The High-Resolution Wavelet Transform: A Generalization of the Discrete Wavelet Transforms

The development of the High-Resolution Wavelet Transform (HRWT) is driven by the need of increasing the high-frequency resolution of widely used discrete Wavelet Transforms (WTs). Based on the Stationary Wavelet Transform (SWT), which is a modification of the Discrete Wavelet Transform (DWT), a novel WT that increases the number of decomposition levels (therefore increasing the previously mentioned frequency resolution) is proposed. In order to show the validity of the HRWT, this paper encompasses a theoretical comparison with other discrete WT methods. First, a summary of the DWT and the SWT, along with a brief explanation of the WT theory, is provided. Then, the concept of the HRWT is presented, followed by a discussion of the adherence of this new method to the WT’s common properties. Finally, an example of the application is performed on a transient waveform analysis from a power system fault event, outlining the benefits that can be obtained from its usage compared to the SWT.