The further study about the conversion theory from the unilateral laplace transform to the fourier transform

In the traditional signal theory, the conversion formulas from the unilateral Laplace transform expression to the Fourier transform expression are classified according to the unilateral Laplace transform expressionpsilas poles which are located on the imaginary axis of the s-plane being or not being repeated when sigma₀ (the abscissa of convergence) equals to zero. It has been pointed out that the traditional conversion theory was not rigorous, and an improved theory has been put forward. But the improved theory is not convenient to use because of the double sum symbols in the formula. In this paper another improved conversion theory is put forward and the original classifying idea is forsaken.