CROSSDEF level v crossing definitions and nomenclature Definition of level v crossing: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the figure below denote local minimum, maximum, first value, last value, down- and up-crossing, respectively. The remaining sampled values are indicated with a '.'. Values that are identical with v, but do not cross the level is indicated with the letter 'o'. We have a level up-crossing at index, k, if x(k) < v and v < x(k+1) or if x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 where di is the index to the previous downcrossing. Similarly there is a level down-crossing at index, k, if x(k) > v and v > x(k+1) or if x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1 where ui is the index to the previous upcrossing. The first (F) value is a up crossing if x(1) = v and x(2) > v. Similarly, it is a down crossing if x(1) = v and x(2) < v. M . . M M . . . . . . F d . . L ----------------------u-------d-------o--------------------- level v . . . . u . m m See also perioddef, wavedef, tpdef, findcross, dat2tp

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level v crossing definitions and nomenclature |

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level v crossing definitions and nomenclature |

001 % CROSSDEF level v crossing definitions and nomenclature 002 % 003 % Definition of level v crossing: 004 %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 005 % Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the 006 % figure below denote local minimum, maximum, first value, last 007 % value, down- and up-crossing, respectively. The remaining 008 % sampled values are indicated with a '.'. Values that are identical 009 % with v, but do not cross the level is indicated with the letter 'o'. 010 % 011 % We have a level up-crossing at index, k, if 012 % 013 % x(k) < v and v < x(k+1) 014 % or if 015 % x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 016 % 017 % where di is the index to the previous downcrossing. 018 % Similarly there is a level down-crossing at index, k, if 019 % 020 % x(k) > v and v > x(k+1) 021 % or if 022 % x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1 023 % 024 % where ui is the index to the previous upcrossing. 025 % 026 % The first (F) value is a up crossing if x(1) = v and x(2) > v. 027 % Similarly, it is a down crossing if x(1) = v and x(2) < v. 028 % 029 % M 030 % . . M M 031 % . . . . . . 032 %F d . . L 033 % ----------------------u-------d-------o--------------------- level v 034 % . . . . u 035 % . m 036 % m 037 % 038 % See also perioddef, wavedef, tpdef, findcross, dat2tp 039 040 % history: 041 % by Per A. Brodtkorb 19.09.1999 042 043 more on 044 help crossdef 045 more off 046

Mathematical Statistics

Centre for Mathematical Sciences

Lund University with Lund Institute of Technology

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