在代数信号处理中可以定义不同的平移算子,建立不同的信号模型,每个信号模型有其对应的滤波,卷积,谱,傅里叶变换等相关的信号处理概念.文中定义了一种新的平移算子,基于该平移算子建立了基于Legendre正交多项式的无限1-D Legendre信号模型和有限1-D Legendre信号模型,并给出了该模型中傅里叶变换,谱以及频率响应等的具体概念.

Various shifts can be defined in the algebraic signal processing, based on this, different signal models are established. Each signal model has its own corresponding signal processing concept of filtering, convolution, spectrum, Fourier transform and others. In this papper, a new shift was redefined and established a new signal model-infinite and finite one-dimensional algebraic signal processing model based on Legendre polynomial. The specific concepts of Fourier transform, spectrum and frequency response in this signal model were also derived.