Q-Transform Analysis of GW230529

Q-Transform Analysis of GW230529 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Q-Transform Analysis of GW230529 Harshith VH, Ambrose Rajkumar Mariadass This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7045919/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The gravitational wave event GW230529 was analyzed using the Q-transform method to isolate the signal and examine its properties. The data used for this analysis was collected from LIGO Livingston. The Q-transform methodology, implemented in Python, began with acquiring strain data and revealing its frequency components using FFT. Key features of the signal over time, including its duration and frequency evolution, were presented. Additionally, the three phases of the event inspiral, merger, and ring-down were analyzed using the Q-transform method. This study demonstrated the effectiveness of the Q-transform method in gravitational wave analysis, highlighting its potential for analyzing complex signals. The results underscored the significance of using Python-based Q-transform techniques for these studies. Q-Transform Gravitational wave astronomy Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION On 5 April 2024, the gravitational wave astronomy community was once again surprised by the announcement from LIGO-VIRGO-KAGRA collaboration for a significant discovery during the first part of fourth Observing run (O4a) (Abac et al. 2024). GW230529 event was classified as the compact binary coalescence (CBCs) which made a new way in understanding the stellar evolution and dynamics of binary system in our universe. Two components were discovered during the observation of GW230529. First component which was discovered was ranging with a mass from 2.5 solar mass to 4.5 solar mass which questions the conventional classification of the systems. This mass range is notably higher than typical neutron stars, which are generally expected to have masses up to around 2 solar masses before collapsing into a black holes under extreme conditions. Also, it is significantly lower than the lower boundary typically associated with stellar black holes, which are believed to form from collapsed massive stars with initial masses exceeding about 20 solar masses. The second component of GW230529 is comparatively more straight forward to classify as it exhibits a mass between 1.2 and 2.0 solar masses, placing it within the expected range for neutron stars (Koustav et al. 2024). One plausible hypothesis is that it could be a so-called "heavy neutron star" — a neutron star with a mass approaching the upper limit of what is traditionally considered possible for such objects. Alternatively, it may represent a new class of compact stellar remnants that challenge our current understanding of stellar evolution and the outcomes of stellar collapse. The analysis of GW230529 involved advance data processing techniques, featuring the Q-transform method. This method is known for extracting detailed time-frequency information about the gravitational waves. This is also crucial for characterizing the properties of merging binary system. By applying the Q-transform, we can know the key features of GW230529, including its frequency evolution, chirp pattern and overall waveform structure. In this paper, we undertake a analysis of GW230529 using Q-transforms method, focusing on extracting meaningful insights. METHODOLOGY This section of the paper outlines the step-by-step methodology used to analyze the gravitational wave event GW230529 from extracting the data to the detailed time-frequency analysis using Q-transforms. Firstly, the gravitational wave strain data was fetched from Gravitational Wave Open Science Centre (GWOSC) using the GPS time associated with the event. The time-series datasets were acquired through ‘TimeSeries’ class from ‘gwpy’ library (Dunkan et al. 2021). The GPS time of the event was specified and the segments around the time was fetched to capture the entire event , a time-series of a few seconds before and after this time was retrieved so that any potential signals leading up to or following the main event , was captured. We chose the data segments to be long enough allowing for comprehensive analysis of these signals. To further analyze the frequency content of the gravitational wave signal , the fft() method from ‘TimeSeries’ (Cornish N.J 2021) class in ‘gwpy’ is used to perform Fast Fourier Transform (FFT) in order to transform time-domain signals to frequency domain representation .The output of FFT is a frequency series object that contains complex values representing the amplitude and phase of each frequency component , so we extract the absolute magnitude of the amplitude by ‘abs()’ method which computes the magnitude of the complex values giving the strength of each frequency component without considering phase information . Also we applied Hann window function ‘get_window’ from ‘scipy.signal’ to the time-series data before performing FFT to minimize the spectral leakage. After windowing the data, we perform the FFT on the windowed time-series and extracted absolute magnitude of the amplitude. Further, the Amplitude Spectral Density (ASD) was computed. The ‘asd()’ method from ‘TimeSeries’ in ‘gwpy’ is used to calculate ASD , the ASD provides the strength of the signal across different frequencies . The FFT length was chosen to be 10 which offers a fine frequency resolution required for detecting compact binary coalescences (CBCs) and ‘median’ method is used to ensure robustness against outliers. Two ASD plots were generated: one with a 10-second FFT length and another with a 4-second FFT length. The second plot used a larger data segment to average out random variations, providing a clearer view of the signal’s frequency content. The shorter the FFT length provides the finer frequency resolution. Since ASD doesn’t capture how these frequencies evolved over the time, to address