Example #1
0
// autotest helper function
//  _b      :   filter coefficients (numerator)
//  _a      :   filter coefficients (denominator)
//  _h_len  :   filter coefficients length
//  _x      :   input array
//  _x_len  :   input array length
//  _y      :   output array
//  _y_len  :   output array length
void iirfilt_crcf_test(float *         _b,
                       float *         _a,
                       unsigned int    _h_len,
                       float complex * _x,
                       unsigned int    _x_len,
                       float complex * _y,
                       unsigned int    _y_len)
{
    float tol = 0.001f;

    // load filter coefficients externally
    iirfilt_crcf q = iirfilt_crcf_create(_b, _h_len, _a, _h_len);

    // allocate memory for output
    float complex y_test[_y_len];

    unsigned int i;
    // compute output
    for (i=0; i<_x_len; i++) {
        iirfilt_crcf_execute(q, _x[i], &y_test[i]);
        
        CONTEND_DELTA( crealf(y_test[i]), crealf(_y[i]), tol );
        CONTEND_DELTA( cimagf(y_test[i]), cimagf(_y[i]), tol );
    }
    
    // destroy filter object
    iirfilt_crcf_destroy(q);
}
Example #2
0
// execute frame synchronizer
//  _q      :   frame synchronizer object
//  _x      :   input sample array [size: _n x 1]
//  _n      :   number of input samples
void gmskframesync_execute(gmskframesync   _q,
                           float complex * _x,
                           unsigned int    _n)
{
    // push through synchronizer
    unsigned int i;
    for (i=0; i<_n; i++) {
        float complex xf;   // input sample
#if GMSKFRAMESYNC_PREFILTER
        iirfilt_crcf_execute(_q->prefilter, _x[i], &xf);
#else
        xf = _x[i];
#endif

#if DEBUG_GMSKFRAMESYNC
        if (_q->debug_enabled)
            windowcf_push(_q->debug_x, xf);
#endif

        switch (_q->state) {
        case STATE_DETECTFRAME:
            // look for p/n sequence
            gmskframesync_execute_detectframe(_q, xf);
            break;

        case STATE_RXPREAMBLE:
            // receive p/n sequence symbols
            gmskframesync_execute_rxpreamble(_q, xf);
            break;

        case STATE_RXHEADER:
            // receive header
            gmskframesync_execute_rxheader(_q, xf);
            break;

        case STATE_RXPAYLOAD:
            // receive payload
            gmskframesync_execute_rxpayload(_q, xf);
            break;
        }
    }
}
Example #3
0
int main() {
    // options
    unsigned int order=4;   // filter order

    unsigned int n = order+1;
    float b[n], a[n];

    // ... initialize filter coefficients ...

    // create filter object
    iirfilt_crcf q = iirfilt_crcf_create(b,n,a,n);

    float complex x;    // input sample
    float complex y;    // output sample
    
    // execute filter (repeat as necessary)
    iirfilt_crcf_execute(q,x,&y);

    // destroy filter object
    iirfilt_crcf_destroy(q);
}
Example #4
0
int main() {
    // options
    unsigned int order=4;   // filter order
    float fc=0.1f;          // cutoff frequency
    float f0=0.25f;         // center frequency (bandpass|bandstop)
    float Ap=1.0f;          // pass-band ripple [dB]
    float As=40.0f;         // stop-band attenuation [dB]
    liquid_iirdes_filtertype ftype  = LIQUID_IIRDES_ELLIP;
    liquid_iirdes_bandtype   btype  = LIQUID_IIRDES_BANDPASS;
    liquid_iirdes_format     format = LIQUID_IIRDES_SOS;

    // CREATE filter object (and print to stdout)
    iirfilt_crcf myfilter;
    myfilter = iirfilt_crcf_create_prototype(ftype,
                                             btype,
                                             format,
                                             order,
                                             fc, f0,
                                             Ap, As);
    iirfilt_crcf_print(myfilter);

    // allocate memory for data arrays
    unsigned int n=128; // number of samples
    float complex x[n]; // input samples array
    float complex y[n]; // output samples array

    // run filter
    unsigned int i;
    for (i=0; i<n; i++) {
        // initialize input
        x[i] = randnf() + _Complex_I*randnf();

