The Improvement of the Discrete Wavelet Transform

Discrete wavelet transforms are widely used in signal processing, data compression and spectral analysis. For discrete data with finite sizes, one always pads the data with zeros or extends the data into periodic data before performing the discrete periodic wavelet transform. Due to discontinuity on the boundaries of the original data, the obtained wavelet coefficients always decay slowly, leading to data compression ratios that are significantly lower. In order to solve this issue, in this study, we coupled polynomial fitting into classic discrete periodic wavelet transforms to mitigate these boundary effects.