Classification of infrasonic signals based on time-frequency representation

1 Introduction

Infrasound refers to sound waves with frequencies below 20 Hz. Due to its physical characteristics—low frequency, low attenuation, and long-distance propagation capabilities—it is widely used in global nuclear explosion monitoring (one of the core technologies of the International Monitoring System under the Comprehensive Nuclear-Test-Ban Treaty), natural disaster early warning, and Earth science research. However, infrasound monitoring for nuclear tests faces significant challenges. Infrasound signals generated by natural phenomena (such as lightning, earthquakes, and volcanic eruptions) and human activities (such as nuclear tests, large-scale chemical explosions, and rocket launches) exhibit certain similarities in duration, waveform morphology, and spectral characteristics, which easily cause interference. Meanwhile, the large-scale deployment of global infrasound monitoring networks and national monitoring stations has led to rapidly increasing data volumes. Traditional manual identification and simple feature-based classification inadequate to meet the demands for real-time processing and accuracy.

Infrasound signal classification methods primarily involve feature extraction and the construction of classification models, with the key to classification accuracy lying in the extraction of effective features. For feature extraction, researchers initially employed various single-feature extraction methods, such as Mel-frequency cepstral coefficients (MFCCs) (Ham et al., 2012), intrinsic mode functions (IMFs) component ratio (Jiang et al., 2014), short-time Fourier transform (STFT) (Fields et al., 2021), wavelet transform (Eckel et al., 2022), Hilbert-Huang transform (HHT) (Luo et al., 2017), information spectral entropy (Li et al., 2016), and wavelet packet decomposition (Jiang et al., 2020), and so on. Due to the complexity of infrasound signal propagation—which is easily influenced by factors such as atmospheric temperature, wind speed and direction, and terrain—relying solely on a single feature is insufficient to capture the global information of infrasound signals, leading to limited classification accuracy. To address this limitation, some scholars (Madankan, 2016; Albert and Linville, 2020; Wu et al., 2020; Meng et al., 2023; Zhang et al., 2023) have adopted multi-feature fusion methods to compensate for the shortcomings of single features and enhance the expressive power of signal features. For the construction of classification models, traditional infrasound signal classify-cation methods often employ support vector machines (SVM) (Chilo et al., 2007; Cannata et al., 2011; Liu et al., 2014; Quanbo LU et al., 2023), decision trees (Chilo et al., 2007; Zhang et al., 2023), K-nearest neighbors (KNN) (Chilo et al., 2007; Bryan et al., 2018; Zhang et al., 2023), random forests (Pásztor et al., 2023), and classifier ensembles (Madankan, 2016) as classification models.

In recent years, convolutional neural networks (CNN) have become a research hotspot in infrasound signal classification due to their capabilities of automatic feature extraction and deep abstract representation. Their application primarily takes two forms. The first approach employs CNN as classifiers to directly categorize pre-manually extracted features. (Tan et al., 2021) extracted features via Welch power spectrum transformation and improved the relatively simple LeNet-5 architecture, achieving a classification accuracy of 82.72% for infrasound events involving chemical explosions and natural earthquakes. Lu and Li (Quanbo and Mei, 2023) proposed a classification model based on variational mode decomposition (VMD) and CNN, which was used to identify three types of signals (earthquakes, tsunamis, and volcanic eruptions) with a classification accuracy of 81%. The second approach is CNN-based end-to-end learning, which automatically extracts features directly from raw or preprocessed infrasound signals and completes classification simultaneously. (Wu et al., 2020) converted four types of infrasound signals—chemical explosions, typhoons, lightning, and noise—into time-frequency images as input to the CNN model, achieving an average recognition accuracy of 96%. Leng et al. (2022) classified five common types of infrasound signals, including debris flow, by generating time-frequency images using continuous wavelet transform (CWT) and directly recognizing them with an improved LeNet-5 network, achieving a recognition accuracy of 84.1%. Yin et al. (2024) proposed an infrasound signal classification method based on STFT and CNN, using this model to identify six types of raw infrasound signals with a recognition accuracy of 96.58%. Whether used solely as a classifier or integrated with both feature extraction and classification, CNN have achieved remarkable results in infrasound signal recognition tasks.

