A ROM-less direct digital frequency synthesizer based on fifth-degree Bezier curve approximation

We report here fifth-degree Bezier curve approximations by genetic algorithm for sine amplitudes that computes the amplitudes from phase values ranging from 0 to π/2. The full period of a sine wave is generated by exploiting the quarter wave symmetry. Sine waves generated by this technique are spectrally very pure, and are produced without ROM in a direct digital frequency synthesizer (DDS). It produces sine waves with a maximum error in amplitude of order 7.6×10
^-06
that is lesser than errors introduced in any typical DDS based sine wave output. DDS circuitry is designed in the Simulink environment. Spectral analysis shows that worst case spurious free dynamic range (SFDR) for a sinusoid is -132 dBc.