this spectrogram was generated to represent the time-frequency content of the signal. The ‘spectogram2’ method from ‘TimeSeries’ class in ‘gwpy’ was used to generate spectrogram , the spectrogram was created using a FFT length of 10 seconds with a 2 second overlap , providing a balance between time and frequency resolution and a Hann window function was applied to minimize the spectral leakage . The spectrogram was scaled to highlight the strain noise. To further enhance the time-frequency analysis, the ‘q_transform’ method was applied to the strain data. The Q-transform is particularly well suited for detecting short-lived signals as it allows for varying time and frequency resolutions. Initially Q-transform was performed for over a broad frequency range (frange) of 30Hz to 1000Hz, providing a overview of signal’s time-frequency structure where the gravitational wave signal is likely to be prominent. This helps in identifying the general characteristics of the signal .We customized the axis properties to enhance the visualization of Q-transform. Subsequently to further refine the time-frequency analysis of gravitational wave signal, we applied Q-transform with a extended frequency range and a specified Q-factor range from 10 to 90, which provides a balance between time and frequency resolution allowing for a visualization of the transient features across different frequencies. The refined Q-transforms provided high-resolution time-frequency plots that were instrumental in pinpointing the exact moment of the merger and understanding the dynamics of the event (Chatterji et al.2004, Abbott et al. 2016, Blackburn et al. 2008). These plots revealed distinct patterns corresponding to the inspiral, merger, and ringdown phases, with the frequency and duration of these phases providing clues about the nature of the binary system involved. RESULTS I. Time-Series data In this case, the first step in our analysis was fetching the gravitational wave strain data around the time of the GW230529 event. In figure 1 above, we present the strain data recorded by LIGO detector at Livingston (L1) over an approximately 19 second long duration, from GPS time 1369419308.0. The x-axis is time in seconds from the beginning of the data segment, whereas the y-axis is the dimensionless quantity of strain data representing relative changes in length of interferometer arms due to passing gravitational waves. Amplitude for the data is measured in units of 10 -17 . This time series plot shows the oscillatory patterns expected to be there in a gravitational wave signal buried under the noise. The amplitude fluctuations show the dynamical nature of such a signal, which would form the characteristics of a gravitational wave event of compact binaries coalescence. The most prominent feature in this plot is the chirp signal, which goes to higher density and the amplitude of the waves toward the middle of the time series, as the two compact objects spiral close before merging. It is clearly visible. The strain data, except for the chirp signal, may also contain fluctuations that could be due to instrumental noise or other astrophysical noises (Leah & Derek 2023, Davis et al. 2021, Acernese et al. 2022). II. Fast-Fourier Transform plot: The FFT transforms the time-domain data into the frequency domain, allowing us to see the frequency components of the signal. In Figure 2a, the FFT of raw strain data is plotted on a log-log scale .The x-axis indicates the frequency in Hertz (Hz), and the y-axis is the strain noise in dimensionless units. This gives a graphical view of the signal in the frequency domain, with bright peaks indicating the strong frequency components present in the signal. The highest peak is near 10 Hz, which would be typical of a binary coalescence source. In order to minimize spectral leakage and improve the appearance of the frequency domain, we applied Hann windowing to the data before taking the FFT. The purpose of using a Hann window is to smooth the discontinuities at the edges of the time-domain signal, which can be introduced as artifacts in the frequency domain. Figure 2b shows the FFT of the windowed data. It can be seen that the application of the Hann window has managed to reduce spectral leakage, showing the representation of the frequency components much smoother and more accurately. The primary peak at approximately 10 Hz is now much more prominent, and the overall noise floor has been lowered such that new features may be observed within the frequency spectrum. These frequency domain plots truly contain the characteristics of the gravitational wave signal and the noise behind it, setting the stage for further analysis and interpretation. III. Amplitude spectral density plot: Figure 3a represents the amplitude spectral density of the gravitational wave strain data using an FFT length of 10 second. The ASD is a crucial tool which provides the insights into the frequency content of the noise of detector. The x-axis is representing the frequency (Hz), which has been plotted on a logarithmic scale from 0.1 Hz to 1000 Hz. The y-axis is in units of Hz −1/2 and, again on a logarithmic scale, the same convention used for the strain. A large peak near 10 Hz suggests that there is a lot of noise there. There is then less noise above 10 Hz. A higher frequency peak is seen from about 100 Hz to 1000 Hz. The peak at 10 Hz is probably seismic noise or mechanical resonances of the detector. The expected decrease of noise beyond 10 Hz is due to the detector being designed to minimize noises at higher frequencies. The rise in noise around 100 Hz to 1000 Hz could be from several instrumental artifacts or electronic noise. Moreover, this plot will further help to identify frequency bands, mostly affected by noises, for filtering and analysis of the gravitational wave signal and transient event. Figure 3b shows the ASD using FFT length of 4 seconds using an extended data range. Increase in time length of