float complex Y1[2*num_symbols][num_channels]; // conventional output // generate input sequence for (i=0; i<num_samples; i++) { //y[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI); y[i] = (i==0) ? 1.0f : 0.0f; y[i] = cexpf(_Complex_I*sqrtf(2.0f)*i*i); printf("y[%3u] = %12.8f + %12.8fj\n", i, crealf(y[i]), cimagf(y[i])); } // // run analysis filter bank // #if 0 unsigned int filter_index = 0; #else unsigned int filter_index = num_channels/2-1; #endif float complex y_hat; // input sample float complex * r; // buffer read pointer int toggle = 0; // flag indicating buffer/filter alignment // for (i=0; i<2*num_symbols; i++) { // load buffers in blocks of num_channels/2 for (j=0; j<num_channels/2; j++) { // grab sample y_hat = y[i*num_channels/2 + j]; // push sample into buffer at filter index windowcf_push(w[filter_index], y_hat); // decrement filter index filter_index = (filter_index + num_channels - 1) % num_channels; //filter_index = (filter_index + 1) % num_channels; } // execute filter outputs // reversing order of output (not sure why this is necessary) unsigned int offset = toggle ? num_channels/2 : 0; toggle = 1-toggle; for (j=0; j<num_channels; j++) { unsigned int buffer_index = (offset+j)%num_channels; unsigned int dotprod_index = j; windowcf_read(w[buffer_index], &r); //dotprod_crcf_execute(dp[dotprod_index], r, &X[num_channels-j-1]); dotprod_crcf_execute(dp[dotprod_index], r, &X[buffer_index]); } printf("***** i = %u\n", i); for (j=0; j<num_channels; j++) printf(" v2[%4u] = %12.8f + %12.8fj\n", j, crealf(X[j]), cimagf(X[j])); // execute DFT, store result in buffer 'x' fft_execute(fft); // scale fft output for (j=0; j<num_channels; j++) x[j] *= 1.0f / (num_channels); // move to output array for (j=0; j<num_channels; j++) Y0[i][j] = x[j]; } // destroy objects for (i=0; i<num_channels; i++) { dotprod_crcf_destroy(dp[i]); windowcf_destroy(w[i]); } fft_destroy_plan(fft); // // run traditional down-converter (inefficient) // // generate filter object firfilt_crcf f = firfilt_crcf_create(h, h_len); float dphi; // carrier frequency unsigned int n=0; for (i=0; i<num_channels; i++) { // reset filter firfilt_crcf_clear(f); // set center frequency dphi = 2.0f * M_PI * (float)i / (float)num_channels; // reset symbol counter n=0; for (j=0; j<num_samples; j++) { // push down-converted sample into filter firfilt_crcf_push(f, y[j]*cexpf(-_Complex_I*j*dphi)); // compute output at the appropriate sample time assert(n<2*num_symbols); if ( ((j+1)%(num_channels/2))==0 ) { firfilt_crcf_execute(f, &Y1[n][i]); n++; } } assert(n==2*num_symbols); } firfilt_crcf_destroy(f); // print filterbank channelizer printf("\n"); printf("filterbank channelizer:\n"); for (i=0; i<2*num_symbols; i++) { printf("%2u:", i); for (j=0; j<num_channels; j++) { printf("%6.3f+%6.3fj, ", crealf(Y0[i][j]), cimagf(Y0[i][j])); } printf("\n"); } #if 0 // print traditional channelizer printf("\n"); printf("traditional channelizer:\n"); for (i=0; i<2*num_symbols; i++) { printf("%2u:", i); for (j=0; j<num_channels; j++) { printf("%6.3f+%6.3fj, ", crealf(Y1[i][j]), cimagf(Y1[i][j])); } printf("\n"); } // // compare results // float mse[num_channels]; float complex d; for (i=0; i<num_channels; i++) { mse[i] = 0.0f; for (j=0; j<2*num_symbols; j++) { d = Y0[j][i] - Y1[j][i]; mse[i] += crealf(d*conjf(d)); } mse[i] /= num_symbols; } printf("\n"); printf(" e:"); for (i=0; i<num_channels; i++) printf("%12.4e ", sqrt(mse[i])); printf("\n"); #endif printf("done.\n"); return 0; }