A fast algorithm for generating sinusoids with polynomial phase

The authors present an algorithm for the generation of frequency-modulation sinusoids (or complex exponentials), which avoids the use of trigonometric or exponential functions. It is shown that a sinusoid (exponential) with a polynomial phase of an arbitrary order N can be recursively generated with N complex multiplications per sample. This result extends a previous algorithm for the generation of complex Gaussian functions and it is derived in a more concise manner. The application of this novel technique in the context of harmonic coding of speech is also briefly described. The proposed technique allows significant computational savings and is therefore important for real-time implementation of harmonic coding algorithms