METHOD OF SYNTHESIZING LOW-FREQUENCY NOISE

• US 3,614,399 A
• Filed: 08/30/1968
• Issued: 10/19/1971
• Est. Priority Date: 08/30/1968
• Status: Expired due to Term

• Current Assignee: John C. Linz
• Original Assignee: John C. Linz
• Inventors: Linz, John C.
• Primary Examiner(s): Morrison, Malcolm A.
• Assistant Examiner(s): Gottman, James F.
• Application Number:
  US04/756,519
• Time in Patent Office: 1,145 Days
• Field of Search: 235/152 328/27 331/78 307/220
• US Class Current: 708/250
• CPC Class Codes: G06F 7/58 Random or pseudo-random number generators

Abstract

A method of synthesizing low-frequency noise wherein the lowfrequency noise has a controllable amplitude distribution, so as to be able to select a desired amplitude-level distribution, such as Gaussian, Poisson, or Uniform distribution. The desired amplitude distribution is derived from a digital-random-variable sequence, having a plurality of characteristics, by selecting the characteristic appropriate to the desired amplitude distribution and performing an appropriate digital operation on the selected characteristic.

Claims

1. A method of synthesizing low-frequency noise, having a controllable amplitude distribution, comprising the steps of:

generating a digital-random-variable sequence having a plurality of characteristics;

selecting a desired digital-random-variable-sequence characteristic from the plurality of characteristics;

deriving a desired amplitude-level distribution solely from the selected desired digital-random-variable sequence characteristic, a different characteristic yielding a different desired amplitude-level distribution; and

obtaining the desired low-frequency noise from the derived amplitude-level distribution.

2. A method in accordance with claim 1, wherein the step of generating a digital-random-variable sequence includes the step of:

generating a plurality of two-state, clocked, digital-random variables in which each of the two states has an equal probability of occurrence, the states being binomially distributed.

3. A method in accordance with claim 2, wherein the step of generating a plurality of two-state, clocked, digital-random variables further includes the steps of:

generating a plurality of analog-random variables; and

deriving the plurality of two-state, clocked, digital-random variables from the generated plurality of analog-random variables.

4. A method in accordance with claim 2, wherein the step of generating a plurality of two-state, clocked, digital-random variables includes the step of:

generating a pseudo-random-binary sequence.

5. A method in accordance with claim 2, wherein the step of selecting a desired digital-random-variable characteristic includes the stops of:

determining a sampling interval and obtaining digital information, from the selected characteristic during the determined sampling interval, equivalent to an amplitude level of the desired amplitude-level distribution.

6. A method in accordance with claim 5, wherein the step of deriving a desired amplitude-level distribution includes the steps of:

storing the obtained digital information during the determined sampling interval while the next successive digital-information equivalent is obtained during the next determined sampling interval.

7. A method in accordance with claim 6, wherein the steps of deriving a desired amplitude-level distribution further includes the step of:

converting the stored, obtained, digital information into an equivalent, analog-amplitude level of the desired amplitude-level distribution.

8. A method in accordance with claim 7, wherein the step of determining a sampling interval includes the further steps of:

deriving a transfer pulse; and

transmitting the derived transfer pulse at the completion of the sampling interval.

9. A method in accordance with claim 8, wherein the step of storing the obtained information includes the further steps of:

receiving the transmitted derived transfer pulse; and

storing the obtained, digital information when the transmitted transfer pulse is received.

10. A method in accordance with claim 9, wherein the further step of converting the stored digital information includes the still further step of:

converting the stored digital information into the equivalent, analog-amplitude level of the desired amplitude-level distribution, when the transfer pulse is received.

11. A method in accordance with claim 10, wherein the step of obtaining the desired low-frequency reproducible noise includes the step of:

filtering the converted equivalent, analog-amplitude level by passing the converted level through a low-pass filtering means.

12. A method in accordance with claim 11, wherein the further step of transmitting the derived transfer pulse at the completion of the sampling interval includes the still further step of:

transmitting the derived transfer pulse at a rate equivalent to at least twice the cutoff frequency of the low-pass filtering means.

