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A p p e n d i x Tw o — L a p l ac e T r an s f o r m 469

TABLE A2.3 Convolution laws.
t
d )
g t
Convolution definition Ct () = f t ()* () = ∫ f( ) ( −ξ g t ξ ξ
0
Commutative property f t()* gt() = gt()* f t()
⎤
⎦
⎦
Associativity ft()* ⎡ ⎣ g t()* h t()⎤ = ⎡ ⎣ ft()* g t() * h t()
⎦
Distributivity ft()* ⎡ ⎣ g t() + h t()⎤ = ft()* g t() + ft()* h t()

References
Sneddon, I. N. (1951). Fourier Transforms, McGraw-Hill, NY.
Spiegl, M. R. (1968). Mathematical Handbook, McGraw-Hill, NY.
Swisher, G. M. (1976). Introduction to Linear Systems Analysis, Matrix, Cleveland.