Optimization of the Quantized Coefficients for DDFS Utilizing Polynomial Interpolation Methods

In this brief, a novel method to find the optimized quantized coefficients for direct digital frequency synthesizers (DDFSs) based on polynomial interpolation methods is introduced. First, a new method is introduced to find the spurious-free dynamic-range upperbound for DDFSs with a polynomial interpolation method, utilizing the discrete Fourier transform and the Chebyshev minimax problem. This method can be modified to obtain quantized coefficients by employing mixed-integer linear programming. In this problem, the polynomial coefficients are presented in a positive sum of powers of two (SPT) and unsigned integer forms. The proposed method is used to design the linear interpolation-based DDFSs with nonuniform segmentations. The VLSI realizations of the designs with nonuniform segmentations are provided, where it is shown that they have a smaller silicon area and higher clock frequencies compared with the state-of-the-art designs reported in literature.