Residue to analog converter

Details Residue to analog converter Residue to analog converter

1984-09-24

1986-04-22

Shoop, Jr., William M.

Communications: electrical

Audible indication

Percussion-type sound producer

340347M, 364746, H03M 112

Patent

active

045845646

ABSTRACT:
A residue to analog converter associated with residue numbers {m1,m2,m3} of the RNS defined by the moduli set {p1=2.sup.n -1, p2=2.sup.n, p3=2.sup.n +1} comprises a pair of ROMs and a pair of standard binary adders. The first ROM stores a look-up table of summations, taken modulo p1*p2, of possible values of m1*S3 and m3*S1 product terms, where S1=(p1*p2)/2 and S3=(p2*p3)/2, with associated memory locations being addressed by m1 and m3. The first binary adder performs a modulo 2.sup.n summation of a binary signal stored by the first ROM and -m2 by ignoring any overflow. The second ROM stores a look-up table of possible values of the products of p1, p3 and the modulo 2.sup.n signal. The second binary adder sums output signals of the two ROMs for producing a binary signal r(m1,m2,m3) that is representative of the residue signal {m1,m2,m3}. The corresponding analog signal is produced with a standard D/A converter. In an alternate embodiment, look-up tables of possible m1*S3 and m3*S1 product terms are stored in associated ROMs and summed in a modulo p1*p3 adder. In yet another embodiment, the second ROM is replaced with means for bit shifting the modulo p2=2.sup.n signal prior to subtracting the latter from the bit shifted signal in a standard binary adder which takes overflow into consideration.

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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