data would help average more number of FFTs, hence it will reduce the random noises and bring clear viewing of the frequency spectrum. The x-axis range is from 10 Hz to 1400 Hz on a logarithmic scale. The y-axis scale is from 10 −24 to 10 −20 Hz −1/2 . This shows the noise levels, in comparison to the first plot, which is much lower overall because an averaging effect occurs. Peaks and troughs in the ASD are much more defined, showing clearer frequency-specific contributions of noise. A more detailed frequency spectrum is possible with both the extended data range and shorter FFT length. It has a clearer noise profile, allowing a better identification of noise sources and more accurate filtering. The key features to this noise, especially around 10 Hz and over 100 Hz, highlight the instrumental and environmental noise areas that affect the detector's sensitivity. Figure 3c focuses on the frequency range from 10 Hz to 1400 Hz, using similar data averaging and FFT length settings as Plot 2(Figure 3b). The curve is generally smooth and identifies peaks where noises have definite sources. As indicated on the plot, the most prominent noise contributions are mostly between 10 Hz and well above 100 Hz. The high-resolution ASD plot underlines the specific frequency bands with the highest levels of noise. By large, the curve on the noise floor should appear smooth, while the peaks show some selected frequencies that have been interfered with by the noise sources. Optimizing the performance of the detector in light of these characteristics of noise will help to increase sensitivity to gravitational waves. Such identification and mitigation of noise sources will increase the ability of detectors to capture and analyze gravitational wave events correctly. IV. Q-transform plot: The plots Figure 4a and Figure 4b presents the Q-transform analysis over a time interval of 20 seconds, ranging from 0 to 20 seconds after the GPS time 1369419308.0.The frequency range goes from 10 Hz to 1000 Hz, plotted logarithmically. The color scale stands for normalized energy. Higher brightness means higher levels of energy. The presence of horizontal lines thus represents persistent noise or signals at certain frequencies, constant over time. These could result from instrumental noise or environmental factors. Any vertical streaks or isolated bright spots may indicate transient signals, such as from gravitational wave events, appearing for short durations. This (Figure 4c) Q-transform plot visualizes the frequency content of the data around GPS time 1369419318.7, with the time axis ranging from -10 to +8 seconds relative to this time. Horizontal lines or bands would show persistent noise sources either environmental noise or instrumental artifacts. The bright spot at around -9.5 s and frequencies below 100 Hz shows a transient event. This might be an indication of interest; for instance, it could possibly be an event of a gravitational wave or even an astrophysical event of a different kind. From the signal's energy distribution in time and frequency, one gets an idea of what the detected event is. The fine representation of time and frequency will facilitate comprehension of the characteristics of the signal in time and frequency. Figure 4d the bright spot between -9.8 seconds and -9.6 seconds at frequencies around 30Hz to 100Hz suggests a transient event. The signal has a well-defined frequency range, with energy concentrated around 30 to 100 Hz during this transient event. Thus this Q-transforms shows a sign of a compact binary coalescences (Siddarth et al. 2023), we can now analyze the phases of transmission of the Q-transform. V. Phases of Q-Transform: Inspiral phase: The inspiral phase of the signal can be identified from the increasing frequency of the signal within the Q-transform plot, between -9.8 and -9.6 s. The signal has a bright spot starting around 30 Hz and moving up towards 100 Hz. It means that the system is in the inspiral stage, and the frequency grows when both objects spiral closer to each other in the motion of orbital motion. The inspiral phase takes only a few seconds, as one can see from the time axis on the plot Merger phase: The merger phase is the stage when two compact objects come into contact with one another and combine. This particular stage possesses waves of gravitational amplitude at their maximum. The merger is a very short event compared to the inspiral, occurring usually only for a fraction of a second. The frequencies during the merger are higher compared to the inspiral phase. The frequency and energy in the inspiral are increasing dramatically; both seem visible as a bright spot in the Q-transform plot around -9.7 s of Figure 4d. There is a last moment with a concentration of energy at high frequencies, up to 100 Hz in this plot, just before the end of the signal. That is how a merger is expected to look like. Ringdown phase: After merger phase takes place, a new single object is likely to be formed (likely a black hole) undergoes ringdown and the signal settles to a stable configuration .This phase is characterized by damping oscillations. The amplitude of the gravitational waves decays exponentially during ringdown. The Q-transform plot in Figure 4d does not depict this phase since it focuses on the inspiral and merger phases. But, if the plot were prolonged in time, the ringdown phase would exhibit a decaying signal at a frequency that is relatively constant (Éanna et al. 1998). Through our Q-transform analysis of GW230529, we identified a significant signal in the time interval from -9.8 to -9.3 seconds, displaying characteristic frequency chirps and energy distribution suggestive of a binary merger event. The observed signal begins at lower frequencies (around 30 Hz) and rises, peaking in energy around 100 Hz. This frequency evolution is consistent with the inspiral phase of a binary system involving significantly different mass objects, hinting at a possible