Method of residue to analog conversion

Details Method of residue to analog conversion Method of residue to analog conversion

1984-09-24

1986-04-22

Shoop, Jr., William M.

Communications: electrical

Audible indication

Percussion-type sound producer

340347M, 364746, H03M 112

Patent

active

045845611

ABSTRACT:
In a residue number system defined by the moduli set {p1=2.sup.n -1, p2=2.sup.n, p3=2.sup.n +1}, a method of converting residue numbers {m1,m2,m3} to associated analog signals r(m1,m2,m3) comprises the steps of selecting a first binary signal satisfying the relationships .vertline.m1*S3+m3*S1.vertline..sub.p1*p3 (where the constant S1=p1*p2/2 and S3=p2*p3/2) from a first look-up table; and summing the n less significant bits of this first digital signal and the negative of the residue digit signal m2 in a first binary adder for generating a second binary signal that is representative of the difference therebetween, taken modulo p2. This second binary signal addresses a second look-up table containing third binary signals which correspond to possible values of the product of the second binary signal and p1 and p3. Selected first and third binary signals are summed in a second binary adder for producing a binary output signal r(m1,m2,m3) that is representative of the residue number {m1,m2,m3}. This binary output signal is converted to a corresponding analog signal in a standard D/A converter. In an alternate method, 2n binary 0's are stuffed as less significant bits of the second binary signal prior to subtracting the latter from this bit shifted signal for producing the third binary signal. In yet another method, the first binary signal is obtained by selecting the binary signals m1*S3 and m3*S1 from associated look-up tables prior to summing them modulo p1*p3.

REFERENCES:
W. K. Jenkins, ICASSP 1978, pp. 804-807, "Residue-to-Analog Conversion".
F. J. Taylor et al., CAS 1981, pp. 1164-1169, "Residue-to-Decimal Converter"; IEEE Transactions.
M. A. Soderstrand et al., 1983 IEEE Trans. CAS-30, pp. 903-907, "RNS D/A Converter".
W. K. Jenkins, IEEE Trans. CAS, vol. 25, 1978, pp. 555-562, "Residue-to-Analog Conversion".
Arora et al., Procs. Fifth Symp. on Computer Arithmetic, "Conversion Scheme in Residue Code", 1981, 5/18-5/19.
M. A. Soderstrand et al., ICAS 1984, pp. 1455-1458, "Pipelined IIR RNS Digital Filters".

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