Recalling that , the output signal from any diagonal state-space model is a linear combination of the modal signals. The two immediate outputs and in Fig.G.3 are given in terms of the modal signals and as
The output signal from the first state variable is
The initial condition corresponds to modal initial state
For this initialization, the output from the first state variable is simply
A similar derivation can be carried out to show that the output is proportional to , i.e., it is in phase quadrature with respect to ). Phase-quadrature outputs are often useful in practice, e.g., for generating complex sinusoids.