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QUESTION: What are the advantages of using modified sine wave products? Modified sine wave products are initially more economical than true sine wave products. In addition, MSW inverters have the advantage when the load is a simple induction load like a motor, or a resistive load like a light bulb.
In either case you don't need to deal with the absolute value. A rectified sine wave is a periodic signal with a period equal to half of the full sinusoid, I would write the sine in exponential form and integrate over one period to find the series coefficients.