Unfolding-synthesis technique for digital pulse processing, Part 2: Synthesis

Abstract

Pulse shaping is an important step in the unfolding-synthesis technique. In this paper we present efficient digital pulse-shaping algorithms that utilize repeated sum polynomials. These algorithms address the most common constraint in pulse shape synthesis — the finite duration of the pulses. The presented digital methods for efficient real-time synthesis use only basic digital signal processing functions (addition, constant multiplication, and shift), thereby minimizing required signal processing resources. A differentiation technique to decompose pulse shapes defined by polynomials is presented and used to synthesize arbitrary trapezoidal/triangular pulse shapes. The synthesis of rational, exponential, trigonometric and other non-polynomial defined pulse shapes can be approximated in real time. A methodology to approximate non-polynomial defined pulse shapes is described, and Gaussian and sinusoidal pulse shapes are synthesized via polynomial approximation and linear interpolation. The pulse shape synthesis algorithms are presented in recursive form and are suitable for efficient implementation by using integer only arithmetic.