The analytic signal combines a real function f with its Hilbert transform Hf to a complex function \(f+ iHf\) . This idea goes back to Denis Gabor “in order to apply the simple and elegant formalism of quantum mechanics” for an interpretation of Heisenberg’s uncertainty relation in communication theory [4]. It leads to the question, under which conditions two real-valued bases or frames \(\{f_{n} : n\in \mathbb {N}\}\) and \(\{g_{n} : n\in \mathbb {N}\}\) form a complex basis or frame \(\{f_{n} + i g_{n}: n\in \mathbb {N}\}\) ? And more general, for which bounded real linear operators A does \(\{f_{n} + i A f_{n} : n\in \mathbb {N}\}\) form a complex-valued orthonormal basis, Riesz basis or frame, when \(\{f_{n} : n\in \mathbb {N}\}\) is a real-valued orthonormal basis, Riesz basis or frame? We have called this approach rebricking and gave necessary and sufficient conditions in Fink et al. (Proc. Appl. Math. Mech. 23:e202300155, 2023). In this short article, we discuss several illustrating examples of rebricking in finite and infinite dimensional Hilbert spaces.