black hole- neutron star merger (BHNS) merger (Jin-Ping et al. 2024). CONCLUSION In this paper , we presented a detailed analysis of GW230529 a gravitational wave event , describing a range of methodologies to examine the Q-Transform of the gravitational wave event. Our study began with knowing the strain data using gwpy followed by performing Fast Fourier Transform , Amplitude spectral density on the data and lastly performing the time frequency analysis i.e Q-Transforms which revealed significant features in the time interval from -9.8 to -9.3 seconds , displaying a characteristic frequency chirp and energy distribution consistent with a binary merger. The Q-Transform highlighted the inspiral phase with a merger frequency starting around 30Hz and rising to approximately 100HZ showing the involvement of two compact objects of different masses. The pattern which we observed is a suggestive for a neutron star- black hole merger, where the lower mass object is a neutron star and little higher mass object is a black hole. To uphold of finding, we recommend further analysis through match filtering and parameter estimation. Future works will focus on refining these analyses and exploring the implications of this event. Declarations Author Contribution Author ContributionHarshith VH: Writing – original draft, Investigation, Data curation, Visualization, Software, Conceptualization. Ambrose Rajkumar M: Writing – review & editing, Supervision, Resources. Acknowledgement "This research has made use of data or software obtained from the Gravitational Wave Open Science Center (gwosc.org), a service of the LIGO Scientific Collaboration, the Virgo Collaboration, and KAGRA. This material is based upon work supported by NSF's LIGO Laboratory which is a major facility fully funded by the National Science Foundation, as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. KAGRA is supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) in Japan; National Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea; Academia Sinica (AS) and National Science and Technology Council (NSTC) in Taiwan. References Abac, A.G., Abbott, R.,Abouelfettouh, I., et al. 2024, ApJL, 970,L34 Koustav, C., Ish, G., Rossella, G., et al. 2024, arXiv, 2,15 Duncan M. M., Joseph S. A., Scott B. C., et al. 2021, SoftwareX, 13, 100657 Cornish, N.J., 2020, Physical Review D, 102(12), p.124038 Chatterji, S., Blackburn, L., Martin,G., 2004, Classical and Quantum Gravity, 21, S1809 Abbott, B.P., Abbott, R., Abbott, T.D., et al. 2016, Classical and Quantum Gravity, 33, 134001 Blackburn, L., Cadonati, L., Caride,S., et al, 2008, Classical and Quantum Gravity, 25, 184004 Leah, V., & Derek, D., 2023, Classical and Quantum Gravity, 40, 035008 Davis, D., Areeda, J.S., Berger, B.K., et al, 2021, Classical and Quantum Gravity, 38, 135014 Acernese, F., Agathos, M., Ain, A., et al, 2022, arXiv, 2205.01555 Siddharth, S., Ethan, M., Erik K., et al. 2023, Classical and Quantum Gravity, 41 , 015012 Éanna, É., Flanagan & Scott A. H., 1998, Phys. Rev. D 57, 4535 Jin-Ping, Z., Rui-Chong, H., Yacheng, K., et al. 2024, ApJ, 974, 211 Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7045919","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486793400,"identity":"fc520eb4-d633-4ebe-b746-b34896917453","order_by":0,"name":"Harshith VH","email":"","orcid":"","institution":"Kristu Jayanti College (Autonomous)","correspondingAuthor":false,"prefix":"","firstName":"Harshith","middleName":"","lastName":"VH","suffix":""},{"id":486793401,"identity":"b876edf4-55bb-45a2-ace4-3cb2e1371d6b","order_by":1,"name":"Ambrose Rajkumar Mariadass","email":"data:image/png;base64,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","orcid":"","institution":"Kristu Jayanti College (Autonomous)","correspondingAuthor":true,"prefix":"","firstName":"Ambrose","middleName":"Rajkumar","lastName":"Mariadass","suffix":""}],"badges":[],"createdAt":"2025-07-04 10:38:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7045919/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7045919/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87043584,"identity":"0c9b638c-5bc0-4da6-aff7-d4e2e1f1a3f8","added_by":"auto","created_at":"2025-07-18 14:18:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":89923,"visible":true,"origin":"","legend":"\u003cp\u003eTime-series strain data plot\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7045919/v1/e0dada0399449720038ae626.png"},{"id":87045004,"identity":"cd20d106-3b26-41ba-a747-c88ea61c7a43","added_by":"auto","created_at":"2025-07-18 14:26:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":76253,"visible":true,"origin":"","legend":"\u003cp\u003ea: FFT plot without windowing\u003c/p\u003e\n\u003cp\u003eb: FFT plot with windowing\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7045919/v1/d16c102b7ff3b7f2dfd9f94b.png"},{"id":87043583,"identity":"8c993cb1-b09a-44f6-bcb9-438ab5558118","added_by":"auto","created_at":"2025-07-18 14:18:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":71549,"visible":true,"origin":"","legend":"\u003cp\u003ea: ASD with FFT length 10\u003c/p\u003e\n\u003cp\u003eb: ASD with FFT length 4\u003c/p\u003e\n\u003cp\u003ec: ASD with detailed frequency range\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7045919/v1/2bd4d82b828a7e3c3710310b.png"},{"id":87042384,"identity":"b4801802-09a6-48f7-ad25-a4b981c028d7","added_by":"auto","created_at":"2025-07-18 14:10:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":275924,"visible":true,"origin":"","legend":"\u003cp\u003ea: Q-transform plot 1\u003c/p\u003e\n\u003cp\u003eb: Q-transform plot 2\u003c/p\u003e\n\u003cp\u003ec: Q-Transform plot 3\u003c/p\u003e\n\u003cp\u003ed: Q-Transform plot 4\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7045919/v1/ea6c34c827bc1ee946509e00.png"},{"id":88366944,"identity":"30463e39-31ff-46c7-b5e0-c37bace8bf5c","added_by":"auto","created_at":"2025-08-05 