切比雪夫多项式在代数信号处理中的应用

On Application of Chebyshev Polynomial in Algebraic Signal Processing

针对切比雪夫多项式零根的插值方法,本文介绍了2个经典的解决切比雪夫插值问题的方案,给出了一种新的基于切比雪夫多项式零根插值的信号重构方法,对信号按照第二型切比雪夫多项式的零根进行非均匀采样,再由采样点得出重建信号,最后给出了这3种方法的仿真实验和误差分析.

Interpolation plays an important role in modern applied mathematical community,among them,the related Chebyshev polynomial interpolation method received much interests.Given that interpolation based on the roots of Chebyshev polynomial has been one of the important contents of signal reconstruction and signal reconstruction has also been the important content of the ASP theory,we introduce two schemes of Chebyshev interpolation,and then give a new kind of signal reconstruction which based on the roots of Chebyshev polynomial（the interpolation is performed based on the Chebyshev nonuniform sampling points associated with the roots of the second kind of Chebyshev polynomial）,at last we give the simulation and error analysis of the three methods.