13. A method in accordance with claim 12, wherein the still further step of transmitting the derived transfer pulse at a rate equivalent to at least twice the cutoff frequency of the low-pass filtering means includes the still further step of:

transmitting at a rate greater than twice the cutoff frequency so as to provide guard bands.

14. A method in accordance with claim 13, wherein the step of obtaining digital information during the sampling interval includes the further step of:

obtaining the digital information within the entire sampling interval.

15. A method in accordance with claim 14, wherein the step of storing the obtained, digital information during the determined sampling interval includes the further step of:

storing the obtained, digital information during the entire determined sampling interval.

16. A method in accordance with claim 15, wherein the step of obtaining the desired low-frequency, reproducible noise includes the step of:

controlling the magnitude of the power spectrum of the low-frequency, reproducible noise.

17. A method in accordance with claim 16, wherein the step of obtaining the desired low-frequency, reproducible noise includes the further step of:

controlling the voltage level of the low-frequency reproducible noise obtained.

18. A method in accordance with claim 17, wherein the step of deriving a desired amplitude-level distribution includes the further step of:

driving a 64 level desired amplitude-level distribution.

19. A method in accordance with claim 2, wherein the step of deriving a desired amplitude-level distribution includes the step of:

deriving a Gaussian-amplitude-level distribution.

20. A method in accordance with claim 19, wherein the step of selecting a desired digital-random-variable-sequence characteristic includes the steps of:

determining a sampling interval; and

counting the number of occurrences of one state in the desired sequence during the determined sampling interval, the number of occurrences being the selected sequence characteristic.

21. A method in accordance with claim 20, wherein the step of deriving a Gaussian-amplitude-level distribution includes the further step of:

storing the count during the determined sampling interval at the completion of the count, while the next-successive count is obtained during the next-determined sampling interval.

22. A method in accordance with claim 21, wherein the step of deriving a Gaussian-amplitude-level distribution includes the still further step of:

converting the stored count into an equivalent, analog-amplitude level of the Gaussian-amplitude-level distribution, the counts being binominally distributed.

23. A method in accordance with claim 22, wherein the step of determining a sampling interval includes the further steps of:

deriving a transfer pulse; and

transmitting the derived transfer pulse at the completion of the sampling interval, the completion of the count being at the completion of the sampling interval.

24. A method in accordance with claim 23, wherein the further step of storing the count includes the still further steps of:

receiving the transmitted transfer pulse; and

storing the count when the transfer pulse is received.

25. A method in accordance with claim 24, wherein the further step of converting the stored count includes the still further step of:

converting the stored count into the equivalent, analog-amplitude level of the Guassian-amplitude-level distribution, when the transfer pulse is received.

26. A method in accordance with claim 25, wherein the step of counting the number of Occurrences includes the further step of:

counting the number of occurrences for a plurality of n counting intervals, the number of n counting intervals conforming to the mathematical expression which is a moment-generating function for the Gaussian-amplitude-level distribution.

27. A method in accordance with claim 26, wherein the further step of counting for a plurality of n counting intervals includes the still further step of:

counting for at least 64 counting intervals.

28. A method in accordance with claim 2, wherein the step of deriving a desired amplitude-level distribution includes the step of:

deriving a uniform-amplitude-level distribution.

29. A method in accordance with claim 28, wherein the step of selecting a desired digital-random-variable-sequence characteristic includes the step of:

determining a sampling interval; and

selecting a sequence characteristic which is the probability of particular sequences, a sequence probability satisfying the expression p(s) ( 1/2 )m, where m is the number of bits in the generated-digital-random-variable sequence, the number of bits in the sequence being the sequence length.

30. A method in accordance with claim 29, wherein the step of deriving a uniform-amplitude-level distribution includes the further step of:

storing the particular, generated sequence of m bits during the determined sampling interval at the completion of the generation of the sequence, while the next-successive-particular sequence is being generated, the stored sequence being a binary number, all numbers between limits 0 and 2m-1 having an equal probability of occurrence.

