We demonstrate a miniaturized broadband spectrometer employing a reconstruction algorithm for resolution enhancement. We use an opto-digital co-design approach, by firstly designing an optical system with certain residual aberrations and then correcting these aberrations with a digital algorithm. The proposed optical design provides an optical resolution less than 1.7 nm in the VIS-channel (400-790 nm) and less than 3.4 nm in the NIR-channel (760-1520 nm). Tolerance analysis results show that the components are within a commercial class, ensuring a cost-efficient design. We build the prototype with a size of 37x30x26 mm3 and demonstrate that by applying a restoration algorithm, the optical resolution can be further improved to less than 1.3 nm (VIS-channel) and less than 2.3 nm (NIR-channel).