Two-Dimensional Discrete Fourier Transform with Variable Parameter in the Spatial-Frequency Domain

Пономарева, О. В.; Пономарев, А. В.; Natalia, Smirnova

doi:10.1109/dspa51283.2021.9535997

Cited by 4 publications

(1 citation statement)

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“…A signal can be changed from the time domain to the frequency domain using a mathematical technique [12] called the Fourier transform. It allows us to obtain helpful information about the spectral characteristics of a signal by breaking down a signal into its individual frequency components.…”

Section: Fourier Transformmentioning

confidence: 99%

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Cabrel,

Mumanikidzwa,

Shen

et al. 2024

JST

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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 nonstationary 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.

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Section: Fourier Transformmentioning

confidence: 99%