  Direct imaging of exoplanets presents a formidable technical challenge owing
to the small angular separation and high contrast between exoplanets and their
host stars. High Dispersion Coronagraphy (HDC) is a pathway to achieve
unprecedented sensitivity to Earth-like planets in the habitable zone. Here, we
present a framework to simulate HDC observations and data analyses. The goal of
these simulations is to perform a detailed analysis of the trade-off between
raw star light suppression and spectral resolution for various instrument
configurations, target types, and science cases. We predict the performance of
an HDC instrument at Keck observatory for characterizing directly imaged
gas-giant planets in near infrared bands. We also simulate HDC observations of
an Earth-like planet using next-generation ground-based (TMT) and spaced-base
telescopes (HabEx and LUVOIR). We conclude that ground-based ELTs are more
suitable for HDC observations of an Earth-like planet than future space-based
missions owing to the considerable difference in collecting area. For
ground-based telescopes, HDC observations can detect an Earth-like planet in
the habitable zone around an M dwarf star at 10$^{-4}$ starlight suppression
level. Compared to the 10$^{-7}$ planet/star contrast, HDC relaxes the
starlight suppression requirement by a factor of 10$^3$. For space-based
telescopes, detector noise will be a major limitation at spectral resolutions
higher than 10$^4$. Considering detector noise and speckle chromatic noise,
R=400 (1600) is the optimal spectral resolutions for HabEx(LUVOIR). The
corresponding starlight suppression requirement to detect a planet with
planet/star contrast=$6.1\times10^{-11}$ is relaxed by a factor of 10 (100) for
HabEx (LUVOIR).
