Signal Scaling by Centered Discrete Dilated Hermite Functions

We present a novel method to generate centered discrete dilated Hermite functions by utilizing Hermite-Gaussian differential equation and DFT commuting matrix proposed by Pei Compared with the conventional methods, our method provides much higher accuracy and wider working range. Based on expansion of compact support signals into discrete dilated Hermite basis, several examples of signal approximation and scaling are demonstrated. Our results in ECG signal compression can achieve lesser approximation error in comparison with discrete Daubechies wavelet transform. Also, our proposed discrete dilated Hermite functions have better ability to do signal scaling than the existing method.