Phase to sine amplitude conversion system and method
First Claim
1. An apparatus for determining an approximation of a sinusoidal amplitude for a given phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by:
- a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements, the apparatus comprising;
(a) a calculation mechanism receiving the signal for generating a set of outputs for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements;
(b) a selector mechanism for selecting (i) one of the set of outputs from the calculation mechanism and (ii) one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; and
(c) an aggregation mechanism for evaluating the approximation of the sinusoidal amplitude as an aggregate of the selected one of the set of outputs from the selector mechanism and the one of the lower vertical-axis bounds.
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Abstract
A phase-to-sinusoid-amplitude conversion system and method for use in, for example, direct digital frequency synthesizer applications. The system and method convert phase data to signal amplitude data using an approximation of the first quadrant of a sine function using a plurality of linear line segments of preferably equal length. Each segment is defined with a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements. Based on the approximation and for a given phase angle a set of values are evaluated, for each linear line segment, representing a product of (i) a horizontal displacement representing a difference between the prescribed phase angle and the lower horizontal-axis bound xi of a selected linear line segment where, for example, xi<X<xi+1 and (ii) each one of the slope elements of the selected linear line segment. The approximation of the sinusoidal amplitude is then obtained by adding one of the sets of values determined above with the lower vertical-axis bound of the selected linear line segment. With appropriate selection of the number of line segments (e.g., integer power of two) and slopes elements (e.g., expressed as a sum of desired powers of two), the operations are computationally efficient and improve spectral purity and reduces implementation costs and power consumption of resulting circuitry.
20 Citations
23 Claims
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1. An apparatus for determining an approximation of a sinusoidal amplitude for a given phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by:
- a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements, the apparatus comprising;(a) a calculation mechanism receiving the signal for generating a set of outputs for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements;
(b) a selector mechanism for selecting (i) one of the set of outputs from the calculation mechanism and (ii) one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; and
(c) an aggregation mechanism for evaluating the approximation of the sinusoidal amplitude as an aggregate of the selected one of the set of outputs from the selector mechanism and the one of the lower vertical-axis bounds. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
- a lower horizontal-axis bound;
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13. In a phase-to-sinusoid-amplitude converter, a method of determining an approximation of a sinusoidal amplitude for a prescribed phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by:
- a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements, the method comprising;(f) evaluating a set of values for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the prescribed phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements; and
(g) aggregating a selected set of values determined in step (a) and a selected one of the lower vertical-axis bounds for a selected linear line segment to form the approximation of the sinusoidal amplitude for the prescribed phase angle. - View Dependent Claims (14, 15)
- a lower horizontal-axis bound;
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16. A computer readable medium having stored thereon computer-executable instructions for determining an approximation of a sinusoidal amplitude for a prescribed phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by:
- a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements, the computer-executable instructions comprising the steps for;(a) step for evaluating a set of values for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the prescribed phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements; and
(b) step for aggregating a selected set of values determined in step (a) and a selected one of the lower vertical-axis bounds for a selected linear line segment to form the approximation of the sinusoidal amplitude for the prescribed phase angle. - View Dependent Claims (17, 18)
- a lower horizontal-axis bound;
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19. An apparatus comprising:
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(a) means for generating a signal approximating a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by;
a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements;
(b) generator means receiving the signal for generating a set of outputs for each one of the plurality of linear line segments as a product of a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and each one of the plurality of slope elements;
(c) selector means for selecting one of the set of outputs from the generator means and one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments;
(d) means for evaluating an approximation of a sinusoidal amplitude as an aggregate of the selected one of the set of outputs from the selector mechanism and the one of the lower vertical-axis bounds; and
(e) means for converting the approximation of the sinusoidal amplitude from the adder means into an analog signal. - View Dependent Claims (20, 21)
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22. In a direct digital frequency synthesizer (DDFS), a method of determining an approximation of a sinusoidal amplitude for a prescribed phase angle, the method comprising:
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(a) generating a signal approximating a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by;
a lower horizontal-axis bound;
a lower vertical-axis bound; and
a slope represented as a sum of a plurality of slope elements;
(b) generating a set of outputs for each one of the plurality of linear line segments as a product of a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and each one of the plurality of slope elements;
(c) selecting one of the set of outputs generated from step (b) and one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; and
(d) evaluating an approximation of a sinusoidal amplitude as an aggregate of the selected one of the set of outputs from step (c) and the one of the lower vertical-axis bounds; and
(e) converting the approximation of the sinusoidal amplitude into an analog signal. - View Dependent Claims (23)
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Specification