Numerically controlled oscillator using quadrant replication and function decomposition

A function generator for generating generally sinusoidally shaped waves approximately 90.degree. out of phase comprising:

• (a) a pair of coarse digital read-only memories, each having an address input and an output, for storing a plurality of digital values coarsely defining one quadrant of a first sinusoidal wave, approximately one-half of the values being stored in each of said coarse memories;
• (b) a pair of fine digital read-only-memories, each having an address input and an output, for storing a plurality of digital values which when added to predetermined values stored in said coarse memories substantially define the one quadrant of the first sinusoidal wave, approximately one-half of the values being stored in each of said fine memories;
• (c) digital addition means connected to the outputs of said coarse and fine memories for combining output values therefrom to substantially define the one quadrant of the first sinusoidally shaped wave and one quadrant of a second sinusoidally shaped wave 90.degree. out of phase with the first wave;
• (d) digital logic means connected to said addition means for shifting the combined output values to substantially define second, third and fourth quadrants of the first and second sinusoidal waves in response to control signals supplied thereto;
• and
• (e) address generating means having outputs connected to said coarse and fine memories and to said logic means for addressing stored values in said coarse and fine memories in a forward sequence to generate the one quadrant of the first sinusoidal wave and for addressing stored values in said coarse and fine memories in a reverse sequence to generate the one quadrant of the second sinusoidal wave, and for supplying control signals to said logic means to generate continuous sinusoidal waves.

A function generator for generating generally sinusoidally shaped waves having a digitally controlled frequency comprising:

• (a) coarse digital memory means, having an address input and an output, for storing a plurality of digital values, sin X and cos X, generally defining one quadrant of a sine and a cosine wave;
• (b) fine digital memory means, having an address input and an output, for storing a plurality of digital values, YcosX and YsinX;
• (c) digital addition means connected to the outputs of said coarse and fine memory means for combining output values therefrom in accordance with the equations
• sin (X+Y)=sin X+Y cos X
• cos (X+Y)=cos X-Y sin X
• to substantially define one quadrant of each of the sinusoidal waves;
• (d) digital logic means, including multiplexers, having the single quadrant of the sin (X+Y) and cos (X+Y) waves supplied thereto and connected for selecting from the single quadrants and inversions of the single quadrants, in response to control signals supplied thereto, to provide continuous sine and cosine sinusoidal waves;
• and
• (e) address generating means having outputs connected to said coarse and fine memory means and to said logic means for addressing stored values in said coarse and fine memory means in a correct sequence to generate the one quadrant of each of the sinusoidal waves in the addition means and for supplying control signals to said logic means to generate continuous sinusoidal waves.

A method of generating generally sinusoidally shaped waves having a digitally controlled frequency and phase comprising the steps of:

• (a) storing a plurality of values defining coarse approximations, sin X and cos X, of a single quadrant of each of sinusoidally shaped waves, sin (X+Y) and cos (X+Y), respectively;
• (b) storing a plurality of fine adjustments, Y cos X and Y sin X, which when added to predetermined coarse values substantially define the single quadrants of the sinusoidally shaped waves;
• (c) receiving a digital input signal dictating the desired frequency and any phase changes;
• (d) generating coarse and fine digital addresses for retrieving stored coarse and fine values in a correct sequence to generate the single quadrants of the sinusoidal waves at the dictated frequency in accordance with the received signal, the generated digital addresses also containing bits for controlling combining of the single quadrants to form continuous sinusoidal waves;
• and
• (e) retrieving and adding the stored coarse and fine values in the sequence dictated by the digital addresses and combining the single quadrants to provide continuous sinusoidally shaped waves.