After 20 years of terahertz cross-correlation spectroscopy (THz-CCS), the performance of the systems has been improved to practical relevance by reaching a bandwidth of ~2 THz. For the development of high-performance THz-CCS systems, it is necessary to get a deeper knowledge of the signal generation from incoherent light sources. In this work, the bandwidth, dynamic range, and peak-to-peak amplitude of a THz-CCS systems using a superluminescent diode as light source and a programmable optical filter for spectral shaping was investigated to obtain a better understanding of the relationship between the optical spectrum and the generated terahertz spectrum. By a periodic structuring of the continuous optical spectrum, an enhancement of the peak dynamic range of more than 10 dB was achieved with a bandwidth of 1.6 THz. The experimental results are confirmed by numerical simulations.