Method and system for generating a trigonometric function

A system for determining a trigonometric value for an angle, comprising:

• an angle separator operable to separate an input angle into a first component angle and a second component angle;
• a generator component coupled to the angle separator and operable to establish one or more trigonometric values of a set of trigonometric values associated with the first component angle and the second component angle, the generator component comprising a component selected from a group consisting of:
• a comparator operable to compare the second component angle to a predetermined threshold to determine the at least one trigonometric value;
• and
• a sine beta device operable to determine the at least one trigonometric value;
• one or more multipliers coupled to the generator component and operable to generate one or more intermediate values of a set of intermediate values in accordance with the one or more trigonometric values;
• and
• one or more adders coupled to the one or more multipliers and operable to determine an output trigonometric value of a set of output trigonometric values in accordance with the one or more intermediate values.

A system for determining a trigonometric value for an angle, comprising:

• means for receiving an input angle;
• means for separating the input angle into a first component angle and a second component angle;
• means for establishing one or more trigonometric values of a set of trigonometric values associated with the first component angle and the second component angle, at least one trigonometric value established according to a procedure selected from a group consisting of:
• comparing the second component angle to a predetermined threshold to determine the at least one trigonometric value;
• and
• determining the at least one trigonometric value at a sine beta device;
• means for generating one or more intermediate values of a set of intermediate values in accordance with the one or more trigonometric values;
• and
• means for determining an output trigonometric value of a set of output trigonometric values in accordance with the one or more intermediate values.

A method for determining a trigonometric value for an angle, comprising:

• receiving an input angle;
• separating the input angle into a first component angle and a second component angle at an angle separator, the first component angle corresponding to one or more most significant bits, the second component angle corresponding to one or more least significant bits, a number of bits corresponding to the first component angle being approximately equal to a number of bits corresponding to the second component angle;
• establishing one or more trigonometric values of a set of trigonometric values associated with the first component angle and the second component angle, the set of trigonometric values consisting of a first cosine value of the first component angle, a second cosine value of the second component angle, a first sine value of the first component angle, and a second sine value of the second component angle, at least one trigonometric value established according to a procedure selected from a group consisting of:
• comparing the second component angle to a predetermined threshold to determine the at least one trigonometric value by comparing the second component angle to the predetermined threshold, by determining that a cosine value of the second component angle comprises a greater cosine value if the second component angle is less than the predetermined threshold, and by determining that the cosine value for the second component angle comprises a lesser cosine value if the second component angle is greater than the predetermined threshold;
• and
• determining the at least one trigonometric value at a sine beta device by establishing a ratio of a maximum sine value of the second component angle to an angle corresponding to the maximum sine value of the second component angle, and by multiplying the second component angle by the ratio to generate a sine value of the second component angle;
• setting a first trigonometric value of the one or more trigonometric values to a constant selected from a group consisting of a maximum cosine value and a minimum cosine value;
• retrieving a second trigonometric value of the one or more trigonometric values from a lookup table, the retrieved trigonometric value corresponding to an angle within a range of zero to two divided by pi, and calculating a new trigonometric value in accordance to the retrieved trigonometric value, the new trigonometric value corresponding to an angle within a range of two divided by pi to two pi;
• generating one or more intermediate values of a set of intermediate values at one or more multipliers in accordance with the one or more trigonometric values, the set of intermediate values consisting of a first intermediate value generated by multiplying the first cosine value with the second cosine value, a second intermediate value generated by multiplying the first sine value with the second sine value, a third intermediate value generated by multiplying the first sine value with the second cosine value, and a fourth intermediate value generated by multiplying the first cosine value with the second sine value;
• determining an output trigonometric value of a set of output trigonometric values at one or more adders in accordance with the one or more intermediate values, the set of output trigonometric values consisting of a cosine value of the input angle determined by subtracting the second intermediate value from the first intermediate value, and a sine value of the input angle determined by adding the third intermediate value and the fourth intermediate value;
• generating a trigonometric waveform signal in accordance to the determined output trigonometric value;
• and
• transmitting the trigonometric waveform signal using a transmitter.

A system for generating a trigonometric function, comprising:

• an angle separator for separating the input angle into a first component angle and a second component angle;
• a look-up table storing sine values corresponding to the first component angle and cosine values corresponding to the first component angle;
• a sine-beta device for determining a sine value for the second component angle independent of a look-up table;
• a multiplier for multiplying a sine value for the first component angle and a sine value for the second component angle to produce a first multiplier output and to multiply a cosine value for the first component angle and the sine value for the second component angle to produce a second multiplier output;
• an adder to subtract the first multiplier output from the cosine value for the first component angle to produce a cosine value for the input angle and to add the second multiplier output and the sine value for the first component angle to produce a sine value for the input angle;
• and
• a function generator for generating the trigonometric function based upon the sine value for the input angle and the cosine value for the input angle.