        // EXECUTE filter (repeat as many times as desired)
        iirfilt_crcf_execute(myfilter, x[i], &y[i]);
    }

    // DESTROY filter object
    iirfilt_crcf_destroy(myfilter);
}
Example #5
0
void do_track(){
    if (local_track_freq != shm_settings.track_frequency_target) {
       if (ff.sosMap.count(shm_settings.track_frequency_target)) { //frequency key exists
            if (track_filterA != NULL)
                iirfilt_crcf_destroy(track_filterA);
            if (track_filterB != NULL)
                iirfilt_crcf_destroy(track_filterB);
            if (track_filterC != NULL)
                iirfilt_crcf_destroy(track_filterC);

            float *b = &((ff.sosMap[shm_settings.track_frequency_target]->b)[0]);
            float *a = &((ff.sosMap[shm_settings.track_frequency_target]->a)[0]);
            track_filterA = iirfilt_crcf_create_sos(b,a,NUMBER_OF_SECTIONS);
            track_filterB = iirfilt_crcf_create_sos(b,a,NUMBER_OF_SECTIONS);
            track_filterC = iirfilt_crcf_create_sos(b,a,NUMBER_OF_SECTIONS);

            shm_results_track.track_state = 0;

            local_track_freq = shm_settings.track_frequency_target;
            float normalized_frequency = (float) shm_settings.track_frequency_target / (float) SAMPLING_FREQUENCY;
            nco_crcf_set_frequency(nco,2*M_PI*normalized_frequency);
        }
        else { //frequency key does not exist. Trigger error state
            shm_results_track.track_state = -1;
            std::cerr << shm_settings.track_frequency_target << " WARN TRACK FREQ NOT IN SOS TABLE" << std::endl;
        }

        shm_setg(hydrophones_results_track, shm_results_track);
    }

    std::complex<float> *chA_ptr, *chA_filtered_ptr;
    std::complex<float> *chB_ptr, *chB_filtered_ptr;
    std::complex<float> *chC_ptr, *chC_filtered_ptr;

    float *mag_ptr;
    windowcf_read(wchA,&chA_ptr);
    windowcf_read(wchB,&chB_ptr);
    windowcf_read(wchC,&chC_ptr);

    std::complex<float> filtOutA, filtOutB, filtOutC;

    for (int i = 0; i < SAMPLING_DEPTH; i++) {
        iirfilt_crcf_execute(track_filterA,chA_ptr[i],&filtOutA);
        iirfilt_crcf_execute(track_filterB,chB_ptr[i],&filtOutB);
        iirfilt_crcf_execute(track_filterC,chC_ptr[i],&filtOutC);
        
        windowcf_read(wchA_filtered,&chA_filtered_ptr);
        windowcf_read(wchB_filtered,&chB_filtered_ptr);
        windowcf_read(wchC_filtered,&chC_filtered_ptr);

        windowcf_push(wchA_filtered,filtOutA);
        windowcf_push(wchB_filtered,filtOutB);
        windowcf_push(wchC_filtered,filtOutC);

        float b_sqrd = std::pow(std::real(filtOutB),2);

        pwr_sum += b_sqrd;
        windowf_read(wmag_buffer,&mag_ptr);
        pwr_sum -= mag_ptr[0];
        windowf_push(wmag_buffer,b_sqrd);

        double normalized_pwr = pwr_sum / (double)TRACK_LENGTH;
        if (normalized_pwr > shm_settings.track_magnitude_threshold &&
            (track_sample_idx - shm_results_track.tracked_ping_time) >= shm_settings.track_cooldown_samples) {
            std::complex<float> dtft_coeff_A = goertzelNonInteger(chA_filtered_ptr,TRACK_LENGTH,shm_settings.track_frequency_target,SAMPLING_FREQUENCY);
            std::complex<float> dtft_coeff_B = goertzelNonInteger(chB_filtered_ptr,TRACK_LENGTH,shm_settings.track_frequency_target,SAMPLING_FREQUENCY);
            std::complex<float> dtft_coeff_C = goertzelNonInteger(chC_filtered_ptr,TRACK_LENGTH,shm_settings.track_frequency_target,SAMPLING_FREQUENCY);
             
            float phaseA = std::arg(dtft_coeff_A);
            float phaseB = std::arg(dtft_coeff_B);
            float phaseC = std::arg(dtft_coeff_C);

