A family of smooth rational spline fractal interpolation function (SRFIF) is presented with the help of classical rational cubic spline. Each SRFIF of the family is identified uniquely by the values of vertical scaling factor s i and shape parameters α i and β i , and the shape of the fractal interpolating curves can be constrained and modified by selecting suitable parameters and vertical scaling factor. In order to meet the needs of practical design, a new method is developed to visualize constrained data in the view of constrained curves. In the special case, the methods of linear constraint and quadratic constraint are discussed. Also, convergence analysis shows that SRFIF gives a good approximation to the original function.

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Funding information Liaoning Provincial Education Department fund project under contact lnjc202013In cognitive radio networks, it is a challenge to increase the performance of cooperative spectrum sensing when the number of cognitive users become large.In this paper, a novel spectrum sensing algorithm based on the cognitive users selection strategy and Adaboost classification is proposed by adaptively selecting uncorrelated cognitive radio users with the difference of the maximum degree based on the K-medoids clustering. Since the proposed users selection strategy is based on the correlation evaluation among the cognitive radio users, it is mandatory to have parameters able to measure the correlation among them and divide into distinct clusters. For this, the spatial correlation coefficient and the clustering quality coefficient are proposed to express the correlation characteristics of cognitive radio users in sensing environments. Performance evaluation is conducted through simulations, and the results are shown to the superior detection performance of the proposed CR user selection strategy based on the K-medoids clustering for cooperative spectrum sensing.