17:46:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":810954,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7045919/v1/29601e74-f38a-4a6b-a1e7-e31c13a4b7a6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Q-Transform Analysis of GW230529","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eOn 5 April 2024, the gravitational wave astronomy community was once again surprised by the announcement from LIGO-VIRGO-KAGRA collaboration for a significant discovery during the first part of fourth Observing run (O4a) (Abac et al. 2024). GW230529 event was classified as the compact binary coalescence (CBCs) which made a new way in understanding the stellar evolution and dynamics of binary system in our universe. Two components were discovered during the observation of GW230529. First component which was discovered was ranging with a mass from 2.5 solar mass to 4.5 solar mass which questions the conventional classification of the systems. This mass range is notably higher than typical neutron stars, which are generally expected to have masses up to around 2 solar masses before collapsing into a black holes under extreme conditions. Also, it is significantly lower than the lower boundary typically associated with stellar black holes, which are believed to form from collapsed massive stars with initial masses exceeding about 20 solar masses. The second component of GW230529 is comparatively more straight forward to classify as it exhibits a mass between 1.2 and 2.0 solar masses, placing it within the expected range for neutron stars (Koustav et al. 2024).\u0026nbsp;One plausible hypothesis is that it could be a so-called \u0026quot;heavy neutron star\u0026quot; \u0026mdash; a neutron star with a mass approaching the upper limit of what is traditionally considered possible for such objects. Alternatively, it may represent a new class of compact stellar remnants that challenge our current understanding of stellar evolution and the outcomes of stellar collapse.\u003c/p\u003e\n\u003cp\u003eThe analysis of GW230529 involved advance data processing techniques, featuring the Q-transform method. This method is known for extracting detailed time-frequency information about the gravitational waves. This is also crucial for characterizing the properties of merging binary system. By applying the Q-transform, we can know the key features of GW230529, including its frequency evolution, chirp pattern and overall waveform structure. In this paper, we undertake a analysis of GW230529 using Q-transforms method, focusing on extracting meaningful insights.\u003c/p\u003e"},{"header":"METHODOLOGY ","content":"\u003cp\u003eThis section of the paper outlines the step-by-step methodology used to analyze the gravitational wave event GW230529 from extracting the data to the detailed time-frequency analysis using Q-transforms.\u003c/p\u003e\n\u003cp\u003eFirstly, the gravitational wave strain data was fetched from Gravitational Wave Open Science Centre (GWOSC) using the GPS time associated with the event. The time-series datasets were acquired through \u0026lsquo;TimeSeries\u0026rsquo; class from \u0026lsquo;gwpy\u0026rsquo; library (Dunkan et al. 2021). The GPS time of the event was specified and the segments around the time was fetched to capture the entire event , a time-series of a few seconds before and after this time was retrieved so that any potential signals leading up to or following the main event , was captured. We chose the data segments to be long enough allowing for comprehensive analysis of these signals. To further analyze the frequency content of the gravitational wave signal , the fft() method from \u0026lsquo;TimeSeries\u0026rsquo; (Cornish N.J 2021) class in \u0026lsquo;gwpy\u0026rsquo; is used to perform Fast Fourier Transform (FFT) in order to transform time-domain signals to frequency domain representation .The output of FFT is a frequency series object that contains complex values \u0026nbsp;representing the amplitude and phase of each frequency component , so we extract the absolute magnitude of the amplitude by \u0026lsquo;abs()\u0026rsquo; method which computes the magnitude of the complex values giving the strength of each frequency component without considering phase information . Also we applied Hann window function \u0026lsquo;get_window\u0026rsquo; from \u0026lsquo;scipy.signal\u0026rsquo; to the time-series data before performing FFT to minimize the spectral leakage. After windowing the data, we perform the FFT on the windowed time-series and extracted absolute magnitude of the amplitude. Further, the Amplitude Spectral Density (ASD) was computed. The \u0026lsquo;asd()\u0026rsquo; method from \u0026lsquo;TimeSeries\u0026rsquo; in \u0026lsquo;gwpy\u0026rsquo; is used to calculate ASD , the ASD provides the strength of the signal across different frequencies . The FFT length was chosen to be 10 which offers a fine frequency resolution required for detecting compact binary coalescences (CBCs) and \u0026lsquo;median\u0026rsquo; method is used to ensure robustness against outliers. Two ASD plots were generated: one with a 10-second FFT length and another with a 4-second FFT length. The second plot used a larger data segment to average out random variations, providing a clearer view of the signal\u0026rsquo;s frequency content. The shorter the FFT length provides the finer frequency resolution. Since ASD doesn\u0026rsquo;t capture how these frequencies evolved over the time, to address this spectrogram was generated to represent the time-frequency content of the signal. The \u0026lsquo;spectogram2\u0026rsquo; method from \u0026lsquo;TimeSeries\u0026rsquo; class in \u0026lsquo;gwpy\u0026rsquo; was used to generate spectrogram , the spectrogram was created using a FFT length of 10 seconds with a 2 second overlap , providing a balance between time and frequency resolution and a Hann window function was applied to minimize the spectral leakage . The spectrogram was scaled to highlight the strain noise. To further enhance