<title>Numerical Considerations In Integrated Functions</title>

Abstract

The harmonic analysis of binary approximations to trigonometric reference functions employed in digital signal processing functions is described. An analytic representation of the decomposition of sine or cosine functions into elementary rational binary functions is suggested which permits a direct solution to the problem of calculating the harmonics of the error of approximation. For applications, such as ROM based frequency -synthesizers, angle-encoders, and discrete Fourier transformations, the approach illustrated provides a convenient method of relating the precision of functional implementation of microelectronically integrated functions to the harmonic content of the functional error.