home/comp_snr_ts.md

+```
+
+# calculate the optimal snr in raw scale
+y_inj_pycbc = scaled_projected_wf_dict['L1_y_inj_pycbc']
+y_inj_pycbc = scaled_projected_wf_dict['L1_y_inj_pycbc']
+snr_ts_pycbc = scaled_projected_wf_dict['L1_snr_ts']
+psd = asd.to_pycbc() ** 2
+psd = pycbc_interpolate(psd, y_inj_pycbc.delta_f)
+opt_snr_inj = pycbc.filter.matchedfilter.sigma(y_inj_pycbc, psd=psd, low_frequency_cutoff=10,
+                                               high_frequency_cutoff=1024)
+print('optimal SNR of the injection: {:.2f}'.format(opt_snr_inj))
+
+
+# calculate the optimal snr in whiten scale
+
+whitened_y_inj_pycbc = whitened_scaled_projected_wf_dict['L1_y_inj_pycbc']
+whitened_y_inj_pycbc_dummy = whitened_scaled_projected_wf_dict['L1_y_inj_pycbc_dummy']
+whitened_gwpy = d_gwpy.whiten(asd=asd, fduration=2, method='median')
+asd_whitened = calcualte_asd(whitened_gwpy)
+
+psd_whitened = asd_whitened.to_pycbc() ** 2
+psd_whitened = pycbc_interpolate(psd_whitened, y_inj_pycbc.delta_f)
+
+
+opt_snr_inj = pycbc.filter.matchedfilter.sigma(whitened_y_inj_pycbc, psd=psd_whitened, low_frequency_cutoff=10, high_frequency_cutoff=1024)
+print('optimal SNR of the injection: {:.2f}'.format(opt_snr_inj))
+
+snr_timeseries_inj = pycbc.filter.matchedfilter.matched_filter(whitened_y_inj_pycbc_dummy, whitened_y_inj_pycbc, psd=psd_whitened,
+                                                               low_frequency_cutoff=10,
+                                                               high_frequency_cutoff=1024)
+
+plt.plot(snr_timeseries_inj.sample_times, np.abs(snr_timeseries_inj.data) , label='whitened scale')
+plt.plot(snr_ts_pycbc.sample_times, np.abs(snr_ts_pycbc.data), label='raw scale')
+plt.legend()
+plt.savefig('test.png')
+plt.close()
+```
+- optimal SNR in whitened space is smaller than the SNR in raw scale by a factor of 2. 
+
+![Screen_Shot_2021-03-11_at_12.46.39_PM](uploads/1be82f43e25524fa5081c74e79770a55/Screen_Shot_2021-03-11_at_12.46.39_PM.png)
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