Currently, research on infrasound signal classification primarily focuses on two aspects, one is multi-feature fusion and the other is CNN-based recognition of two-dimensional time-frequency images. Essentially, both approaches aim to enhance information representation capabilities by increasing feature dimensions. Multi-feature fusion methods generate features with clear physical meanings through signal processing techniques, but the effectiveness of these features heavily relies on domain expertise of specialists. The faint nature of infrasound signals increases the difficulty of feature extraction and may lead to handcrafted features failing to capture discriminative information, posing a risk of information loss. Furthermore, such methods often involve feature sets designed for specific scenarios, resulting in limited generalization. In contrast, end-to-end CNN models simplify the classification pipeline by automatically mining deep abstract features directly from infrasound signals. This reduces dependence on expert experience and further improves the universality and transferability of the method.

While end-to-end CNN are conducive to improving the classification performance of infrasound signals, current research still exhibits certain shortcomings. (1) The selection criteria for time-frequency analysis methods lack empirical support. Existing studies only briefly compare the mathematical characteristics of STFT, CWT, and HHT at a theoretical level, directly choosing one method to generate time-frequency images as model input. There is no quantitative analysis of the impact of different time-frequency images on CNN feature extraction under a unified dataset and model architecture. (2) There is a lack of balance between classification performance and efficiency. Most studies focus solely on classification accuracy, neglecting the computational complexity of time-frequency image generation and the impact of model convergence speed on real-time monitoring. To address these issues, this paper carries out the following work.

• Construct a standardized infrasound dataset comprising 2,306 samples containing six types of signals, with uniform sampling rates and preprocessing procedures.
• Implement one-dimensional signal to two-dimensional time-frequency image conversion using STFT, CWT, and HHT, optimizing key parameters for each method to generate high-quality time-frequency images.
• Design a unified multi-scale convolutional CNN architecture to capture features at different scales of time-frequency images, eliminating interference from model disparities in result comparison.
• Systematically compare the efficacy of the three methods across multiple dimensions, using accuracy, precision, recall, F1-score, and Cohen’s Kappa as core metrics, combined with time-frequency image generation time and model convergence speed, to validate the superiority of STFT in real-time classification of noisy infrasound signals.

2 Materials and methods

This study aims to systematically compare the classification performance of different time-frequency representations for infrasound signals. The implementation steps are illustrated in Figure 1. First, we perform simple preprocessing on the raw infrasound signals. Then, we convert the one-dimensional time-series infrasound signals into two-dimensional time-frequency representations using STFT, CWT, and HHT, respectively. Finally, we construct a CNN model with multi-scale convolutional layers to train and test the input time-frequency representations, followed by performance evaluation of the model. The experiment follows the controlled variable principle, ensuring consistency in the dataset, model architecture, and training strategy to guarantee the objectivity of the comparative results.

2.1 Dataset construction and preprocessing

This section briefly introduces the infrasound signal dataset used in the study and describes the data interpolation and normalization processes applied to the dataset.

2.1.1 Data source

The infrasound signal dataset used in this study was collected from infrasound monitoring stations, comprising a total of 2,306 samples. The dataset includes six types of infrasound signals: nuclear test, chemical explosion, volcanic eruption, rocket launch, earthquake, and lightning. The corresponding sample counts are shown in Table 1.

TABLE 1. Infrasound signal dataset.

2.1.2 Data preprocessing

To improve data quality and lay a solid foundation for subsequent signal analysis and model training, we performed simple preprocessing on the infrasound data. The steps are illustrated in Figure 2.

Since the dataset was collected from different monitoring stations, the sampling rates of original infrasound signals are inconsistent. To address this, we applied a shape-preserving piecewise cubic interpolation method to interpolate the infrasound data, unifying the sampling rate of all signals to 100 Hz. This method was chosen because it produces relatively smooth interpolated waveforms while maintaining the convexity requirements of the signals, making the results more consistent with actual signal characteristics.

After interpolating the collected infrasound signals, we further applied a simple normalization process to ensure consistency across data from diverse sources.

2.2 Time-frequency representation generation

After preprocessing the original infrasound signals, we employed three methods—STFT, CWT, and HHT—to convert the preprocessed one-dimensional infrasound signals into two-dimensional time-frequency representations, which serve as inputs to the CNN classification model.

2.2.1 STFT time-frequency representation

Plays a critical role. To quantify the impact of the window function, this study compared the effects of parameters on the quality of time-frequency representations through controlled variable experiments. The overlap rate of the sliding window was uniformly set to 50% to reduce information gaps between adjacent time windows and enhance the continuity of the time-frequency representations. We compared the time-frequency representations of Hamming and Hanning windows with window lengths (L w) and FFT computation points (NFFT), where L w =0.32,1,2.56 (s), NFFT = 512,1024,2048.

