Journal
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
Volume 71, Issue -, Pages -Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIM.2022.3165267
Keywords
Cairns basis functions; electrocardiogram (ECG) signal; extended Euler formula; instantaneous spectral analysis (ISA); microplasma signal; nonstationary spectrum
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This work introduces an extended form of the instantaneous spectral analysis technique (E-ISA), which is capable of dealing with nonergodic signal sources with nonstationary spectra and has a smaller bandwidth utilization compared to the standard Fourier transform.
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(jax) 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 min, where in 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...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.
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