An iterative algorithm for optimal design of non-frequency-selective FIR digital filters

Abstract

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response (FIR) digital filters based on the windowing method. Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter, the key idea of the algorithm is minimizing the approximation error by successively modifying the design result through an iterative procedure under the condition of a fixed window length. In the iterative procedure, the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration. Because the approximation error can be specified variably, the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain. A design example is employed to illustrate the efficiency of the algorithm.

Exact analysis of spurious signals in Direct Digital Frequency Synthesizers due to amplitude quantization

“…These spurious signals (errors) are deterministic and periodic in the time domain. Therefore, they appear as line spectra (undesired components: spurs) in the frequency domain [11] . Amplitude quantization, being present permanently, and phase truncation are the two separate mechanisms which lead to the occurrence of spurs in the NCO.…”