The contribution of this paper is two-fold. First, it introduces a new orthogonal series approach to the state-space analysis of linear time-invariant systems. This approach yields explicit expressions for the state and output vector coefficient matrices. These expressions only involve the multiplication of matrices of small dimensions. No algebraic system of equations needs to be solved, and therefore no inversion of large matrices is required here, as compared to other known techniques. The second contribution consists of using this new orthogonal series technique to solve the state-space identification problem. It is shown that by appropriately manipulating the aforementioned state-space analysis results, an algorithm is derived which yields the state-space system matrixA. This algorithm gives a new outlook and a better insight into the state-space identification problem.