            shm_results_track.diff_phase_y = phase_difference(phaseC,phaseB);
            shm_results_track.diff_phase_x = phase_difference(phaseA,phaseB);

            float kx = SOUND_SPEED * shm_results_track.diff_phase_x / (NIPPLE_DISTANCE * 2 * M_PI * shm_settings.track_frequency_target);
            float ky = SOUND_SPEED * shm_results_track.diff_phase_y / (NIPPLE_DISTANCE * 2 * M_PI * shm_settings.track_frequency_target);

            float kz_2 = 1 - kx * kx - ky * ky;
            if (kz_2 < 0) {
              std::cerr << "WARNING: z mag is negative! " << kz_2 << std::endl;
              kz_2 = 0;
            }

            shm_results_track.tracked_ping_heading_radians = std::atan2(ky, kx);
            shm_results_track.tracked_ping_elevation_radians = std::acos(std::sqrt(kz_2));

            shm_results_track.tracked_ping_count++;
            shm_results_track.tracked_ping_frequency = shm_results_spectrum.most_recent_ping_frequency;  
            shm_results_track.tracked_ping_time = track_sample_idx; 

            std::cout << "PING DETECTED @ n=" << track_sample_idx << " w/ pwr="<< normalized_pwr<< std::endl;
            std::cout << "@ HEADING=" << shm_results_track.tracked_ping_heading_radians*(180.0f/M_PI) << std::endl; 

            shm_setg(hydrophones_results_track, shm_results_track);
        }
        track_sample_idx++;

    }
}
int main()
{
    // spectral periodogram options
    unsigned int nfft        =   1200;  // spectral periodogram FFT size
    unsigned int num_samples =  64000;  // number of samples
    float        fc          =   0.20f; // carrier (relative to sampling rate)

    // create objects
    iirfilt_crcf   filter_tx    = iirfilt_crcf_create_lowpass(15, 0.05);
    nco_crcf       mixer_tx     = nco_crcf_create(LIQUID_VCO);
    nco_crcf       mixer_rx     = nco_crcf_create(LIQUID_VCO);
    iirfilt_crcf   filter_rx    = iirfilt_crcf_create_lowpass(7, 0.2);

    // set carrier frequencies
    nco_crcf_set_frequency(mixer_tx, fc * 2*M_PI);
    nco_crcf_set_frequency(mixer_rx, fc * 2*M_PI);

    // create objects for measuring power spectral density
    spgramcf spgram_tx  = spgramcf_create_default(nfft);
    spgramf  spgram_dac = spgramf_create_default(nfft);
    spgramcf spgram_rx  = spgramcf_create_default(nfft);

    // run through loop one step at a time
    unsigned int i;
    for (i=0; i<num_samples; i++) {
        // STEP 1: generate input signal (filtered noise with offset tone)
        float complex v1 = (randnf() + randnf()*_Complex_I) + 3.0f*cexpf(-_Complex_I*0.2f*i);
        iirfilt_crcf_execute(filter_tx, v1, &v1);

        // save spectrum
        spgramcf_push(spgram_tx, v1);

        // STEP 2: mix signal up and save real part (DAC output)
        nco_crcf_mix_up(mixer_tx, v1, &v1);
        float v2 = crealf(v1);
        nco_crcf_step(mixer_tx);

        // save spectrum
        spgramf_push(spgram_dac, v2);

        // STEP 3: mix signal down and filter off image
        float complex v3;
        nco_crcf_mix_down(mixer_rx, v2, &v3);
        iirfilt_crcf_execute(filter_rx, v3, &v3);
        nco_crcf_step(mixer_rx);

        // save spectrum
        spgramcf_push(spgram_rx, v3);
    }

    // compute power spectral density output
    float   psd_tx  [nfft];
    float   psd_dac [nfft];
    float   psd_rx  [nfft];
    spgramcf_get_psd(spgram_tx,  psd_tx);
    spgramf_get_psd( spgram_dac, psd_dac);
    spgramcf_get_psd(spgram_rx,  psd_rx);

    // destroy objects
    spgramcf_destroy(spgram_tx);
    spgramf_destroy(spgram_dac);
    spgramcf_destroy(spgram_rx);

    iirfilt_crcf_destroy(filter_tx);
    nco_crcf_destroy(mixer_tx);
    nco_crcf_destroy(mixer_rx);
    iirfilt_crcf_destroy(filter_rx);