Figures 3, 4 show the spectrograms corresponding to different parameters for the Hamming and Hanning windows, respectively (using a chemical explosion signal as an example; the same applies below). For the same window function, when L w is fixed while NFFT is different, the time-frequency representation of the signal shows no significant variation. When NFFT is fixed, increasing L w improves the frequency resolution but reduces the time resolution. For the same L w and NFFT, the Hamming window exhibits faster sidelobe attenuation, resulting in cleaner time-frequency image background (fewer artifacts) and higher resolution in the mid-to-high frequency regions (sharper details). In contrast, the Hanning window has a wider main lobe but smaller spectral leakage, leading to more concentrated energy distribution in low-frequency components. Overall, the Hanning window is more suitable for representing the time-frequency characteristics of noisy infrasound signals, as it provides clearer distinction between target signals and noise.

2.2.2 CWT time-frequency representation

The effectiveness of the wavelet transform depends on the selection of the wavelet basis function. Different wavelet basis functions directly influence the performance of the transformation and the interpretation of the results. To accurately reflect the characteristics of the original signal, selecting an appropriate wavelet basis function is crucial for ensuring feature significance. Although many functions satisfy the basic conditions of wavelet basis, theoretical considerations such as compact support, symmetry, orthogonality, and the order of vanishing moments must be prioritized when selecting wavelet function. However, these properties cannot be simultaneously optimized in practical applications. Therefore, it is necessary to balance orthogonality, compact support, and the order of vanishing moments when choosing wavelet basis functions. Additionally, the frequency distribution, time-domain characteristics, and application requirements of the signal must be comprehensively considered.

Infrasound signals are typically non-stationary and contain both low-frequency sustained oscillations and potential transient impact components. The Morlet wavelet, whose waveform resembles a damped oscillating sine wave, exhibits excellent frequency localization properties and strong “focusing” capabilities in the frequency domain, making it suitable for analyzing sustained oscillations and precise frequency components in infrasound signals. The Mexican Hat (abbreviated as Mexh) wavelet is a real-valued wavelet that is highly concentrated in the time domain, exhibits no oscillations, and is extremely sensitive to transient features such as mutations and spikes in signals. Therefore, this study employs these two wavelets to achieve time-frequency representation of infrasound signals from different perspectives, with scale factors set to 64 and 128.

As shown in Figure 5, the Morlet wavelet time-frequency representation offers higher frequency resolution, with energy more concentrated in the low-frequency region. The Mexh wavelet time-frequency representation provides higher time resolution and exhibits no oscillations (featuring only one main lobe and two side lobes). It captures richer details in the high-frequency region but struggles to clearly distinguish different frequency components for low-frequency infrasound signals with close or precisely resolvable frequencies. When the scale factor increases, the Morlet wavelet time-frequency representation further enhances frequency resolution at the cost of significantly reduced time resolution, making it more suitable for analyzing low-frequency signals. In contrast, the Mexh wavelet time-frequency representation suffers from more severe spectral leakage (side lobe broadening) while maintaining relatively better time resolution.

2.2.3 HHT time-frequency representation

The time-frequency representation based on EMD decomposition, as shown in Figure 6. It clearly demonstrates how the energy of different frequency components in the infrasound signal changes over time. However, the sifting process of EMD is prone to distortion at both ends (start and end points) of the signal, leading to inaccuracies in the IMFs and instantaneous frequencies near the endpoints. This phenomenon is known as the end effect.

2.3 CNN model architecture design

This paper constructs an end-to-end CNN classification model based on a multi-scale feature extraction mechanism. The model architecture, as shown in Figure 7, consists of 4 convolutional modules and 3 fully connected layers.

Each convolutional module comprises four components: a convolutional layer, batch normalization, a max-pooling layer, and a non-linear rectified activation function. The kernel sizes in the convolutional layers are not fixed but gradually decrease. This hierarchically progressive design of kernel sizes effectively captures multi-level feature information from global to local details in the time-frequency images. Batch normalization is applied after the convolutional layers to accelerate model convergence. Max-pooling is used to reduce the dimensionality of the feature maps output by the convolutional layers, decreasing the input dimensions for subsequent network layers and compressing the number of model parameters, thereby enhancing the model’s fault tolerance and computational efficiency. The non-linear rectification function (Leaky ReLU) is employed to non-linearly map the output of the convolutional layers, which not only alleviates the vanishing gradient problem and speeds up training but also effectively prevents information loss caused by feature space compression.

