Function generator
First Claim
1. Apparatus for generating an output digital signal that approximates the value of a predetermined mathematical function lying in the X-Y plane at a point defined by an input digital signal comprising:
- position storage means having stored therein a plurality of precalculated points, Ri, each lying on a different linear least-means-squares line segment approximating a different section of the mathematical function, said position stroage means having an input connected to receive at least a portion of the input digital signal, and an output, for providing an output signal at the output thereof representative of an appropriate one of the stored precalculated points in response to the input of at least the portion of the input digital signal;
slope storage means having stored therein the plurality of precalculated slopes, Si, each defining the slope of a different one of the line segments, said slope storage means having an input connected to receive at least a portion of the input digital signal, and an output, for providing an output signal at the output thereof representative of an appropriate one of the stored slopes in response to the input of at least the portion of the input digital signal;
means having an input connected to receive at least a portion of the input digital signal and an output, for determining the distance, Δ
X, along the X axis, from the point Ri to the point defined by the input digital signal and providing at the output thereof an output signal representative of Δ
X;
multiplication means connected to the outputs of said slope storage means and said distance determining mean for providing on an output thereof an output signal which is the product, Si Δ
X, of the applied output signals, andsumming means connected to the outputs of said position storage means and said multiplication means for providing on an output thereof an output signal which is the sum, Ri +Si Δ
X, of the output signal applied thereto and which is an approximation of the value of the mathematical function at the point defined by the input digital signal.
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Accused Products
Abstract
Apparatus for generating an output digital signal that approximates the value of a predetermined mathematical function lying in the X-Y plane at a point defined by an input digital signal. The mathematical function is approximated by a plurality of linear least-mean-square line segments each of which includes a central point, R, and a slope, S, with the desired point being defined by the equation F(X) approximates R+SΔX, where ΔX is the X distance between the central point R and the desired point. R, S and ΔX are precalculated and stored in PROM lookup tables and combined as stated in the above equation.
49 Citations
6 Claims
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1. Apparatus for generating an output digital signal that approximates the value of a predetermined mathematical function lying in the X-Y plane at a point defined by an input digital signal comprising:
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position storage means having stored therein a plurality of precalculated points, Ri, each lying on a different linear least-means-squares line segment approximating a different section of the mathematical function, said position stroage means having an input connected to receive at least a portion of the input digital signal, and an output, for providing an output signal at the output thereof representative of an appropriate one of the stored precalculated points in response to the input of at least the portion of the input digital signal; slope storage means having stored therein the plurality of precalculated slopes, Si, each defining the slope of a different one of the line segments, said slope storage means having an input connected to receive at least a portion of the input digital signal, and an output, for providing an output signal at the output thereof representative of an appropriate one of the stored slopes in response to the input of at least the portion of the input digital signal; means having an input connected to receive at least a portion of the input digital signal and an output, for determining the distance, Δ
X, along the X axis, from the point Ri to the point defined by the input digital signal and providing at the output thereof an output signal representative of Δ
X;multiplication means connected to the outputs of said slope storage means and said distance determining mean for providing on an output thereof an output signal which is the product, Si Δ
X, of the applied output signals, andsumming means connected to the outputs of said position storage means and said multiplication means for providing on an output thereof an output signal which is the sum, Ri +Si Δ
X, of the output signal applied thereto and which is an approximation of the value of the mathematical function at the point defined by the input digital signal. - View Dependent Claims (2, 3, 4, 5, 6)
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Specification