## 2 Non-Parameterized Time-Frequency Analysis
### Short-Time Fourier Transform
#### 2.1.2 Application  
First, the integration with classical models elevates their performance to a higher level while better aligning with signal characteristics. For instance, a method that first processes the signal using STFT and further integrates it with Google-Net CNN [4] demonstrated in its experimental results that this innovation not only enhances the accuracy of signal processing but also effectively reduces the false alarm rate. Another study significantly improved diagnostic accuracy by combining STFT with CNN [5]. These achievements fully showcase the unique advantages of STFT in enhancing signal processing performance.  
Furthermore, significant breakthroughs have been made in optimizing the time-frequency resolution of STFT. The introduction of the ASTFT-CMGW-FVVA method [6], which employs multi-window techniques and linear frequency modulation Gaussian windows, notably improves time-frequency resolution, enabling more refined signal analysis. Meanwhile, the integration of STFT into models has played a pivotal role in bearing health assessment and enhancing the time resolution of PET detectors. An autoencoder modeling approach based on STFT and ensemble strategies [7] effectively extracts deep vibration features of bearings. Another study combined STFT with residual neural networks [8], significantly improving time-of-flight estimation and coincidence time resolution for PET detectors.  
STFT also plays a crucial role in sparse representation and synchrosqueezing transforms. By combining these techniques with STFT, researchers have achieved optimized signal processing and applications [9]. This innovation not only expands the application scope of STFT but also introduces new ideas and methods to the field of signal processing. Target localization algorithms represent another important area of STFT application. Researchers have proposed an improved target localization algorithm based on STFT [10], and it significantly enhances the accuracy of target instantaneous frequency estimation and localization by dynamically adjusting the window function and introducing a new distribution estimator.  
Beyond the aforementioned applications, STFT also plays a vital role in signal processing decomposition, linear axis misalignment diagnosis, and train wheel anomaly detection. A decomposition method based on STFT [11] was shown to improve the time and frequency resolution of signal processing. Another study, based on servo motor current data and an STFT-based linear axis misalignment diagnosis method [12], had the aim of diagnosing faults without using sensors and external data collection systems but rather by capturing motor current data from the servo motor of the machine. Additionally, a train wheel anomaly detection method using STFT and unsupervised learning algorithms [13] was shown to effectively monitor wheel health. Furthermore, STFT has been applied to analyze multi-time scale variations [14], further expanding its application scope.  
Notably, researchers have also conducted innovative studies by combining STFT with fractal theory and the uncertainty principle. They have investigated the fractal uncertainty principle of STFT and Gaussian windows [15] and explored its application in discrete Gaussian Gabor multipliers. This innovation not only provides new perspectives and methods for STFT research but also brings new insights to the study of fractal theory and the uncertainty principle.  
Some researchers have introduced ST-QPFT and studied the fundamental properties and uncertainty inequalities of STFT, contributing to the field of short-time quadratic-phase Fourier transforms [16]. Another study proposed the FrFTSG method related to short time fractional Fourier transforms [11], improving the time and frequency resolution of signal processing.