Spurious signals due to amplitude quantization in direct digital frequency synthesizers

Amplitude quantization and phase truncation are two main mechanisms which lead to the occurrence of spurious signals in direct digital frequency synthesizers (DDFSs). These signals are deterministic and periodic in the time domain, so they appear as line spectra in the frequency domain. In this paper, the discrete time versions of two types of spurious signals due to amplitude quantization in DDFSs are expressed and their time-domain characteristics are detailedly analyzed and compared. Then, the spectral properties of the amplitude-quantization spurs in the absence or presence of phase-accumulator truncation are derived by waveform symmetry and uniform-permutation estimation along with discrete Fourier transform. The effects of phase truncation and parameter variation on the amplitude-quantization spurs are studied by computer simulation. The derivation and simulation give strong insight into the spur magnitude and spectral location, and can provide theoretical and empirical supports for practical DDFS implementation and performance evaluation.