the time-frequency analysis, the \u0026lsquo;q_transform\u0026rsquo; method was applied to the strain data. The Q-transform is particularly well suited for detecting short-lived signals as it allows for varying time and frequency resolutions. Initially Q-transform was performed for over a broad frequency range (frange) of 30Hz to 1000Hz, providing a overview of signal\u0026rsquo;s time-frequency structure where the gravitational wave signal is likely to be prominent. This helps in identifying the general characteristics of the signal .We customized the axis properties to enhance the visualization of Q-transform. Subsequently to further refine the time-frequency analysis of gravitational wave signal, we applied Q-transform with a extended frequency range and a specified Q-factor range from 10 to 90, which provides a balance between time and frequency resolution allowing for a visualization of the transient features across different frequencies. The refined Q-transforms provided high-resolution time-frequency plots that were instrumental in pinpointing the exact moment of the merger and understanding the dynamics of the event (Chatterji et al.2004, Abbott et al. 2016, Blackburn et al. 2008). These plots revealed distinct patterns corresponding to the inspiral, merger, and ringdown phases, with the frequency and duration of these phases providing clues about the nature of the binary system involved.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eI. Time-Series data\u003c/p\u003e\n\u003cp\u003eIn this case, the first step in our analysis was fetching the gravitational wave strain data around the time of the GW230529 event. In figure 1 above, we present the strain data recorded by LIGO detector at Livingston (L1) over an approximately 19 second long duration, from GPS time 1369419308.0. The x-axis is time in seconds from the beginning of the data segment, whereas the y-axis is the dimensionless quantity of strain data representing relative changes in length of interferometer arms due to passing gravitational waves. Amplitude for the data is measured in units of 10\u003csup\u003e-17\u003c/sup\u003e. This time series plot shows the oscillatory patterns expected to be there in a gravitational wave signal buried under the noise. The amplitude fluctuations show the dynamical nature of such a signal, which would form the characteristics of a gravitational wave event of compact binaries coalescence. The most prominent feature in this plot is the chirp signal, which goes to higher density and the amplitude of the waves toward the middle of the time series, as the two compact objects spiral close before merging. It is clearly visible. The strain data, except for the chirp signal, may also contain fluctuations that could be due to instrumental noise or other astrophysical noises\u0026nbsp;(Leah \u0026amp; Derek 2023, Davis et al. 2021, Acernese et al. 2022).\u003c/p\u003e\n\u003cp\u003eII. Fast-Fourier Transform plot:\u003c/p\u003e\n\u003cp\u003eThe FFT transforms the time-domain data into the frequency domain, allowing us to see the frequency components of the signal. In Figure 2a, the FFT of raw strain data is plotted on a log-log scale .The x-axis indicates the frequency in Hertz (Hz), and the y-axis is the strain noise in dimensionless units. This gives a graphical view of the signal in the frequency domain, with bright peaks indicating the strong frequency components present in the signal. The highest peak is near 10 Hz, which would be typical of a binary coalescence source.\u003c/p\u003e\n\u003cp\u003eIn order to minimize spectral leakage and improve the appearance of the frequency domain, we applied Hann windowing to the data before taking the FFT. The purpose of using a Hann window is to smooth the discontinuities at the edges of the time-domain signal, which can be introduced as artifacts in the frequency domain.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 2b shows the FFT of the windowed data. It can be seen that the application of the Hann window has managed to reduce spectral leakage, showing the representation of the frequency components much smoother and more accurately. The primary peak at approximately 10 Hz is now much more prominent, and the overall noise floor has been lowered such that new features may be observed within the frequency spectrum. These frequency domain plots truly contain the characteristics of the gravitational wave signal and the noise behind it, setting the stage for further analysis and interpretation.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;III. Amplitude spectral density plot:\u003c/p\u003e\n\u003cp\u003eFigure 3a represents the amplitude spectral density of the gravitational wave strain data using an FFT length of 10 second. The ASD is a crucial tool which provides the insights into the frequency content of the noise of detector. The x-axis is representing the frequency (Hz), which has been plotted on a logarithmic scale from 0.1 Hz to 1000 Hz. The y-axis is in units of Hz\u003csup\u003e\u0026minus;1/2\u003c/sup\u003e and, again on a logarithmic scale, the same convention used for the strain. A large peak near 10 Hz suggests that there is a lot of noise there. There is then less noise above 10 Hz. A higher frequency peak is seen from about 100 Hz to 1000 Hz. The peak at 10 Hz is probably seismic noise or mechanical resonances of the detector. The expected decrease of noise beyond 10 Hz is due to the detector being designed to minimize noises at higher frequencies. The rise in noise around 100 Hz to 1000 Hz could be from several instrumental artifacts or electronic noise. Moreover, this plot will further help to identify frequency bands, mostly affected by noises, for filtering and analysis of the gravitational wave signal and transient event.