Enhanced Fourier Series for Precise Signal Analysis

This study introduces an innovative enhancement to the Fourier series expansion by incorporating novel correction terms. We rigorously examine the relationship between the root-mean-square error (RMSE) and the number of expansion terms, considering various correction frequencies and bandwidths. Our method significantly improves convergence efficiency within a limited bandwidth, thereby optimizing the signal expansion process. When applied to electrocardiography (ECG), this enhanced algorithm demonstrates its capability in detecting noise and improving signal analysis accuracy. This advancement holds potential for refined analysis in various signal processing applications.