31. A method in accordance with claim 30, wherein the step of deriving a uniform-amplitude-level distribution includes the still further step of:

converting the stored-particular sequence into an equivalent, analog-amplitude level of the uniform-ampltitude-level distribution, the distribution of the amplitude levels approaching a continuous uniform distribution between the limits 0 and 2m-1.

32. A method in accordance with claim 31, wherein the step of determining a sampling interval includes the further steps of:

deriving a transfer pulse; and

transmitting the derived transfer pulse at the completion of the sampling interval, the completion of the sequence being at the completion of the sampling interval.

33. A method in accordance with claim 32, wherein the further step of storing the particular sequence includes the still further steps of:

receiving the transmitted transfer pulse; and

storing the sequence when the transfer pulse is received.

34. A method in accordance with claim 33, wherein the step of converting the stored, particular sequence includes the still further step of:

converting the transferred, stored sequence into the equivalent, analog-amplitude level of the uniform-amplitude-level distribution, when the transfer pulse is received.

35. A method in accordance with claim 34, wherein the still further step of converting the transferred, stored sequence includes the still further step of:

dividing an available voltage source into 2m equally probable discrete steps, each discrete step being a possible amplitude level.

36. A method in accordance with claim 35, wherein the further step of storing a sequence of m bits includes the still further step of:

storing a sequence of six bits in length, m being equal to six.

37. A method in accordance with claim 2, wherein the step of deriving a desired amplitude-level distribution includes the step of:

deriving a Poisson-amplitude-level distribution.

38. A method in accordance with claim 37, wherein the step of deriving a desired amplitude-level distribution further includes the step of:

producing a highly biased binomial distribution which is a function of the original dIgital-random-variable sequence from the selected characteristic.

39. A method in accordance with claim 38, wherein the step of selecting a desired digital-random-variable-sequence characteristic includes the steps of:

selecting the condition when a desired number r of adjacent bits of the generated sequence is the same, the number r being dependent solely on the desired fidelity of the Poisson-amplitude-level distribution; and

transmitting one desired state of a two-state, digital-random variable when the selected condition occurs, the probability of occurrence (p) of the desired state satisfying the expression p 2 r.

40. A method in accordance with claim 39, wherein the step of selecting a desired digital-random-variable-sequence characteristic includes the further steps of:

determining a sampling interval;

receiving the desired state being transmitted; and

counting the number of occurrences of the one-desired state in the desired sequence during the determined sampling interval, the number of occurrences being the selected characteristic.

41. A method in accordance with claim 40, wherein the step of deriving a Poisson-amplitude-level distribution includes the further step of:

storing the count during the determined sampling interval at the completion of the count, while the next-successive count is obtained during the next-determined, sampling interval.

42. A method in accordance with claim 41, wherein the step of deriving a Poisson-amplitude-level distribution includes the still further step of:

converting the stored count into an equivalent, analog-amplitude level of the Poisson-amplitude-level distribution, the counts yielding a highly biased binomial distribution.

43. A method in accordance with claim 42, wherein the step of determining a sampling interval includes the further steps of:

deriving a transfer pulse; and

transmitting the derived transfer pulse at the completion of the sampling interval, the completion of the count being at the completion of the sampling interval.

44. A method in accordance with claim 43, wherein the further step of storing the count includes the still further steps of:

receiving the transmitted transfer pulse; and

storing the count when the transfer pulse is received.

45. A method in accordance with claim 44, wherein the further step of converting the stored count includes the still further step of:

converting the transferred, stored count into the equivalent, analog-amplitude level of the Poisson-amplitude-level distribution, when the transfer pulse is received.

46. A method in accordance with claim 45, wherein the step of selecting the desired digital-random-variable-sequence characteristic includes the further step of selecting the condition having a probability of occurrence of less than one-tenth, the desired number r being equal to at least four.