\u003c/p\u003e\n\u003cp\u003eFigure 3b shows the ASD using FFT length of 4 seconds using an extended data range. Increase in time length of data would help average more number of FFTs, hence it will reduce the random noises and bring clear viewing of the frequency spectrum. The x-axis range is from 10 Hz to 1400 Hz on a logarithmic scale. The y-axis scale is from 10\u003csup\u003e\u0026minus;24\u003c/sup\u003e to 10\u003csup\u003e\u0026minus;20\u003c/sup\u003e Hz\u003csup\u003e\u0026minus;1/2\u003c/sup\u003e. This shows the noise levels, in comparison to the first plot, which is much lower overall because an averaging effect occurs. Peaks and troughs in the ASD are much more defined, showing clearer frequency-specific contributions of noise. A more detailed frequency spectrum is possible with both the extended data range and shorter FFT length. It has a clearer noise profile, allowing a better identification of noise sources and more accurate filtering. The key features to this noise, especially around 10 Hz and over 100 Hz, highlight the instrumental and environmental noise areas that affect the detector\u0026apos;s sensitivity.\u003c/p\u003e\n\u003cp\u003eFigure 3c focuses on the frequency range from 10 Hz to 1400 Hz, using similar data averaging and FFT length settings as Plot 2(Figure 3b). The curve is generally smooth and identifies peaks where noises have definite sources. As indicated on the plot, the most prominent noise contributions are mostly between 10 Hz and well above 100 Hz. The high-resolution ASD plot underlines the specific frequency bands with the highest levels of noise. By large, the curve on the noise floor should appear smooth, while the peaks show some selected frequencies that have been interfered with by the noise sources. Optimizing the performance of the detector in light of these characteristics of noise will help to increase sensitivity to gravitational waves. Such identification and mitigation of noise sources will increase the ability of detectors to capture and analyze gravitational wave events correctly.\u003c/p\u003e\n\u003cp\u003eIV. Q-transform plot:\u003c/p\u003e\n\u003cp\u003eThe plots Figure 4a and Figure 4b presents the Q-transform analysis over a time interval of 20 seconds, ranging from 0 to 20 seconds after the GPS time 1369419308.0.The frequency range goes from 10 Hz to 1000 Hz, plotted logarithmically. The color scale stands for normalized energy. Higher brightness means higher levels of energy. The presence of horizontal lines thus represents persistent noise or signals at certain frequencies, constant over time. These could result from instrumental noise or environmental factors. Any vertical streaks or isolated bright spots may indicate transient signals, such as from gravitational wave events, appearing for short durations.\u003c/p\u003e\n\u003cp\u003eThis (Figure 4c) Q-transform plot visualizes the frequency content of the data around GPS time 1369419318.7, with the time axis ranging from -10 to +8 seconds relative to this time. Horizontal lines or bands would show persistent noise sources either environmental noise or instrumental artifacts. The bright spot at around -9.5 s and frequencies below 100 Hz shows a transient event. This might be an indication of interest; for instance, it could possibly be an event of a gravitational wave or even an astrophysical event of a different kind. From the signal\u0026apos;s energy distribution in time and frequency, one gets an idea of what the detected event is. The fine representation of time and frequency will facilitate comprehension of the characteristics of the signal in time and frequency.\u003c/p\u003e\n\u003cp\u003eFigure 4d the bright spot between -9.8 seconds and -9.6 seconds at frequencies around 30Hz to 100Hz suggests a transient event. The signal has a well-defined frequency\u0026nbsp;range, with energy concentrated around 30 to 100 Hz during this transient event. Thus this Q-transforms shows a sign of a compact binary coalescences (Siddarth et al. 2023), we can now analyze the phases of transmission of the Q-transform.\u003c/p\u003e\n\u003cp\u003eV. Phases of Q-Transform:\u003c/p\u003e\n\u003col class=\"decimal_type\"\u003e\n \u003cli\u003eInspiral phase: The inspiral phase of the signal can be identified from the increasing frequency of the signal within the Q-transform plot, between -9.8 and -9.6 s. The signal has a bright spot starting around 30 Hz and moving up towards 100 Hz. It means that the system is in the inspiral stage, and the frequency grows when both objects spiral closer to each other in the motion of orbital motion. The inspiral phase takes only a few seconds, as one can see from the time axis on the plot\u003c/li\u003e\n \u003cli\u003eMerger phase: The merger phase is the stage when two compact objects come into contact with one another and combine. This particular stage possesses waves of gravitational amplitude at their maximum. The merger is a very short event compared to the inspiral, occurring usually only for a fraction of a second. The frequencies during the merger are higher compared to the inspiral phase. The frequency and energy in the inspiral are increasing dramatically; both seem visible as a bright spot in the Q-transform plot around -9.7 s of Figure 4d. There is a last moment with a concentration of energy at high frequencies, up to 100 Hz in this plot, just before the end of the signal. That is how a merger is expected to look like.\u003c/li\u003e\n \u003cli\u003eRingdown phase: After merger phase takes place, a new single object is likely to be formed (likely a black hole) undergoes ringdown and the signal settles to a stable configuration .This phase is characterized by damping oscillations.\u0026nbsp;The amplitude of the gravitational waves decays exponentially during ringdown. The Q-transform plot in Figure 4d does not depict this phase since it focuses on the inspiral and merger phases. But, if the plot were prolonged in time, the ringdown phase would exhibit a decaying signal at a frequency that is relatively constant (\u0026Eacute;anna et al. 1998).