Quadrature Modulated (QM) Waveform, Ideal

In a quadrature modulates (QM) system, the QM ideal waveform is the sum of the I and Q component of a signal as follows:

To obtain the QM waveform, the baseband components are modulated orthogonally as

thus

where i(t) and q(t) are the baseband I and Q waveforms, respectively.