The convolutional modules act as feature extractors, with their primary function being to extract features from the input data. As illustrated in Figure 7, the feature maps from the convolutional modules are flattened and passed through 3 fully connected layers.

The fully connected layers serve as classifiers. As shown in Figure 8, the number of hidden units in the fully connected layers gradually decreases to balance the model’s parameter count and generalization capability, reducing model complexity and preventing overfitting.

2.4 Experimental environment and settings

2.4.1 Experimental environment

The experiments in this study were conducted on a computer running the Windows 10 operating system, equipped with an Intel(R) Core (TM) i9-14900K 3.20 GHz CPU and an NVDIA GeForce RTX 4090 D graphics card (64G memory). Python programming was implemented using Jupyter notebook from Anaconda 1.11.0. The CNN classification model was developed based on the Pytorch 1.12.0 framework.

2.4.2 Experimental settings

The infrasound signal dataset was randomly divided into training, validation, and test sets in an 8:1:1 ratio. In our experiments, the training, validation, and test sets consisted of 1,840, 228, and 236 samples, respectively. During model training, the Adam optimizer was uniformly adopted due to its ease of implementation, relatively low computational cost compared to other optimizers, and ability to handle sparse gradient problems. This study employed a batched training strategy, with the batch size set to 32 for all models and the learning rate set to 0.001. The Cross-Entropy Loss Function was used as the loss function, as it is well-suited for multi-class classification tasks.

2.5 Performance evaluation metrics

Evaluation metrics are tools used to measure the efficiency and performance of classification algorithms. The evaluation metrics employed in this study consist of primary metrics and auxiliary metrics.

2.5.1 Primary metrics

Commonly used performance evaluation metrics for classification models include accuracy, precision, recall, F1-score, and Cohen’s Kappa. Their mathematical expressions are as follows,

Accuracy = T P + T N T P + F P + T N + F N

Precision = T P T P + F P

Recall = T P T P + F N

F 1 − Score = 2 × Precision × Recall Precision + Recall

Cohen ′ s Kappa = P o − P e 1 − P e

Accuracy is a metric used to evaluate the overall classification performance of a model, representing the proportion of correctly predicted samples among all samples. Precision measures the accuracy of the model in predicting positive-class samples, indicating the proportion of actual positive-class samples among those predicted as positive. Recall evaluates the model’s ability to identify positive-class samples, representing the proportion of actual positive-class samples correctly identified by the model. The F1-score is a comprehensive metric that balances both precision and recall, calculated as the harmonic mean of the two. Cohen’s Kappa is a statistical metric used to assess the consistency and reliability of a classifier. Unlike simple accuracy, this coefficient accounts for the effect of chance agreement, providing a more accurate measure of model performance.

2.5.2 Auxiliary metrics

In addition to the commonly used metrics for evaluating classification models, we also utilize two auxiliary metrics to further assess algorithm efficiency: time-frequency representation generation time and model convergence speed. Time-frequency representation generation time refers to the time taken to convert a time-series signal into a time-frequency representation using time-frequency analysis. Model convergence speed is measured by the trajectory of the loss function decline.

3 Experimental results

3.1 Classification performance comparison

Different time-frequency representations were generated using the parameter settings described in above. These representations were used as inputs to the CNN model for training and testing the classification algorithm. This section compares the classification results of different time-frequency methods on the test.

3.1.1 Classification results of STFT + CNN

The performance of the STFT time-frequency representations on the test set after being input into the CNN is shown in Table 2. The classification accuracy is influenced by the choice of window function, window length, and other parameters. Different combinations of window functions, window lengths, and FFT points resulted in significant variations in classification accuracy, ranging from 94.86% to 98.35%. In terms of the impact of the window function, the Hanning window generally outperformed the Hamming window. Regarding parameter sensitivity, the window length had a greater effect on performance than the NFFT. As the window length increased, the accuracy gradually improved.

TABLE 2. Classification results of STFT + CNN.

