Lifting-Based Fractional Wavelet Filter: Energy-Efficient DWT Architecture for Low-Cost Wearable Sensors

Abstract

This paper proposes and evaluates the LFrWF, a novel lifting-based architecture to compute the discrete wavelet transform (DWT) of images using the fractional wavelet filter (FrWF). In order to reduce the memory requirement of the proposed architecture, only one image line is read into a buffer at a time. Aside from an LFrWF version with multipliers, i.e., the LFr ${\text{WF}}_{\text{m}}$ , we develop a multiplier-less LFrWF version, i.e., the LFr ${\text{WF}}_{\text{ml}}$ , which reduces the critical path delay (CPD) to the delay $T_a$ of an adder. The proposed LFr ${\text{WF}}_{\text{m}}$ and LFr ${\text{WF}}_{\text{ml}}$ architectures are compared in terms of the required adders, multipliers, memory, and critical path delay with state-of-the-art DWT architectures. Moreover, the proposed LFr ${\text{WF}}_{\text{m}}$ and LFr ${\text{WF}}_{\text{ml}}$ architectures, along with the state-of-the-art FrWF architectures (with multipliers (Fr ${\text{WF}}_{\text{m}}$ ) and without multipliers (Fr ${\text{WF}}_{\text{ml}}$ )) are compared through implementation on the same FPGA board. The LFr ${\text{WF}}_{\text{m}}$ requires 22% less look-up tables (LUT), 34% less flip-flops (FF), and 50% less compute cycles (CC) and consumes 65% less energy than the Fr ${\text{WF}}_{\text{m}}$ . Also, the proposed LFr ${\text{WF}}_{\text{ml}}$ architecture requires 50% less CC and consumes 43% less energy than the Fr ${\text{WF}}_{\text{ml}}$ . Thus, the proposed LFr ${\text{WF}}_{\text{m}}$ and LFr ${\text{WF}}_{\text{ml}}$ architectures appear suitable for computing the DWT of images on wearable sensors.