Conventional undulators are used in synchrotron light sources to produce radiation with a narrow relative spectral width as compared to bending magnets or wigglers. The spectral width of the radiation produced by conventional undulators is determined by the number of undulator periods and by the energy spread and emittance of the electron beam. In more compact electron sources like for instance laser plasma accelerators the energy spread becomes the dominating factor. Due to this effect these electron sources cannot in general be used for high-gain free electron lasers (FELs). In order to overcome this limitation, modified undulator schemes, so-called transverse gradient undulators (TGUs), were proposed and a first superconducting TGU was built at Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany. In this paper simulations of the expected synchrotron radiation spectral distribution are presented. An experimental test with that device is under preparation at the laser wakefield accelerator at the JETI laser at the University of Jena, Germany.