This is Krishna, We are collecting the time series data through detectors. In the tutorial(1.4 Generating Waveforms), we are generating hp,hc using both time domain and frequency wave approximations. When we are performing the matched-filtering, if we use the frequency domain wave approximation, how can we match frequency domain waveforms with time domain strain data? There aren’t any differences in either data domain.
Can you explain the main difference between them, which is essential, accurate, and fast in case of data analysis.?
Hi Krishna, the matched-filtering is performed on 2 signals in the same domain, mostly in the time domain. So if you’re using the data in the time-domain and templates in the frequency domain, the next step before doing matched-filtering is to use IFFT to convert frequency domain templates to the time domain.
In the LISA data challenge, they have different types of sources(MBHB, GBs, EMRIs, …) Data from different sources are generated differently. Although the final data is in the time domain, if you check the source code you will find some of them first generated in the frequency domain, and then IFFT is applied for the conversion.
However, since the inner product of 2 time-domain signals is equivalent to the ones in the frequency domain, so probably it’s ok to do matched-filtering in the frequency domain as well.