Fourier Decomposition for Calculating Fundamental Wave RMS Value, Phase Angle, and Harmonic RMS Values with Phase Angles

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Original text: Fourier decomposition for calculating fundamental wave RMS value, phase angle, and harmonic RMS values with phase angles

Enhanced version: In power systems, Fourier decomposition serves as a critical mathematical technique for calculating the RMS value and phase angle of the fundamental wave, along with the RMS values and phase angles of various harmonic components. This analysis enables better understanding of power signal spectral characteristics and facilitates necessary optimizations and adjustments during power transmission and distribution processes. The implementation typically involves applying Fast Fourier Transform (FFT) algorithms to sampled waveform data, where the fundamental frequency component corresponds to the system's operating frequency (e.g., 50/60 Hz), while harmonics represent integer multiples of this fundamental frequency. Key computational steps include windowing the time-domain signal to reduce spectral leakage, performing FFT to obtain frequency-domain components, calculating RMS values from magnitude spectra, and determining phase angles from complex Fourier coefficients.