| 摘要 |
Convergent and extrapolated samples are provided for synthesizing sine waves. In a first embodiment, memory having the sine function, sin(x), mapped therein provides convergent samples. Memory size is reduced in a second embodiment by summing the outputs of two memories to produce convergent samples, one memory having an auxiliary function, f(x), mapped therein and a second having the sine function less the auxiliary function, sin(x)-f(x), mapped therein. A sine wave quadrant is conceptually divided into a plurality of uniform phase sectors demarked by boundaries phases. Additional memory provides extrapolation value sets uniquely associated with the sectors. In a given sector, extrapolation samples are produced by serially adding values of the associated extrapolation set to the convergent samples selected in the sector. An auxiliary function is chosen to closely approximate the sine function at at least the sector boundary phases, the difference between it and the sine function never exceeding the dynamic range of the sin(x)-f(x) memory. Each extrapolation value set can define a ramp having a slope closely matching the sine function slope within the set's associated sector. The first embodiment's extrapolation sets are derived from the second terms of Taylor Series expansions of the sine function at sector boundary phases. The second embodiment's extrapolation sets can be likewise derived but are adjusted as needed to compensate for quantization errors introduced by truncating the f(x) samples and limiting there number, both done to reduce memory size.
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