    // 
    // export output 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\n");

    fprintf(fid,"nfft   = %u;\n", nfft);
    fprintf(fid,"f      = [0:(nfft-1)]/nfft - 0.5;\n");
    fprintf(fid,"psd_tx = zeros(1,nfft);\n");
    fprintf(fid,"psd_dac= zeros(1,nfft);\n");
    fprintf(fid,"psd_rx = zeros(1,nfft);\n");
    
    for (i=0; i<nfft; i++) {
        fprintf(fid,"psd_tx (%6u) = %12.4e;\n", i+1, psd_tx [i]);
        fprintf(fid,"psd_dac(%6u) = %12.4e;\n", i+1, psd_dac[i]);
        fprintf(fid,"psd_rx (%6u) = %12.4e;\n", i+1, psd_rx [i]);
    }

    fprintf(fid,"figure;\n");
    fprintf(fid,"hold on;\n");
    fprintf(fid,"  plot(f, psd_tx,  '-', 'LineWidth',1.5,'Color',[0.7 0.7 0.7]);\n");
    fprintf(fid,"  plot(f, psd_dac, '-', 'LineWidth',1.5,'Color',[0.0 0.5 0.3]);\n");
    fprintf(fid,"  plot(f, psd_rx,  '-', 'LineWidth',1.5,'Color',[0.0 0.3 0.5]);\n");
    fprintf(fid,"hold off;\n");
    fprintf(fid,"xlabel('Normalized Frequency [f/F_s]');\n");
    fprintf(fid,"ylabel('Power Spectral Density [dB]');\n");
    fprintf(fid,"grid on;\n");
    fprintf(fid,"axis([-0.5 0.5 -100 60]);\n");
    fprintf(fid,"legend('transmit (complex)','DAC output (real)','receive (complex)','location','northeast');\n");

    fclose(fid);
    printf("results written to %s.\n", OUTPUT_FILENAME);

    printf("done.\n");
    return 0;
}
Example #7
0
void ModemFMStereo::demodulate(ModemKit *kit, ModemIQData *input, AudioThreadInput *audioOut) {
    ModemKitFMStereo *fmkit = (ModemKitFMStereo *)kit;
    size_t bufSize = input->data.size();
    liquid_float_complex u, v, w, x, y;
    
    double audio_resample_ratio = fmkit->audioResampleRatio;
    
    if (demodOutputData.size() != bufSize) {
        if (demodOutputData.capacity() < bufSize) {
            demodOutputData.reserve(bufSize);
        }
        demodOutputData.resize(bufSize);
    }
    
    size_t audio_out_size = (size_t)ceil((double) (bufSize) * audio_resample_ratio) + 512;
    
    freqdem_demodulate_block(demodFM, &input->data[0], bufSize, &demodOutputData[0]);
    
    if (resampledOutputData.size() != audio_out_size) {
        if (resampledOutputData.capacity() < audio_out_size) {
            resampledOutputData.reserve(audio_out_size);
        }
        resampledOutputData.resize(audio_out_size);
    }
    
    unsigned int numAudioWritten;
    
    msresamp_rrrf_execute(fmkit->audioResampler, &demodOutputData[0], bufSize, &resampledOutputData[0], &numAudioWritten);
    
    if (demodStereoData.size() != bufSize) {
        if (demodStereoData.capacity() < bufSize) {
            demodStereoData.reserve(bufSize);
        }
        demodStereoData.resize(bufSize);
    }
    
    float phase_error = 0;
    
    for (size_t i = 0; i < bufSize; i++) {
        // real -> complex
        firhilbf_r2c_execute(fmkit->firStereoR2C, demodOutputData[i], &x);
        
        // 19khz pilot band-pass
        iirfilt_crcf_execute(fmkit->iirStereoPilot, x, &v);
        nco_crcf_cexpf(fmkit->stereoPilot, &w);
        
        w.imag = -w.imag; // conjf(w)
        
        // multiply u = v * conjf(w)
        u.real = v.real * w.real - v.imag * w.imag;
        u.imag = v.real * w.imag + v.imag * w.real;
        
