Modern Smart Grids (SGs) are characterized by the simultaneous presence of time-varying and non-linear loads as well as distributed energy sources with power converters which contribute to wide spectra waveform distortions. Moreover, one of the crucial device of the SG architectures is the smart metering systems which utilize high frequencies for the power line communication (PLC) transmission. In particular, the presence of spectral components in the range of 2\div 150kHz (supraharmonics) has recently become an issue of great interest due to the interaction between widespread diffusion of high-spectral emission devices (e.g., end-user devices and converter-interfaced distributed generation systems) and power line communication systems. The complexity of these waveforms distortions makes their assessment a challenge. This paper critically analyses and compares two methods proposed in recent literature which seem particularly suitable for the spectral analysis of waveforms with wide spectra. One of the methods is based on the sliding-window discrete Fourier transform (SWDFT) referring to IEC standard harmonic estimation. The second method utilizes the sliding-window wavelet-modified ESPRIT-based method (SWWMEM). This is a companion document to a paper of the same title, Part II, where the methods are tested on synthetic and measured waveforms in terms of accuracy and computational efforts.