基于压缩查找表的高精度正弦信号生成算法

使用直接数字频率综合（direct digital synthesizer, DDS）技术生成正弦信号时，幅度精度与查找表容量两个条件相互制约，由于容量限制，高精度需要的超大容量查找表在实际中往往无法实现。针对该问题，提出了一种基于压缩查找表的高精度正弦信号生成算法。首先,推导了DDS输出信号精度与查找表容量的关系，为查找表的设计提供了理论依据。然后，依据精度需求构造了一种高效的压缩查找表，给出了查找表容量与压缩比的关系。最后，给出了算法的实现流程，通过仿真验证了信号精度及压缩比，信号幅度为10⁶，精度为10^-5时，压缩比达到10⁷倍。

High-precision sine signal generation based on compressed look-up table

When using direct digital synthesizer(DDS) technology to generate sine signals,the amplitude precision and the look-up table scale restrict each other;a large-scale look-up table for high precision output is often impractical owing to the limitation of capacity.To this problem,a high-precision sine signal generation algorithm based on compressed look-up table is proposed.Firstly,an analysis is given between the relationship of the DDS precision and the look-up table scale,which provides theoretical rules for the design of the look-up table.Then,an efficient compressed look-up table is constructed according to the requirement of precision,the relationship between look-up table scale and compression ratio is given.Finally,the implementation of the algorithm is presented,signal precision and compression ratio are confirmed through simulation,for a signal with an amplitude of 106 and a precision of 10-5,the compression ratio of 107 is obtained.