Digital circuit produces rational output pulse rate at fraction of continuous input pulse rate. Output pulses have average rate with least possible deviation from absolute correct time spacing. Circuit uses include frequency synthesizing, fraction generation, and approximation of irrational sequences

Cohn, M.

Even, S.

Lincoln, S. J.

English

NASA Technical Reports Server

INPUT FROM
A FIXED CLOCK
OUTPUT: 
SMOOTH 
SEQUENCE 
GATE (TYP) 
August 1971
	 Brief 71-10304 
NASA TECH BRIEF 
Manned Spacecraft Center
	
-4r 
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commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
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be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
A Continued Fraction Generator for Smooth Pulse Sequences 
an-I
a1 COUNTER (TYP) 
Continued Fraction Generator 
The problem: 
To develop a simplified digital circuit to produce 
a rational output pulse rate at a fraction of a continuous 
input pulse rate. In addition, the output pulses must be 
smooth, i.e., have an average rate with the least possible 
deviation from the absolute correct time spacing. 
The solution: 
A digital circuit consisting of counters which pro-
duce one pulse for every ai of input pulses received, 
and inhibit gates which set as conductors unless a pulse 
appears on the inhibit line. In which case, the next input 
pulse is blocked but reset for the following pulse. The 
value of the at's are determined from an algorithm.
How it's done: 
Let A/B be a given pulse rate when A is the num-
ber of output pulses desired and B is the number of 
input pulses. A/B is given in lowest terms and 0 <A/B < 1. 
The a1 's are simply the coefficients of the simple con-
tinued fraction for A/B and can be derived from the 
Euclidean Algorithm. To find the at's, let the quotient 
be a ai and the remainder r1. 
B
- a + r 1 where Oigr1<'A 
Next, divide A by r1, 
a2 + r2 where 0:^r2<r1 
rl
(continued overleaf) 
Now
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https://ntrs.nasa.gov/search.jsp?R=19710000303 2020-03-17T02:21:39+00:00Z
And 
r1 
- 
= a3 + r3
 where 0:!^r3<r2 
r2 
Then in general, 
rn3
= a 1 + ml 
rn2 
And, 
ml 
n-1 = an (rn is thefirst remainder to be zero) 
Finally, the rate A/B can be described by: 
A
	 1 
B	 a1+	 1 
a2 +	 1 
a3 +	 1 
a4 +	 1 
an 
-I
an
Notes: 
1. This configuration is believed to be, on the average, 
more economical than previous devices, yet has all 
the advantages of the previous configurations. 
2. Smooth pulse sequences are described by A. J. Lin-
coln, S. Even, and M. Cohn in "Smooth Pulse Se-
quences, "Proceeding of the Third Annual Princeton 
Conference on Information Sciences Systems, 1969. 
3. Possible uses for this circuit include frequency syn-
thesizing, the generation of fractions, and the ap-
proximation of irrational sequences. 
4. Requests for further information may be directed to: 
Technology Utilization Officer 
Manned Spacecraft Center, Code JM7 
Houston, Texas 77058 
Reference: TSP71- 10304 
Patent status: 
No patent action is contemplated by NASA. 
Source: Martin Cohn, S. James Lincoln and 
Shirnon Even 
Sperry Rand 
under contract to 
Manned Spacecraft Center 
(MSC-13697) 
Brief 71-10304	 Category 01


A continued fraction generator for smooth pulse sequences

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