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Computational spectrometers have mobile application potential, such as on-site detection and self-diagnosis, by offering compact size, fast operation time, high resolution, wide working range, and low-cost production. Although these spectrometers have been extensively studied, demonstrations are confined to a few examples of straightforward spectra. This study demonstrates deep learning (DL)-based single-shot computational spectrometer for narrow and broad spectra using a multilayer thin-film filter array. For measuring light intensities, the device was built by attaching the filter array, fabricated using a wafer-level stencil lithography process, to a complementary metal-oxide-semiconductor image sensor. All the intensities were extracted from a monochrome image captured with a single exposure. A DL architecture comprising a dense layer and a U-Net backbone with residual connections was employed for spectrum reconstruction. The measured intensities were fed into the DL architecture for reconstruction as spectra. We reconstructed 323 continuous spectra with an average root mean squared error of 0.0288 in a 500-850 nm wavelength range with 1-nm spacing. Our computational spectrometer achieved a compact size, fast measuring time, high resolution, and wide working range.