## 1 Introduction  
[PERSON]'s General Theory of Relativity, proposed in 1915, predicts the existence of GW, a phenomenon stemming from distant and large-scale astronomical events. The detection of these waves is one of the most significant achievements in contemporary physics. GW are signals characterized by amplitudes smaller than the atomic scale [1, 2, 3, 4, 5, 6, 7, 8]. This minuscule scale poses a formidable challenge for observation, as physical systems at these dimensions are highly susceptible to various sources of noise. However, a groundbreaking moment occurred on 14 September 2015, when the Laser Interferometer Gravitational Wave Observatory (LIGO) [9] collaboration detected the first GW in history. This milestone marked the birth of GW astronomy. Since then, the LIGO-Virgo-Kagra (LVK) collaboration has confirmed almost 100 events in the first, second, and third observing runs, originating from compact binary systems [10, 11]. However, ongoing research is now exploring new sources of gravitational radiation, particularly those generated by stellar explosion events known as CCSN [12; 13; 14]. This source holds the primary observational expectations for our Galaxy as a significant emitter of GW due to its substantial energy release and luminosity [15; 16; 17]. Although CCSN events occur at a relatively low rate in our Galaxy, approximately two per century [18], they have been recorded, studied, and analyzed by astronomers around the world since ancient times [15]. To compensate for the lack of observational data associated with Galactic CCSN, the development of robust computational tools [19], numerical simulation methods [6], and artificial intelligence techniques [20], provides essential information to understand, categorize, and model such systems. In this regard, the numerical simulations of GW from CCSN show that this type of emission is characterized by a strongly stochastic component in its time evolution [1; 4; 6; 7; 8; 17; 21; 22], amplitudes of the order of \(10^{-22}\) m to \(10^{-25}\) m, and the presence of signatures in its time-frequency evolution that can be categorize as deterministic [2; 3; 23] such signatures are known as high-frequency features (HFFs). A central task in GW astronomy involves the classification and quantification of HFFs, along with the correlation of these signals with the physical parameters of the GW source. To achieve this, the implementation of computational routines is crucial. In recent work, such as [3; 24], authors have developed machine learning algorithms to classify different oscillation modes in GW sources originating from CCSN. Furthermore, in [2; 25], a systematic study is presented, which establishes relationships between CCSN GW features in simulated interferometric noise using deep learning techniques. Lastly, Ref. [26] introduces a computational pipeline designed to model GW signals from CCSN events, highlighting specific features with a low computational cost in real interferometric noise. CCSN GW signals can be modulated by the g-mode oscillations inherent to the newly formed neutron star. These oscillations have the potential to imprint a unique signature on the GW signal, thereby offering valuable insights into the characteristics of the neutron star and the underlying mechanisms driving the supernova explosion. Nonetheless, the detection of g-mode signals within CCSN GW presents significant challenges due to their low amplitude and the intricate nature of the overall signal. The current suite of GW detectors, such as LIGO, Virgo, and KAGRA, lack the requisite sensitivity to reliably discern these signals. However, future detectors, including the Einstein Telescope and Cosmic Explorer, are anticipated to possess the enhanced sensitivity necessary to observe these elusive phenomena. The successful detection of g-mode signals could potentially yield profound insights into the equation of the state of dense matter, neutrino emission mechanisms, and the dynamics of core-collapse supernovae.