Enhanced Fourier Transform Using Wavelet Packet Decomposition  

作　　者：Wouladje Cabrel Golden Tendekai Mumanikidzwa Jianguo Shen Yutong Yan Wouladje Cabrel;Golden Tendekai Mumanikidzwa;Jianguo Shen;Yutong Yan(Department of Physics and Electronic Information Engineering, Optical Engineering, Zhejiang Normal University, Jinhua, China;Department of Computer Science and Technology, Software Engineering, Zhejiang Normal University, Jinhua, China;Department of Physics and Electronic Information Engineering, Electronic Engineering, Zhejiang Normal University, Jinhua, China)

机构地区：[1]Department of Physics and Electronic Information Engineering, Optical Engineering, Zhejiang Normal University, Jinhua, China [2]Department of Computer Science and Technology, Software Engineering, Zhejiang Normal University, Jinhua, China [3]Department of Physics and Electronic Information Engineering, Electronic Engineering, Zhejiang Normal University, Jinhua, China

出　　处：《Journal of Sensor Technology》2024年第1期1-15,共15页传感技术（英文）

摘　　要：Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

关 键 词：Fourier Transform Wavelet Packet Decomposition Time-Frequency Analysis Non-Stationary Signals 

分 类 号：O17[理学—数学]