In this paper, a hybrid time-frequency analysis method, specially developed to decompose harmonic subgroups and interharmonics of the electric arc furnace (EAF) currents, which are highly time varying due to the operation principles of the EAFs, is presented. The main objective is accurate perception of harmonics and interharmonics in cases of rapid changes or power quality (PQ) events in power system voltages and currents. Harmonic and interharmonics detection has been achieved using discrete wavelet transform (DWT), which provides time-localization in cases of highly time-varying signals. Although DWT elicits accurate spectral decomposition at low frequencies, and especially at the baseband, bandwidths of the band-pass filters increase which results in loss of accuracy at higher frequencies. In order to avoid this problem, power signals are modulated by complex exponential waveforms, which corresponds to shifting the required harmonic sub-band contents to the baseband, where the accuracy of the DWT is the best. Using the proposed hybrid combination of DWT and complex exponential modulation, time domain waveform of each harmonic sub-band of the EAF currents can be estimated close to ideal values. The method also enables to focus on any required inter-harmonic sub-band in addition to the harmonics. To optimize the performance of the DWT in cases of PQ events, various windowing approaches are discussed. The proposed harmonic and interharmonic estimation method has been verified on both synthetic data and EAF currents collected from the electricity transmission system. Estimated harmonic and interharmonic waveforms can serve as a good reference in many areas including active power filtering operations, limit violation determinations, etc., in the power system.