The plans for the second Run of the LHC changes the focus in the Higgs sector from searches to precision measurements. Effective Lagrangians can be used for parameterisation. A signal morphing method is developed to take all parameters into account simultaneously and model interference effects. It provides a continues description of arbitrary physical signal observables such as cross sections or differential distributions in a multidimensional space of coupling parameters. This method is capable of morphing signal distributions and rates based on a minimal orthogonal set of independent base samples and therefore allows to directly fit the coupling parameters that describe the Standard Model and possible non-Standard Model interactions for, for example, the Higgs boson.