  Time-delay interferometry (TDI) is essential for space-based gravitational
wave (GW) missions to effectively suppress laser frequency noise and achieve
targeting sensitivity. The principle of the TDI is to synthesize multiple laser
link measurements between spacecraft and create virtual equal-arm
interferometry. This process blends instrumental noises and tunes the response
function to GW, yielding data characterized by TDI combinations. Extracting
signals requires modeling GW signals under TDI operations in the frequency
domain. In this work, we introduce a versatile framework, SATDI, which
integrates simulation and analysis for TDI. The simulation aims to implement
TDI to instrumental noises and GW signals, investigate influential factors in
noise suppressions, and explore GW characterizations across different TDI
configurations. The analysis component focuses on developing robust algorithms
for modeling TDI responses to extract GWs and accurately determine source
parameters. LISA is selected as the representative space mission to demonstrate
the effectiveness of our framework. We simulate and analyze data containing GW
signals from massive black hole binary coalescence, examining data from both
first-generation and second-generation TDI Michelson configurations. The
results not only validate the framework but also illustrate the influence of
different factors on parameter estimation.
