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This paper presents designs for both bit-parallel (BP) and digit-serial (DS) precision-optimized implementations of the discrete wavelet transform (DWT), with specific consideration given to the impact of depth (the number of levels of DWT) on the overall computational accuracy. These methods thus allow customizing the precision of a multilevel DWT to a given error tolerance requirement and ensuring an energy-minimal implementation, which increases the applicability of DWT-based algorithms such as JPEG 2000 to energy-constrained platforms and environments. Additionally, quantization of DWT coefficients to a specific target step size is performed as an inherent part of the DWT computation, thereby eliminating the need to have a separate downstream quantization step in applications such as JPEG 2000. Experimental measurements of design performance in terms of area, speed, and power for 90-nm complementary metal-oxide-semiconductor implementation are presented. Results indicate that while BP designs exhibit inherent speed advantages, DS designs require significantly fewer hardware resources with increasing precision and DWT level. A four-level DWT with medium precision, for example, while the BP design is four times faster than the digital-serial design, occupies twice the area. In addition to the BP and DS designs, a novel flexible DWT processor is presented, which supports run-time configurable DWT parameters.