Falsification has garnered much interest recently as a way to validate complex CPS designs with respect to a specification expressed via temporal logics. Using their quantitative semantics, the falsification problem can be formulated as robustness minimization problem. To make this infinite-dimensional problem tractable, a common approach is to restrict to classes of signals that can be defined using a finite number of parameters, such as piecewise-constant or piecewise-linear signals with fixed time intervals). A major drawback of this approach is that when the input signals must satisfy non-trivial temporal constraints, encoding these constraints into bounded domains for parameters can be difficult. In this work, to better capture temporal constraints on the input signal space, we use timed automata (TA) and make use of a transformation that allows sampling TA traces by sampling points in the unit box. We exploit this transformation to efficiently encode constrained CPS signals in the robustness minimization problem. This transformation also allows us to define an effective coverage measure of the constrained signal space so as to provide quantitative guarantees when no falsifying behaviour is found. In addition, this coverage is used to improve the black-box optimisation performance by detecting situations where the search is stuck near a local optimum. The approach is demonstrated on a ∆Σ modulator and a model of car automatic transmission subject to constraints describing usual driving patterns.