On the SFDR Upperbound in DDFS Utilizing Polynomial Interpolation Methods

In this brief, the theoretical analysis that obtains the upperbound of the spurious free dynamic range (SFDR) of the direct digital frequency synthesizers (DDFSs) with phase-to-sine mapper (PSM) structured by polynomial interpolation is revisited. A complete analysis of the SFDR upperbound of these DDFS architectures was provided by Ashrafi and Adhami in 2007, where the authors formulated the SFDR upperbound as the Chebyshev minimax solution to an overdetermined system of linear equations. However, some issues in finding the Chebyshev minimax solution were not made clear in that paper regarding the minimax error at the fundamental harmonic of the output sinusoid. These issues, along with the erroneous behavior of numerical computation packages used for solving the Chebyshev minimax problem, misled Chau and Chen to claim that the results of the aforementioned paper were wrong. This brief clarifies the issues with the original paper, exhibits the problems with some of the available numerical computation packages, and refutes the claims that Chau and Chen made.