Digital function generator

Digital function generator apparatus for providing an output Y from an input X according to ##EQU6## where the coefficients A.sub.j are predetermined, said apparatus comprising:

• first means comprising digital memory means for storing and supplying serial digital data representative of said coefficients A.sub.0 through A.sub.n ;
• second and third means comprising, respectively, serial digital adder means and serial digital multiplier means, each of said second and third means having first and second data input means and a data output means, said first data input means of said second means connected for receiving serial digital data from said first means, said first data input means of said third means connected for receiving serial digital data representative of at least one particular value x.sub.i of the input X, said second data input means of said second means connected for receiving serial digital data from said data output means of said third means, and said second data input means of said third means connected for receiving serial digital data from said data output means of said second means;
• fourth means including clock source means and timing generator means receiving the output of said clock source means, said fourth means comprising timing control means for
• i. effecting multiplication by said third means of A.sub.n and X.sub.i such that the output of said third means is serial digital data representative of a first product A.sub.n.sup.. X.sub.i =P.sub.1,
• ii. effecting the addition by said second means of said first product P.sub.1 and A.sub.n.sub.-1 such that the output of said second means is serial digital data representative of a first sum (P.sub.1 +A.sub.n.sub.-1)=W.sub.1,
• iii. effecting the multiplication by said third means of said first sum W.sub.1 and X.sub.i such that the output of said third means is serial digital data representative of a second product W.sub.1.sup.. X.sub.i =P.sub.2,
• iv. effecting the addition by said second means of P.sub.2 and A.sub.n.sub.-2 so that the output of said second means is serial digital data representative of a second sum (P.sub.2 +A.sub.n.sub.-2)=W.sub.2, and
• v. repetitively effecting similar alternating multiplications and additions so as to produce a series of products and sums wherein any particular jth sum W.sub.j is equal to P.sub.j +A.sub.n.sub.-j for j=1 through n, where the jth product P.sub.j =W.sub.j.sub.-1.sup.. X.sub.i and W.sub.0 is defined to be equal to A.sub.n, said fourth means repetitively effecting said multiplications and additions at least until serial digital data representative of the sum W.sub.n.sub.-1.sup.. X.sub.i +A.sub.0 appears at the data output means of said second means, said sum W.sub.n.sub.-1.sup.. X.sub.i +A.sub.0 being equal to ##EQU7##