Extended Instantaneous Spectral Analysis (E-ISA) for Advanced Signal Processing
Amr Elsonbaty, Anis Allagui, Ahmed S. Elwakil · IEEE Transactions on Instrumentation and Measurement · 2022
This work is devoted to introducing an extended form of the instantaneous spectral analysis (ISA) technique recently reported. ISA is based on the extension of Euler’s formula$e^{jx}=\cos (x)+j\sin (x)$to fractional powers of$j$of the special form$e^{j^{a}x}$with$a=2^{(2-m)}$and integer values of$m$. Here, we generalize the technique to the case where the exponent$a$in the extended Euler’s formula is an arbitrary fraction${m}/{n}$, where$m$and$n$are integers with no common factors. Hence, we propose an extended form of ISA (E-ISA), which is not restricted to the values of$a= 0.5, 0.25, 0.125\ldots$Compared to the standard Fourier transform (FT), E-ISA is shown to be more suitable in dealing with nonergodic signal sources having nonstationary spectra. In addition, the bandwidth utilized by E-ISA is much smaller than the corresponding one in standard FT. Application of E-ISA to synthetic data, an electrocardiogram signal, and nonstationary current time series data from a submerged electrochemical microplasma system are demonstrated.