The conventional direct digital frequency synthesizer (DDFS) based on polynomial approximations has a very high complexity. This paper describes a low complexity DDFS with a high spectral purity. It is based on the cubic spline approximation for sine and cosine functions, exploiting the symmetry of the sine function. The proposed DDFS offers maximum smoothness of the output signal and has a high SFDR (spurious free dynamic range) of about 121.7 dBc.Keywords -DDFS, cubic spline, spurious free dynamic range, frequency control word (FeW), quarter wave symmetry.