Further extension to a time-to-frequency domain matrix formulation

A time-to-frequency domain matrix formulation gives a relation between the coefficients of the numerator and the denominator polynomials of a transfer function of a linear system through a matrix formed from the initial conditions of the impulse response. Using this formulation it is not possible to obtain a transform in the complex frequency domain, even if complete data about the initial conditions of the time response are known. To remove this limitation an extension to the time-to-frequency domain matrix formulation is given. By using this new formulation it is possible to determine the complete Laplace transform if initial conditions of the time response are known.