While it becomes more challenging to improve the energy efficiency of incremental delta-sigma data converters (IDCs) from the analog circuit design perspective, we propose two novel linear reconstruction filters for IDCs to enhance their performance in a digital way, including the L${}_{\mathbf{2}}$min${}^{\mathbf{2}}$ filter and its symmetric version, the L${}_{\mathbf{2}}$min${}^{\mathbf{2s}}$ filter. Compared to the classical linear reconstruction filters, such as the cascade-of-integrators (CoI) and cascaded integrator-comb (CIC) filter (an implementation of sinc filter), the proposed filters can achieve efficient quantization and thermal noise suppression, with the lowest thermal noise penalty factor of 1.2 among the high-order linear reconstruction filters. In this paper, we present analytical, numerical, and experimental results to demonstrate the superior performance of the filters for first-order and second-order IDC output reconstruction. The proposed filters are hardware-friendly and example digital implementations in a standard complementary metal-oxide-semiconductor (CMOS) and field-programmable gate array (FPGA) platforms are included in this paper.