Claims
- 1. A method for generating at least one sequence of random numbers of 1/f noise, which comprises the steps of:
determining a desired spectral value β; determining a number of the random numbers of the 1/f noise to be generated; determining an intensity constant const; setting a starting value for a running variable n; performing a loop-type repetition until a desired number of elements y(n) of a vector y of length n is calculated from 1/f-distributed random numbers, by the steps of:
increasing a current value of the running variable n by 1; setting a simulation time step [tn−1; tn]; determining elements Cij of a covariance matrix C of dimension (n×n) according to: Cij:=const·(−|tj−ti|β+1+|tj−1−ti|β+1+|tj−ti−1|β+1−|tj−1−ti−1|β+1) i, j=1, . . . , n
determining an inverted covariance matrix C−1 by inverting the covariance matrix C; determining a variable σ in accordance with σ=sqrt(1/e(n,n)), where sqrt denotes a square root function, and e(n,n) denotes an element of the inverted covariance matrix C−1 indexed by (n,n); determining a (0,1)-normally distributed random number which forms an nth component of a vector x of length n; forming a variable μ from first (n−1) components of an nth row of the inverted covariance matrix C−1 and (n−1) elements of the vector y calculated for a preceding (n−1) simulation time step, according to: 24μ:=-y(n-1)T·C=• ,n-1C=n,n-1where y(n−1) denotes first (n−1) elements of the vector y, C·,n−1 denotes the first (n−1) components of the nth row of the inverted covariance matrix C−1, and Cn,n−1 denotes a component of the inverted covariance matrix C−1 indexed by (n,n); and calculating an element y(n) of the vector y of length n from the 1/f-distributed random numbers, according to: y(n)=x(n)*σ+μ.
- 2. A method for generating at least one sequence of random numbers of 1/f noise, which comprises the steps of:
determining a desired spectral value β; determining a number of the random numbers of the 1/f noise to be generated; determining an intensity constant const; setting a starting value for a running variable n; calculating q sequences of the random numbers of the 1/f noise simultaneously, by performing loop-type repetitions until a desired number of elements yk,n of a vector y of length n is calculated from 1/f-distributed random numbers, by the steps of:
increasing a current value of the running variable n by 1; setting a simulation time step [tn−1; tn]; determining elements Cij of a covariance matrix C of dimension (n×n) according to: Cij:=const·(−|tj31 ti|β+1+|tj−1−ti|β+1+|tj−ti−1|β+1−|tj−1−ti−1|β+1) i, j=1, . . . , n
determining an inverted covariance matrix C−1 by inverting the covariance matrix C; determining a variable σ in accordance with σ=sqrt(1/e(n,n)), where sqrt denotes a square root function, and e(n,n) denotes an element of the inverted covariance matrix C−1 indexed by (n,n); determining a quantity q of (0,1)-normally distributed random numbers xk,n which form a respective last component of vectors xk of length n, where k=1, . . . , q, forming q variables μk according to: 25μk:=-y(n-1),kT·C=• ,n-1C=n,n-1where y(n−1),k denotes first (n−1) components of the vectors yk that were calculated for a preceding simulation time step, C·,n−1 denotes the first (n−1) components of the nth row of the inverted covariance matrix C−1, and Cn,n−1 denotes the element of the inverted covariance matrix C−1 indexed by (n,n), where k=1, . . . , q; and calculating q elements yk,n which form a respective nth component of the vector yk of length n from 1/f-distributed random numbers, according to: yk,n=xk,n*σ+μk, where k=1, . . . , q.
- 3. A method for simulating a technical system subject to 1/f noise, which comprises the steps of:
determining random numbers according to claim 1; and using the random numbers for modeling variables present on input channels of the technical system.
- 4. A method for simulating a technical system subject to 1/f noise, which comprises the steps of:
determining random numbers according to claim 2; and using the random numbers for modeling variables present on input channels of the technical system.
- 5. A computer program, comprising:
computer-executable instructions for carrying out the method according to claim 1 for determining the sequences of random numbers of the 1/f noise.
- 6. A computer program, comprising:
computer-executable instructions for carrying out the method according to claim 2 for determining the sequences of random numbers of the 1/f noise.
- 7. A computer-readable data medium having the computer-executable instructions according to claim 5.
- 8. A computer-readable data medium having the computer-executable instructions according to claim 6.
- 9. A downloading method, which comprises the step of:
downloading the computer program according to claim 5 from an electronic data network onto a computer connected to the electronic data network.
- 10. The method according to claim 10, which further comprises using the Internet as the electronic data network.
- 11. A downloading method, which comprises the step of:
downloading the computer program according to claim 6 from an electronic data network onto a computer connected to the electronic data network.
- 12. The method according to claim 11, which further comprises using the Internet as the electronic data network.
- 13. A computer system, comprising:
means for executing the method for determining the sequences of random numbers of the 1/f noise according to claim 1.
- 14. A computer system, comprising:
means for executing the method for determining the sequences of random numbers of the 1/f noise according to claim 2.
- 15. A computer system, comprising:
means for executing the method for determining the sequences of random numbers of the 1/f noise according to claim 3.
- 16. A computer system, comprising:
means for executing the method for determining the sequences of random numbers of the 1/f noise according to claim 4.
- 17. A method for simulating a technical system subject to 1/f noise, which comprises the steps of:
determining random numbers according to claim 1; and using the random numbers for fixing variables present on input channels of the technical system.
- 18. A method for simulating a technical system subject to 1/f noise, which comprises the steps of:
determining random numbers according to claim 1; and using the random numbers for fixing variables present on input channels of the technical system.
Priority Claims (1)
Number |
Date |
Country |
Kind |
100 64 688.3 |
Dec 2000 |
DE |
|
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of copending International Application No. PCT/DE01/04376, filed Nov. 22, 2001, which designated the United States and was not published in English.
Continuations (1)
|
Number |
Date |
Country |
Parent |
PCT/DE01/04376 |
Nov 2001 |
US |
Child |
10601537 |
Jun 2003 |
US |