\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThrough our Q-transform analysis of GW230529, we identified a significant signal in the time interval from -9.8 to -9.3 seconds, displaying characteristic frequency chirps and energy distribution suggestive of a binary merger event. The observed signal begins at lower frequencies (around 30 Hz) and rises, peaking in energy around 100 Hz. This frequency evolution is consistent with the inspiral phase of a binary system involving significantly different mass objects, hinting at a possible black hole- neutron star merger (BHNS) merger (Jin-Ping et al. 2024).\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eIn this paper , we presented a detailed analysis of GW230529 a gravitational wave event , describing a range of methodologies to examine the Q-Transform of the gravitational wave event. Our study began with knowing the strain data using gwpy followed by performing Fast Fourier Transform , Amplitude spectral density on the data and lastly performing the time frequency analysis i.e Q-Transforms which revealed significant features in the time interval from \u0026nbsp;-9.8 to -9.3 seconds , displaying a characteristic frequency chirp and energy distribution consistent with a binary merger. The Q-Transform highlighted the inspiral phase with a merger frequency starting around 30Hz and rising to approximately 100HZ showing the involvement of two compact objects of different masses. The pattern which we observed is a suggestive for a neutron star- black hole merger, where the lower mass object is a neutron star and little higher mass object is a black hole. To uphold of finding, we recommend further analysis through match filtering and parameter estimation. Future works will focus on refining these analyses and exploring the implications of this event.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor ContributionHarshith VH: Writing \u0026ndash; original draft, Investigation, Data curation, Visualization, Software, Conceptualization. Ambrose Rajkumar M: Writing \u0026ndash; review \u0026amp; editing, Supervision, Resources.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026quot;This research has made use of data or software obtained from the Gravitational Wave Open Science Center (gwosc.org), a service of the LIGO Scientific Collaboration, the Virgo Collaboration, and KAGRA. This material is based upon work supported by NSF\u0026apos;s LIGO Laboratory which is a major facility fully funded by the National Science Foundation, as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. KAGRA is supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) in Japan;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNational Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea; Academia Sinica (AS) and National Science and Technology Council (NSTC) in Taiwan.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbac, A.G., Abbott, R.,Abouelfettouh, I., et al. 2024, ApJL, 970,L34\u003c/li\u003e\n\u003cli\u003eKoustav, C., Ish, G., Rossella, G., et al. 2024, arXiv, 2,15\u003c/li\u003e\n\u003cli\u003eDuncan M. M., Joseph S. A., Scott B. C., et al. 2021, SoftwareX, 13, 100657 \u003c/li\u003e\n\u003cli\u003eCornish, N.J., 2020, Physical Review D, 102(12), p.124038\u003c/li\u003e\n\u003cli\u003eChatterji, S., Blackburn, L., Martin,G., 2004, Classical and Quantum Gravity, 21, S1809\u003c/li\u003e\n\u003cli\u003eAbbott, B.P., Abbott, R., Abbott, T.D., et al. 2016, Classical and Quantum Gravity, 33, 134001\u003c/li\u003e\n\u003cli\u003eBlackburn, L., Cadonati, L., Caride,S., et al, 2008, Classical and Quantum Gravity, 25, 184004\u003c/li\u003e\n\u003cli\u003eLeah, V., \u0026amp; Derek, D., 2023, Classical and Quantum Gravity, 40, 035008\u003c/li\u003e\n\u003cli\u003eDavis, D., Areeda, J.S., Berger, B.K., et al, 2021, Classical and Quantum Gravity, 38, 135014\u003c/li\u003e\n\u003cli\u003eAcernese, F., Agathos, M., Ain, A., et al, 2022, arXiv, 2205.01555\u003c/li\u003e\n\u003cli\u003eSiddharth, S., Ethan, M., Erik K., et al. 2023, Classical and Quantum Gravity, 41\u003cstrong\u003e,\u003c/strong\u003e 015012\u003c/li\u003e\n\u003cli\u003e\u0026Eacute;anna, \u0026Eacute;., Flanagan \u0026amp; Scott A. H., 1998, Phys. Rev. D 57, 4535\u003c/li\u003e\n\u003cli\u003eJin-Ping, Z., Rui-Chong, H., Yacheng, K., et al. 2024, ApJ, 974, 211\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Q-Transform, Gravitational wave astronomy","lastPublishedDoi":"10.21203/rs.3.rs-7045919/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7045919/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe gravitational wave event GW230529 was analyzed using the Q-transform method to isolate the signal and examine its properties. The data used for this analysis was collected from LIGO Livingston. The Q-transform methodology, implemented in Python, began with acquiring strain data and revealing its frequency components using FFT. Key features of the signal over time, including its duration and frequency evolution, were presented. Additionally, the three phases of the event inspiral, merger, and ring-down were analyzed using the Q-transform method. This study demonstrated the effectiveness of the Q-transform method in gravitational wave analysis, highlighting its potential for analyzing complex signals. The results underscored the significance of using Python-based Q-transform techniques for these studies.\u003c/p\u003e","manuscriptTitle":"Q-Transform Analysis of GW230529","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-18 14:10:23","doi":"10.21203/rs.3.rs-7045919/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ec5c83d7-fefc-490b-ac9b-6d210d645d69","owner":[],"postedDate":"July 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-05T17:38:34+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-18 14:10:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7045919","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7045919","identity":"rs-7045919","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}