Ultra-wideband submillimeter observations are crucial to study the process of star and galaxy formation and for characterizing cosmic dust in the interstellar medium. The Deep Spectroscopic High-redshift Mapper 2.0 (DESHIMA 2.0) will use an integrated superconducting spectrometer chip with a 220-440 GHz band coverage and a spectral resolution of f/df = 500, enabling submillimeter observations with an unprecedented instantaneous band coverage. However, the octave bandwidth of DESHIMA 2.0 poses a challenge: the atmospheric transmission is highly nonlinear in the broad frequency window of DESHIMA 2.0, complicating the removal of atmosphere noise from the signal. In this thesis, I present the Time-dependent End-to-end Model for Post-process Optimization (TiEMPO). TiEMPO provides realistic time-dependent simulations of high-redshift galaxy observations. It consists of the following components: Galaxy model. A galaxy is modeled using a two-component modified blackbody spectrum as a template. The model outputs the flux density, which is converted to power spectral density using the frequency-dependent effective aperture area of the telescope. Atmosphere model. TiEMPO makes use of atmosphere model ARIS, which models a spatially and dynamically varying atmosphere and outputs Extra Path Length. TiEMPO converts this to precipitable water vapor using a relation that was found with the Smith-Weintraub value of the Extra Path Length and the ideal gas law. Telescope beam. TiEMPO can be adapted to use any arbitrary beam shape for the near-field telescope beam. The far-field beam is modeled using the effective aperture area. Finally, the output of TiEMPO is given at multiple positions, enabling simulations of sky chopping and nodding in two directions. Radiation transfer. A static model of the sensitivity of DESHIMA, determining the attenuation and the emission of the atmosphere and transmitting the signal through each component of the telescope and instrument. Spectrometer chip. TiEMPO can adopt any filter transmission of the channels inside a spectrometer chip. In this work, they are approximated with Lorentzian curves. The photon and recombination noise are modeled with the NEP and the noise distribution is approximated with a normal distribution. The noise is incorporated with an integration over the filter response, treating photon-bunching over the wide bandwidth of DESHIMA 2.0 accurately. Conversion to sky temperature.Finally, the power measured in the chip is related to the sky temperature with an interpolation made with a skydip simulation in the radiation transfer model. We compare the first TiEMPO simulations to observation data by comparing the time signal, power spectral density and noise equivalent flux density. Apart from a small offset in the power spectral density, the simulation data closely resembles the observation data. TiEMPO allows us to test algorithms for atmosphere removal and galaxy detection, to study the effect of different weather conditions and to evaluate the performance of different observing techniques. TiEMPO is modular, making it usable for the original DESHIMA instrument and its successor DESHIMA 2.0. The use of TiEMPO can be extended to other spectrometers besides DESHIMA 2.0, like a grating spectrometer, and other telescopes, such as the promising 50m-aperture AtLAST/LST telescope.