A compact multi-energy soft x-ray diagnostic is being installed on the W Environment in Steady-state Tokamak (WEST), which was designed and built to test ITER-like tungsten plasma facing components in a long pulse (∼1000 s) scenario. The diagnostic consists of a pinhole camera fielded with the PILATUS3 photon-counting Si-based detector (≲100 kpixel). The detector has sensitivity in the range 1.6-30 keV and enables energy discrimination, providing a higher energy resolution than conventional systems with metal foils and diodes with adequate space and time resolution (≲1 cm and 2 ms). The lower-absorption cut-off energy is set independently on each one of the ∼100 kpixels, providing a unique opportunity to measure simultaneously the plasma emissivity in multiple energy ranges and deduce a variety of plasma parameters (e.g., Te, nZ, and ΔZeff). The energy dependence of each pixel is calibrated here over the range 3-22 keV. The detector is exposed to a variety of monochromatic sources - fluorescence emission from metallic targets - and for each pixel, the lower energy threshold is scanned to calibrate the energy dependence. The data are fit to a responsivity curve ("S-curve") that determines the mapping between the possible detector settings and the energy response for each pixel. Here, the calibration is performed for three energy ranges: low (2.3-6 keV), medium (4.5-13.5 keV), and high (5.4-21 keV). We determine the achievable energy resolutions for the low, medium, and high energy ranges as 330 eV, 640 eV, and 950 eV, respectively. The main limitation for the energy resolution is found to be the finite width of the S-curve.