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The one-dimensional new Mersenne number transform (NMNT) was proposed for the calculation of error free convolutions and correlations for signal processing purposes. The aim of this paper is to develop the split-radix decimation-in-time algorithm for fast calculation of the onedimensional NMNT with a sequence length equal to a power of two. The arithmetic complexity of this algorithm is analysed and the number of multiplications and additions is calculated. An example is given to prove the validity of the algorithm and the exact nature of this transform.

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Surface texture is one of the most important morphology properties of coarse aggregates. It has an important effect on the performances of asphalt mixtures, such as the stiffness modulus and high temperature stability. Accurate characterization of the coarse aggregate texture is important for the quality control of coarse aggregates and the design of asphalt mixtures. The two-dimensional (2-D) image analysis method has been used to study the texture property of coarse aggregates in the past two decades. Because of the spatial and mesoscopic properties of the surface texture of coarse aggregates, the traditional 2-D image analysis method is not accurate enough to characterize the texture. In this study, a three-dimensional (3-D) image analysis method (Laplacian smoothing algorithm) was employed to study the coarse aggregate texture property based on the high-precision 3-D image. A minor improvement was added into the Laplacian smoothing algorithm to determine the smoothing scale. Three parameters (deviation limit, iteration number, and smoothness level) are used in the improved Laplacian smoothing algorithm to control the final smoothing result. The 3-D images with the precision of 0.05 mm and 0.1 mm of two sizes of limestone aggregates and two sizes of basalt aggregates were used to study the effect of the three parameters on the smoothing results. The optimal combination of the three parameters was determined based on the parameter study. The results indicate that the deviation limit should be set to 3%, the iteration number should be set to 1, and the smoothness level should be set to 1. A preliminary discussion on the scanning precision was presented based on the 3-D aggregate images with the precision of 0.05, 0.1, 0.2, and 0.5 mm. The results indicate that the 3-D images with average point spacing greater than or equal to 0.2 mm cannot provide sufficient texture details for the evaluation.