Digital first order hold circuit

There is provided a digitally controlled first order hold circuit and waveform synthesizer for digitally controlling the representation of a function over an approximation interval. In accordance with the operation of the invention, the first order hold circuit and waveform generator receives a digital data input signal which contains initial condition data, up/down data, and slope data for the approximation interval. The initial condition data is loaded into an up/down counter which is incremented using counting data at a rate depending on the value of the slope data and in a direction depending on the value of the up-down data. In order to minimize delays arising from data acquistion, two frequency synthesizer circuits are provided such that one frequency synthesizer provides counting data while the other frequency synthesizer receives slope data. During alternating intervals, the other frequency synthesizer circuit provides counting data while the other circuit receives slope data. In addition, long length data input signals covering a plurality of approximation intervals are provided to reduce the demands on a main system central processing unit.