Organizations: Graduate School of Integrative Science and Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Department of Physics, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan · Graduate School of Information and Data Science and Department of Design and Data Science, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-ku, Yokohama, Kanagawa 224-8551, Japan · Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
Damped sinusoidal oscillations are widely observed in many physical systems, and their analysis provides access to underlying physical properties. However, parameter estimation becomes difficult when the signal decays rapidly, multiple components are superposed, and observational noise is present. In this study, we develop an autoencoder-based method that uses the latent space to estimate the frequency, phase, decay time, and amplitude of each component in noisy multi-component damped sinusoidal signals. We investigate multi-component cases under Gaussian-distribution training and further examine the effect of the training-data distribution through comparisons between Gaussian and uniform training. The performance is evaluated through waveform reconstruction and parameter-estimation accuracy. We find that the proposed method can estimate the parameters with high accuracy even in challenging setups, such as those involving a subdominant component or nearly opposite-phase components, while remaining reasonably robust when the training distribution is less informative. This demonstrates its potential as a tool for analyzing short-duration, noisy signals.
Figures & tables
Figure 1: Schematic overview of the analysis pipeline, including data generation (left) and the autoencoder architecture (middle and right). For illustration, the figure shows the two-component case.
Case
Explanation
#Components
Training
Validation
Noise level (SNR [dB])
Result
Special setting
2G-sub
2.2.1 , Fig. 2 , Table 3
2
G (8,000)
G (2,000)
1/2(8.8)
3.1 , Fig. 8 , Table 10
Subdominant component
2G-opp
2.2.1 , Fig. 3 , Table 4
2
G (8,000)
G (2,000)
1/23(14.3)
3.1 , Fig. 9 , Table 10
Nearly opposite phases
5G
2.2.2 , Fig. 4 , Table 5
5
G (8,000)
G (2,000)
5(−5.2)
3.2 , Figs. 10 11 , Table 12
1G
2.2.3 , Fig. 5 , Table 6
1
G (4,000)
G (1,000)
1/23(4.6)
3.3.1 , Figs. 12 , 14 , Table 13
1U
2.2.3 , Fig. 5 , Table 6
1
U (4,000)
G (1,000)
1/23(4.6)
3.3.1 , Figs. 13 , 14 , Table 13
2G
2.2.4 , Fig. 6 , Table 7
2
G (990,000)
G (10,000)
1/23(15.7)
3.3.2 , Fig. 15 , Table 14
Table 2: Summary of the cases considered in this study. In the Training and Validation columns, G and U denote Gaussian and uniform parameter distributions, respectively. Numbers in parentheses indicate the numbers of training and validation samples used in each case. The compact descriptive case labels encode the number of components, the training distribution (G or U), and, where applicable, the special setting in the suffix.
Figure 2: Case 1 : A two-component waveform including a rapidly decaying, low-amplitude component.
Figure 3: 2G-opp : A two-component waveform with nearly opposite phases.
Figure 4: 5G : A five-component superposed damped sinusoidal waveform.
Figure 5: 1G and 1U : Training and validation parameter distributions for the single-component case.
Figure 6: 2G and 2U : Training and validation parameter distributions for the two-component case.
Figure 7: 3U : Training and validation parameter distributions for the three-component case.
Case
Learning rate
Encoder epochs
Decoder epochs
2G-sub
0.001
350
200
2G-opp
0.001
500
500
5G
0.005
350
200
1G
0.001
350
400
1U
0.001
350
400
2G
0.0001
250
150
Table 9: Training settings for 2G-sub – 3U .
Figure 8: Results for 2G-sub .
Figure 9: Results for 2G-opp .
Figure 10: Results for 5G .
Figure 11: Scatter plots of the match score against each parameter for 5G .
Figure 12: Results for 1G .
Figure 13: Results for 1U .
Figure 14: Comparison of match scores for 1G (black) and 1U (cyan).
Ringdown gravitational waves from binary black hole mergers can be modeled as superpositions of quasinormal modes (QNMs), whose frequencies and excitation factors encode properties of the remnant Kerr black hole. Reliable extraction of multiple QNM components is challenging because of mode overlap and noise. We develop an autoencoder-based framework for multi-component QNM analysis, in which the latent space is trained to represent the physical parameters of individual modes, enabling waveform denoising and parameter estimation within a common framework. Using controlled model waveforms constructed as finite sums of Kerr QNMs with recently established high-precision frequencies and excitation factors, including their nontrivial spin dependence near resonant excitation, we assess the method across partitioned spin intervals. The model achieves good in-domain waveform reconstruction and parameter recovery for the two longest-lived components of eight-component input waveforms, while its performance degrades when the validation spins lie far outside the training range. In a selected spin interval, the framework also recovers the 32 parameters of an eight-component waveform with good overall agreement. These results demonstrate the feasibility of physics-informed autoencoder-based inference for a prescribed multi-component ringdown waveform family and motivate further tests with progressively more realistic signals.
Momoka Iida, Hayato Motohashi, Hirotaka Takahashi
Graduate School of Integrative Science and Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Department of Physics, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan +2
Denoising of periodic signals and accurate waveform estimation are core tasks across many signal processing domains, including speech, music, medical diagnostics, radio, and sonar. Although deep learning methods have recently shown performance improvements over classical approaches, they require substantial computational resources and are usually trained separately for each signal observation. This study proposes a computationally efficient method based on DCNN and Re-sampling, termed R-DCNN, designed for operation under strict power and resource constraints. The approach targets signals with varying fundamental frequencies and requires only a single observation for training. It generalizes to additional signals via a lightweight resampling step that aligns time scales in signals with different frequencies to re-use the same network weights. Despite its low computational complexity, R-DCNN achieves performance comparable to state-of-the-art classical methods, such as autoregressive (AR)-based techniques, as well as conventional DCNNs trained individually for each observation. This combination of efficiency and performance makes the proposed method particularly well suited for deployment in resource-constrained environments without sacrificing denoising or estimation accuracy.
Eli Gildish, Michael Grebshtein, Igor Makienko
RSL Electronics LTD, Migdal Ha'Emek, 23100, Israel
A differentiable digital signal processing (DDSP) autoencoder reconstructs a monophonic harmonic sound through three types of synthesis parameters: fundamental frequency, loudness, and timbre features. To handle mixtures of harmonic sounds within the DDSP approach, we have previously proposed a DDSP mixture model (DDSPMM). It represents a mixture as the sum of source signals synthesized by the decoders of pretrained DDSP autoencoders. Although DDSPMM enables direct estimation of synthesis parameters of each source from mixtures, it does not explicitly model temporal variations in the synthesis parameters and can produce excessive temporal fluctuations. In this paper, we propose a method for estimating synthesis parameters with temporally plausible trajectories by incorporating a denoising diffusion probabilistic model (DDPM) into the DDSPMM-based estimation. The DDPM is trained as a generative model of synthesis parameters. During estimation, the proposed method guides the DDPM reverse diffusion process with the reconstruction error between the observed mixture and the mixture synthesized by DDSPMM from the current estimates. Experiments on woodwind and string instrument ensembles showed that the DDPM-based regularization improves synthesis parameter estimation by imposing temporal plausibility on the estimated trajectories.