Method and circuit for calculating multiple of unit value and generating a periodic function

A method of generating a dependent variable of a periodic function whose independent variable is a multiple of a unit U, N times U, by a digital circuit, where U is a rational number and N is a natural number, comprising the steps of:

• providing at least one memory device, a first circuit, and a second circuit;
• storing values A, B, and C in the memory device, where A, B, and C are natural numbers, A>1, B>C and U=A+C/B;
• generating a multiple of C, N times C by the first circuit;
• comparing the value B with the multiple of C by the first circuit;
• generating a multiple of A, N times A by the second circuit;
• modifying, by the second circuit, the multiple of A according to the output of the first circuit;
• and
• extracting a value corresponding to the modified multiple of A from a function table, which represents relationship between the dependent and independent variables of the periodic function and is previously stored in the memory device, as the dependent variable corresponding to the multiple of U.

A digital circuit for generating a multiple of a unit U, N times U, where U is a rational number and N is a natural number, comprising:

• first, second and third registers for storing values A, B and C, respectively, where A, B and C are natural numbers, A>1, B>C and U=A+C/B;
• first and second calculating circuits for generating a multiple of A, N times A, and a multiple of C, N times C, respectively;
• a subtractor for generating a difference between the multiple of C and the value B;
• and
• a modifying circuit for modifying the multiple of A according to the output of the subtractor, wherein the first calculating circuit outputs the modified multiple of A as the multiple of U.

A digital circuit for generating a dependent variable of a periodic function whose independent variable is a multiple of a unit U, N times U, where U is a rational number and N is a natural number, comprising:

• first, second and third register for storing values A, B and C respectively, where A, B and C are natural numbers, A>1, B>C and U=A+C/B;
• first and second calculating circuits for generating a multiple of A, N times A, and a multiple of C, N times C, respectively;
• a subtractor for generating a difference between the multiple of C and the value B;
• a modifying circuit for modifying the multiple of A according to the output of the subtractor;
• and
• a memory device for storing a function table which represents relationship between the dependent and independent variables of the periodic function and for outputting a value corresponding to the modified multiple of on the function table as the dependent variable corresponding to the multiple of U.