High Spectral Purity Digital Direct Synthesizer Implementation by means of a Fuzzy Approximator

Fuzzy systems are used in many applications because of their implementation simplicity both in software and in hardware. Some papers in literature have shown the behavior of SISO fuzzy systems as function approximators. If the approximation function have certain analytical properties, it can be used to develop interesting solutions of classical problems. In particular, the authors have studied a new method suitable to implement systems whose behavior is described through a function having the derivative continuity. This paper shows how this approach can be used to implement a sinusoidal wave synthesizer that is the core of the digital direct synthesizers (DDS), widely used in modern communications and measurements devices. This work presents how tuning the fuzzy system in order to achieve a very clean sinusoidal wave in output. Both the theoretical behavior of the algorithm and the performance taking into account the errors due to the fixed point arithmetic have been inspected in detail. The results of the simulations and those obtained from the hardware implementation of the device show excellent features especially in the case that a very high spectral purity is required.