Authors' reply to comments on "The inverse S-transform in filters with time-frequency localization"

Pinnegar points in his comment to a mistake in our paper on the inverse S-transform. It seems, in fact, that the error should mainly be attributed to the discretization of the S-transform, not to our inverse S-transform. Pinnegar bases his approach on the discrete S-transform by using its representation in the frequency domain. It is shown in an accompanying paper by Simon et al that there are differences whether one discretizes the S-transform using the time-domain or the frequency-domain expression. As a consequence, both inverse S-transforms suffer from different small artifacts. There are no changes in the physics, understanding, and conclusions of our publication.