made an account to ask about this >The Laplace Transform, on the other hand, decomposes a signal into both its exponential factors in what sense is this true?

made an account to ask about this >The Laplace Transform, on the other hand, decomposes a signal into both its exponential factors in what sense is this true? yes the s in e^(-st) is complex but that factors the kernel of the transform into e^(-at)e^(-iwt). individually the factors do what you say (decompose over a basis) but as a product they do not do that.