Any periodic waveform can be built by summing harmonic sinusoids with chosen amplitudes

Evidence

Equation A1.1 states that, provided we know the correct values for the amplitudes of the sinusoids an and bn, we can add them up to make any periodic signal f(t) we like. Different signals will need different values for an and bn. The act of summing the harmonic sinusoids together to make a signal is called Fourier synthesis. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2740

Categorization

• DEFINE: Names Fourier synthesis and explains the mechanism by which arbitrary periodic signals are constructed.