Asymmetric waveforms require combining sine and cosine coefficients into one spectrum

Evidence

However, there are many functions that are neither odd nor even. They will have both a sine and a cosine part to their Fourier series. So in order to plot the magnitude frequency spectrum in this case, we must combine the two coefficients as follows: The Fourier coefficients discussed earlier are not found by trial and error. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2749

Categorization

• DEFINE: Clarifies why two coefficient sets must be merged into a single magnitude spectrum for asymmetric signals.