The test facility and synchrotron light source ANKA at the Karlsruhe Institute of Technology (KIT) operates in the energy range from 0.5 to 2.5 GeV and can generate brilliant coherent synchrotron radiation in the THz range employing a dedicated bunch length-reducing optic at 1.3 GeV beam energy. The high degree of spatial compression leads to complex longitudinal dynamics and to time evolving sub-structures in the longitudinal phase space of the electron bunches. The results of the micro-bunching instability are time-dependent fluctuations and strong bursts in the radiated THz power. To study these fluctuations in the emitted THz radiation simultaneously for each individual bunch in a multi-bunch environment, fast THz detectors are combined with KAPTURE, the dedicated Karlsruhe Pulstaking and Ultrafast Readout Electronics system, developed at KIT. In this contribution we present measurements conducted to study possible multi-bunch effects on the characteristic bursting behavior of the micro-bunch instability. Supported by BMBF (05K13VKA, 05K16VKA), the HGF (VH-NG-320) and the HIRST.