The Hanning window with a window length of 1 s and NFFT = 1,024 achieved the best classification performance. This parameter combination balanced time resolution (L w =1 s, providing a moderate time window width) and frequency resolution (NFFT = 1,024, achieving a frequency resolution of 0.0977 Hz). It effectively captured the temporal features of short-duration signals while distinguishing subtle frequency differences in low-frequency signals. Additionally, the Hanning window’s minimal spectral leakage made it suitable for the global representation of multi-category infrasound signals.

3.1.2 Classification results of CWT + CNN

The performance of the CWT time-frequency representations on the test set after being input into the CNN is shown in Table 3. The Morlet wavelet slightly outperformed the Mexh wavelet, with an average accuracy improvement of 0.3%, as the time-domain compact support of the Morlet wavelet is more suitable for the impulsive characteristics of infrasound signals. Performance with a scale factor of 64 was better than that with a scale factor of 128, with an average accuracy improvement of 0.6%, as larger scales lead to reduced time resolution, making it difficult for the model to capture the transient features of short-duration signals.

TABLE 3. Classification results of CWT + CNN.

Compared to STFT, the optimal accuracy of CWT (94.02%) was 4.33% lower than that of STFT (98.35%). The primary reason is that the energy distribution of CWT time-frequency representations for signals with multiple frequency components is less uniform than that of STFT, making it challenging for the CNN to extract globally discriminative features.

3.1.3 Classification results of HHT + CNN

The performance of the HHT time-frequency representations on the test set after being input into the CNN is shown in Table 4. The classification accuracy was 93.59%, which is similar to that of CWT. Across the performance metrics—accuracy, precision, recall, F1-score, and Cohen’s Kappa—the classification results of STFT + CNN were superior to those of the other two methods.

TABLE 4. Classification results of HHT + CNN.

3.2 Computational efficiency comparison

3.2.1 Time-frequency representation generation time

In addition to comparing the performance differences of different time-frequency representations in the same classification model, we also compared the time required to generate different time-frequency representations. First, the time required for STFT under different parameter settings was calculated (using a rocket launch signal as an example), as shown in Tables 5, 6. The comparison revealed that when the window function, window length (L w), and NFFT parameters were consistent, the time required for the time-frequency transformation was nearly identical for both window functions. When the window length was fixed, an increase in NFFT inevitably led to an increase in the time required for the time-frequency transformation. For example, when L w =0.32 s and NFFT increased from 512 to 2048, the time increased by approximately 71%. When NFFT was fixed, the time required for the time-frequency transformation gradually decreased as L w increased. For instance, when NFFT = 512 and L w increased from 0.32 s to 2.56 s, the time decreased by approximately 36%. The shortest time required for the time-frequency transformation occurred when the window length was the longest and NFFT was the smallest.

TABLE 5. Comparison of STFT time-frequency representation generation time (Hamming window).

TABLE 6. Comparison of STFT time-frequency representation generation time (Hanning window).

The time required for time-frequency analysis using CWT is shown in Table 7. When the scale factor was consistent, the time required for the Morlet and Mexh wavelet basis functions was similar, with a difference of less than 0.2%. Notably, as the scale factor increased, the time required for both wavelet functions increased significantly, with an approximate 53% increase in time. This is because the length of the wavelet basis increases at larger scales, leading to greater computational load for convolution operations. Compared to STFT, the average time required for CWT was 3.6 times that of the optimal STFT time.

TABLE 7. Comparison of CWT time-frequency representation generation time.

As shown in Table 8, the time required for HHT is positively correlated with the complexity of the decomposition. EMD is an iterative sifting process that is relatively time-consuming, and the computational time of HHT highly depends on the characteristics of the input signal (distribution of extreme points, non-stationarity, and degree of nonlinearity). EEMD requires multiple noise additions and ensemble averaging, while CEEMDAN requires iterative decomposition of noise residuals. Therefore, the time required for these two methods is significantly longer than that for EMD. The average time required for HHT was 65.3 times that of the optimal STFT time, indicating the poorest real-time performance.

TABLE 8. Comparison of HHT time-frequency representation generation time.

3.2.2 Model convergence speed

This section compares the convergence speed of the model when different time-frequency representations are used as inputs, as shown in Figure 9. When STFT time-frequency representations were used as inputs, the overall convergence speed was the fastest. When CWT time-frequency representations were used, the model convergence speed was moderate. When HHT time-frequency representations were used, the convergence speed was the slowest. Figure 10 shows the convergence of the model when different STFT time-frequency representations were used as inputs. From Figures 10A,B, it was observed that the model converged fastest when the window length was 2.56 s and slowest when the window length was 0.32 s. When NFFT = 512, the model converged quickly initially but slightly slower later. When NFFT = 2048, the model converged slightly slower initially but faster later.