        // cargf(u)
        phase_error = atan2f(u.imag,u.real);
        
        // step pll
        nco_crcf_pll_step(fmkit->stereoPilot, phase_error);
        nco_crcf_step(fmkit->stereoPilot);
        
        // 38khz down-mix
        nco_crcf_mix_down(fmkit->stereoPilot, x, &y);
        nco_crcf_mix_down(fmkit->stereoPilot, y, &x);
        
        // complex -> real
        firhilbf_c2r_execute(fmkit->firStereoC2R, x, &demodStereoData[i]);
    }
    
    //            std::cout << "[PLL] phase error: " << phase_error;
    //            std::cout << " freq:" << (((nco_crcf_get_frequency(stereoPilot) / (2.0 * M_PI)) * inp->sampleRate)) << std::endl;
    
    if (audio_out_size != resampledStereoData.size()) {
        if (resampledStereoData.capacity() < audio_out_size) {
            resampledStereoData.reserve(audio_out_size);
        }
        resampledStereoData.resize(audio_out_size);
    }
    
    msresamp_rrrf_execute(fmkit->stereoResampler, &demodStereoData[0], bufSize, &resampledStereoData[0], &numAudioWritten);
    
    audioOut->channels = 2;
    if (audioOut->data.capacity() < (numAudioWritten * 2)) {
        audioOut->data.reserve(numAudioWritten * 2);
    }
    audioOut->data.resize(numAudioWritten * 2);
    for (size_t i = 0; i < numAudioWritten; i++) {
        float l, r;
        float ld, rd;

        if (fmkit->demph) {
            iirfilt_rrrf_execute(fmkit->iirDemphL, 0.568f * (resampledOutputData[i] - (resampledStereoData[i])), &ld);
            iirfilt_rrrf_execute(fmkit->iirDemphR, 0.568f * (resampledOutputData[i] + (resampledStereoData[i])), &rd);
            
            firfilt_rrrf_push(fmkit->firStereoLeft, ld);
            firfilt_rrrf_execute(fmkit->firStereoLeft, &l);
            
            firfilt_rrrf_push(fmkit->firStereoRight, rd);
            firfilt_rrrf_execute(fmkit->firStereoRight, &r);
        } else {
            firfilt_rrrf_push(fmkit->firStereoLeft, 0.568f * (resampledOutputData[i] - (resampledStereoData[i])));
            firfilt_rrrf_execute(fmkit->firStereoLeft, &l);
            
            firfilt_rrrf_push(fmkit->firStereoRight, 0.568f * (resampledOutputData[i] + (resampledStereoData[i])));
            firfilt_rrrf_execute(fmkit->firStereoRight, &r);
        }
        
        audioOut->data[i * 2] = l;
        audioOut->data[i * 2 + 1] = r;
    }
}
Example #8
0
int main() {
    unsigned int m           = 12;      // filter semi-length (actual length: 4*m+1)
    float        As          = 60.0f;   // stop-band attenuation [dB]
    unsigned int num_samples = 400;     // number of input samples

    unsigned int i;

    // allocate memory for data arrays
    float complex x [num_samples];  // input signal
    float complex y0[num_samples];  //
    float complex y1[num_samples];  //

    // generate the two signals
    iirfilt_crcf lowpass = iirfilt_crcf_create_lowpass(6,0.02);
    for (i=0; i<num_samples; i++) {
        // signal at negative frequency: tone
        float complex x_neg = cexpf(-_Complex_I*2*M_PI*0.059f*i);

        // signal at positive frequency: filtered noise
        float complex v;
        iirfilt_crcf_execute(lowpass, 4*randnf(), &v);
        float complex x_pos = v * cexpf(_Complex_I*2*M_PI*0.073f*i);

        // compsite
        x[i] = (x_neg + x_pos) * hamming(i,num_samples);
    }
    iirfilt_crcf_destroy(lowpass);

    // create/print the half-band resampler, with a specified
    // stopband attenuation level
    resamp2_cccf q = resamp2_cccf_create(m,-0.25f,As);
    resamp2_cccf_print(q);

    // run filter
    for (i=0; i<num_samples; i++)
        resamp2_cccf_filter_execute(q,x[i],&y0[i],&y1[i]);

    // 
    // print 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\n");
    fprintf(fid,"num_samples=%u;\n", num_samples);

