Codas in Reflection and Transmission Responses and Their Mutual Relations

Obtaining the reflection response including its coda from the transmission response Equation (17) shows that the real part of the reflection response can be obtained from the transmission response. Since the reflection response is causal the imaginary part can be obtained via the Hilbert transform of the real part. Alternatively � � �� � � � � � � � � � � can be transformed to the time domain and subsequently be multiplied by the Heaviside step-function yielding the time domain version of� � � � � � � � � � . We illustrate this with a one-dimensional