Based on the classification accuracy results in Table 2; Figure 10C shows the convergence of models with accuracy exceeding 96%. When the input time-frequency representation was generated using a Hamming window with a window length of 2.56 s and NFFT = 512, the model converged the fastest. When the input time-frequency representation was generated using a Hanning window with a window length of 2.56 s and NFFT = 2048, the model achieved the smallest loss value during convergence. Therefore, considering the evaluation metrics—accuracy, precision, recall, F1-score, Cohen’s Kappa, time-frequency representation computational efficiency, and model convergence speed—the Hanning window with a window length of 1 s and NFFT = 1,024 was identified as the optimal parameter configuration.

4 Discussion

From the perspective of classification performance, we observed a phenomenon: STFT outperforms CWT and HHT in the task of classifying noisy infrasound signals. The core of HHT is EMD, and the inherent limitations of EMD are significantly amplified in noisy environments. As described in above, EMD causes severe distortion at both ends of the signal, and signal noise further exacerbates the unpredictability of the end effect. The essence of EMD is decomposition based on the extreme points of the signal, and noise introduces a large number of spurious extreme points. This means that even minor noise disturbances can lead to completely different IMF sequences in EMD decomposition. More importantly, mode mixing is the most significant issue with EMD. Noise severely disrupts the adaptive decomposition process of EMD, causing one IMF to contain vastly different frequency components or one frequency component to be dispersed across multiple IMFs. This makes the decomposition results highly unstable. For these reasons, the time-frequency representations generated by HHT lack consistency in the presence of noise. Even for two signals of the same category, their time-frequency representations may differ significantly due to minor differences in noise. For a CNN, it is challenging to learn stable and common features from these highly variable time-frequency representations, leading to degraded classification performance. The high resolution of HHT time-frequency representations becomes “high variance” and “instability” in the face of noise.

Although Morlet wavelet time-frequency representations offer high frequency resolution, their oscillatory nature makes them sensitive to periodic signals and equally sensitive to periodic or quasi-periodic noise. Noise energy is also captured by the Morlet wavelet and clearly displayed in the time-frequency representation, forming interfering backgrounds or spurious features. The Mexh wavelet is extremely sensitive to pulses and abrupt changes, and the numerous random spikes in noise are perfectly captured and amplified by the Mexh wavelet, similarly constituting useless and interfering features. CWT provides better resolution than STFT, but this high resolution is a double-edged sword. It amplifies both the features of the true signal and, equally or even more severely, the features of the noise. The resulting time-frequency representations have cluttered backgrounds filled with noise-induced details, significantly reducing the visual and feature-space signal-to-noise ratio. The classifier struggles to distinguish between signal patterns and noise patterns.

In the task of classifying noisy infrasound signals, the disadvantages of STFT conversely become its greatest advantages in this scenario. Hanning or Hamming windows are fixed, with their length and shape unchanged by the signal. Although this sacrifices adaptive resolution, it provides extremely high stability. For the same signal with added noise, the variation in its STFT time-frequency representation is much smaller than that of CWT and HHT. The fixed window function effectively performs filtering or smoothing in the time-frequency plane, and this smoothing naturally suppresses the random fluctuations of noise. Noise in STFT time-frequency representations typically appears as a low-energy, uniform background, rather than forming sharp artifacts as in CWT. For machine learning, STFT produces stable and consistent feature representations. Even when signals of the same category are disturbed by noise, their STFT time-frequency representations remain highly similar in overall patterns and contours. The classifier can more easily capture these macroscopic and robust patterns without being confused by detailed noise.

From the perspective of computational complexity, the essence of STFT is performing FFTs within a series of overlapping fixed windows. FFT is one of the most efficient and optimized algorithms in signal processing, making STFT computationally the most efficient. CWT requires computing the convolution of the signal with a series of wavelet basis functions at different scales. Each scale requires a full convolution operation, and the computational load is linearly related to the number of scales. To cover the low-frequency range of infrasound, a large number of scales are typically needed, further increasing the time required. Thus, the computational load of CWT is much greater than that of STFT. The first step of HHT is EMD, which is an iterative, data-driven process. EMD requires repeated iterations to extract each IMF until the stopping criterion is met. This iterative process is computationally intensive. Moreover, each iteration requires calculating the upper and lower envelopes of the signal (usually via spline interpolation), and the interpolation calculations are also time-consuming. The time required for HHT is similar to or even greater than that of CWT because it lacks optimized computational methods like convolution.