    // output results
    for (i=0; i<num_samples; i++) {
        fprintf(fid,"x( %3u) = %12.4e + j*%12.4e;\n", i+1, crealf( x[i]), cimagf( x[i]));
        fprintf(fid,"y0(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y0[i]), cimagf(y0[i]));
        fprintf(fid,"y1(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y1[i]), cimagf(y1[i]));
    }

    // plot temporal results
    fprintf(fid,"\n\n");
    fprintf(fid,"t = 0:(num_samples-1);\n");
    fprintf(fid,"figure;\n");
    fprintf(fid,"subplot(3,1,1);\n");
    fprintf(fid,"  hold on;\n");
    fprintf(fid,"  plot(t,real(x),'Color',[1 1 1]*0.7,'LineWidth',1);\n");
    fprintf(fid,"  plot(t,imag(x),'Color',[1 1 1]*0.5,'LineWidth',2);\n");
    fprintf(fid,"  hold off;\n");
    fprintf(fid,"  grid on;\n");
    fprintf(fid,"  legend('real','imag','location','northeast');\n");
    fprintf(fid,"  axis([0 num_samples -2 2]);\n");
    fprintf(fid,"  ylabel('original');\n");
    fprintf(fid,"subplot(3,1,2);\n");
    fprintf(fid,"  hold on;\n");
    fprintf(fid,"  plot(t,real(y0),'Color',[1 1 1]*0.7,'LineWidth',1);\n");
    fprintf(fid,"  plot(t,imag(y0),'Color',[0 0.5 0.2],'LineWidth',2);\n");
    fprintf(fid,"  hold off;\n");
    fprintf(fid,"  grid on;\n");
    fprintf(fid,"  legend('real','imag','location','northeast');\n");
    fprintf(fid,"  axis([0 num_samples -2 2]);\n");
    fprintf(fid,"  ylabel('negative band');\n");
    fprintf(fid,"subplot(3,1,3);\n");
    fprintf(fid,"  hold on;\n");
    fprintf(fid,"  plot(t,real(y1),'Color',[1 1 1]*0.7,'LineWidth',1);\n");
    fprintf(fid,"  plot(t,imag(y1),'Color',[0 0.2 0.5],'LineWidth',2);\n");
    fprintf(fid,"  hold off;\n");
    fprintf(fid,"  grid on;\n");
    fprintf(fid,"  legend('real','imag','location','northeast');\n");
    fprintf(fid,"  axis([0 num_samples -2 2]);\n");
    fprintf(fid,"  ylabel('positive band');\n");
    fprintf(fid,"  xlabel('sample index');\n");

    // plot spectrum results
    fprintf(fid,"\n\n");
    fprintf(fid,"nfft=2400;\n");
    fprintf(fid,"f  = [0:(nfft-1)]/nfft - 0.5;\n");
    fprintf(fid,"w  = hamming(num_samples)' / num_samples;\n");
    fprintf(fid,"X  = 20*log10(abs(fftshift(fft( x.*w, nfft))));\n");
    fprintf(fid,"Y0 = 20*log10(abs(fftshift(fft(y0.*w, nfft))));\n");
    fprintf(fid,"Y1 = 20*log10(abs(fftshift(fft(y1.*w, nfft))));\n");
    fprintf(fid,"figure('Color','white');\n");
    fprintf(fid,"  hold on;\n");
    fprintf(fid,"  plot(f,X, 'Color',[1 1 1]*0.7,'LineWidth',2);\n");
    fprintf(fid,"  plot(f,Y0,'Color',[0 0.2 0.5]);\n");
    fprintf(fid,"  plot(f,Y1,'Color',[0 0.5 0.2]);\n");
    fprintf(fid,"  hold off;\n");
    fprintf(fid,"legend('original','negative','positive','location','northeast');\n");
    fprintf(fid,"grid on;\n");
    fprintf(fid,"axis([-0.5 0.5 -120 20]);\n");
    fprintf(fid,"xlabel('Normalized Frequency [f/F_s]');\n");
    fprintf(fid,"ylabel('Power Spectral Density [dB]');\n");

    fclose(fid);
    printf("results written to %s\n",OUTPUT_FILENAME);

    printf("done.\n");
    return 0;
}