From the perspective of model convergence speed, the convergence speed of the model depends on the quality of the input features. For deep learning models, clear, stable, and consistent features enable the model to learn patterns more quickly. As mentioned earlier, the fixed window of STFT creates a smoothing effect, suppressing random noise details and generating time-frequency representations with high consistency and low variance. The model can easily capture these clear and stable macroscopic patterns, and the gradient descent direction is clear, resulting in fast convergence. The high resolution of CWT amplifies all details, including both signal and noise details. This leads to cluttered backgrounds in the time-frequency representations, filled with irrelevant features. The CWT time-frequency representations of signals of the same category can vary significantly due to differences in noise. The model requires many iterations to learn which features are important and which are noise to be ignored. This introduces uncertainty, causing significant oscillations in the loss function, a tortuous convergence paths, and slower speeds. The sensitivity of EMD to noise causes mode mixing and unstable decomposition results. This means that even for the same signal with slightly different noise, the IMFs decomposed by EMD may be entirely different, leading to significant variations in HHT time-frequency representations. The model receives highly nonlinear and inconsistent features. It struggles to learn reliable patterns because the input features themselves change drastically. This makes it difficult for the model’s loss function to decrease, and it may even fail to converge or become trapped in local minima.

In summary, for the task of classifying noisy infrasound signals, STFT provides cleaner and more robust feature representations for machine learning classifiers due to its stability, consistency, and inherent smoothing and denoising effects. Therefore, STFT + CNN achieves the best classification performance and strong generalization ability, with high computational efficiency suitable for real-time processing. Although HHT and CWT theoretically offer higher time-frequency resolution, their high sensitivity to noise results in low signal-to-noise ratios and unstable features in the generated time-frequency representations, offsetting the advantages of high resolution and instead harming the classifier’s generalization performance. The design of a real-time infrasound monitoring system must balance classification performance and computational efficiency. We recommend choosing the STFT + CNN approach, sacrificing some fine representation capability for nonlinear signals in exchange for high real-time performance and strong generalization.

5 Conclusion

This study employed three classical time-frequency analysis methods—STFT, CWT, and HHT—to convert six categories of original (noisy) infrasound signals (nuclear tests, chemical explosions, volcanic eruptions, rocket launches, earthquakes, and lightning) into two-dimensional time-frequency representations. A multi-scale convolutional neural network model was constructed for classification. Under the same model, the performance and efficiency of the three time-frequency representations were systematically compared, leading to the following conclusions:

• The time-frequency representation method significantly affects the classification performance of CNN. STFT achieves the best overall performance, and the Hanning window with a window length of 1 s and NFFT = 1,024 achieves the optimal balance between time and frequency resolution, enabling the CNN to accurately capture globally discriminative features. The model achieved accuracy, precision, recall, F1-score, and Cohen’s Kappa values of 98.35%, 98.44%, 98.38%, 98.37%, and 0.9751, respectively, on the six categories of infrasound signals, significantly outperforming CWT and HHT (optimal accuracy).
• Computational efficiency varies significantly. The time required to generate STFT time-frequency representations (1.18 s) is much lower than that for CWT and HHT, and the model convergence speed is the fastest (stabilizing within 30 epochs).
• The choice of time-frequency representation is closely related to the application scenario. STFT is the preferred method for real-time scenarios or large-scale data classification due to its fast-processing speed and stable convergence. HHT can be chosen for offline nonlinear analysis, and CWT can be used for low-frequency local feature analysis.

The findings of this study provide important guidance for parameter optimization and method selection for time-frequency analysis methods based on deep learning. They can be directly applied to systems such as nuclear explosion monitoring and disaster warning to improve their accuracy and real-time performance. In the future, we could consider incorporating attention mechanisms to enhance the CNN’s focus on key time-frequency regions, further improving classification performance. Alternatively, we could explore lightweight CNN models to enhance computational efficiency.

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Footnotes

Edited by: Farook Sattar, University of Victoria, Canada

Reviewed by: Quanbo Lu, ChongQing College of Electronic Engineering, China

Huicong Xu, Xi’an University of Science and Technology, China