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-/Limits [(equation.5.12a) (equation.5.14b)] +/Names [(equation.4.10) 732 0 R (equation.4.11) 733 0 R (equation.4.12) 741 0 R (equation.4.13) 742 0 R (equation.4.14) 743 0 R (equation.4.15) 744 0 R] +/Limits [(equation.4.10) (equation.4.15)] >> endobj 906 0 obj << -/Names [(equation.5.15) 817 0 R (equation.5.2) 769 0 R (equation.5.3) 770 0 R (equation.5.4) 775 0 R (equation.5.4a) 776 0 R (equation.5.4b) 777 0 R] -/Limits [(equation.5.15) (equation.5.4b)] +/Names [(equation.4.16) 754 0 R (equation.4.17) 755 0 R (equation.4.18) 757 0 R (equation.4.18a) 758 0 R (equation.4.18b) 759 0 R (equation.4.18c) 760 0 R] +/Limits [(equation.4.16) (equation.4.18c)] >> endobj 907 0 obj << -/Names [(equation.5.4c) 778 0 R (equation.5.5) 779 0 R (equation.5.5a) 780 0 R (equation.5.5b) 781 0 R (equation.5.5c) 782 0 R (equation.5.6) 783 0 R] -/Limits [(equation.5.4c) (equation.5.6)] +/Names [(equation.4.18d) 761 0 R (equation.4.2) 689 0 R (equation.4.3) 691 0 R (equation.4.3a) 693 0 R (equation.4.3b) 694 0 R (equation.4.3c) 695 0 R] +/Limits [(equation.4.18d) (equation.4.3c)] >> endobj 908 0 obj << -/Names [(equation.5.6a) 784 0 R (equation.5.6b) 785 0 R (equation.5.6c) 786 0 R (equation.5.7) 792 0 R (equation.5.8) 793 0 R (equation.5.9) 794 0 R] -/Limits [(equation.5.6a) (equation.5.9)] +/Names [(equation.4.4) 711 0 R (equation.4.4a) 712 0 R (equation.4.4b) 713 0 R (equation.4.5) 714 0 R (equation.4.6) 716 0 R (equation.4.6a) 717 0 R] +/Limits [(equation.4.4) (equation.4.6a)] >> endobj 909 0 obj << -/Names [(equation.6.1) 823 0 R (equation.6.1a) 824 0 R (equation.6.1b) 825 0 R (equation.6.1c) 826 0 R (equation.6.2) 827 0 R (equation.6.3) 828 0 R] -/Limits [(equation.6.1) (equation.6.3)] +/Names [(equation.4.6b) 718 0 R (equation.4.6c) 720 0 R (equation.4.6d) 721 0 R (equation.4.6e) 722 0 R (equation.4.7) 723 0 R (equation.4.8) 728 0 R] +/Limits [(equation.4.6b) (equation.4.8)] >> endobj 910 0 obj << -/Names [(equation.6.4) 833 0 R (equation.6.4a) 834 0 R (equation.6.4b) 835 0 R (equation.6.4c) 836 0 R (equation.6.4d) 837 0 R (equation.6.4e) 838 0 R] -/Limits [(equation.6.4) (equation.6.4e)] +/Names [(equation.4.8a) 729 0 R (equation.4.8b) 730 0 R (equation.4.9) 731 0 R (equation.5.1) 774 0 R (equation.5.10) 801 0 R (equation.5.11) 802 0 R] +/Limits [(equation.4.8a) (equation.5.11)] >> endobj 911 0 obj << -/Names [(equation.6.4f) 839 0 R (equation.6.4g) 840 0 R (page.0) 400 0 R (page.1) 412 0 R (page.10) 606 0 R (page.11) 615 0 R] -/Limits [(equation.6.4f) (page.11)] +/Names [(equation.5.12) 811 0 R (equation.5.12a) 812 0 R (equation.5.12b) 813 0 R (equation.5.13) 819 0 R (equation.5.14) 820 0 R (equation.5.14a) 821 0 R] +/Limits [(equation.5.12) (equation.5.14a)] >> endobj 912 0 obj << -/Names [(page.12) 623 0 R (page.13) 639 0 R (page.14) 655 0 R (page.15) 670 0 R (page.16) 681 0 R (page.17) 704 0 R] -/Limits [(page.12) (page.17)] +/Names [(equation.5.14b) 822 0 R (equation.5.15) 823 0 R (equation.5.2) 775 0 R (equation.5.3) 776 0 R (equation.5.4) 781 0 R (equation.5.4a) 782 0 R] +/Limits [(equation.5.14b) (equation.5.4a)] >> endobj 913 0 obj << -/Names [(page.18) 721 0 R (page.19) 734 0 R (page.2) 448 0 R (page.20) 743 0 R (page.21) 767 0 R (page.22) 774 0 R] -/Limits [(page.18) (page.22)] +/Names [(equation.5.4b) 783 0 R (equation.5.4c) 784 0 R (equation.5.5) 785 0 R (equation.5.5a) 786 0 R (equation.5.5b) 787 0 R (equation.5.5c) 788 0 R] +/Limits [(equation.5.4b) (equation.5.5c)] >> endobj 914 0 obj << -/Names [(page.23) 791 0 R (page.24) 804 0 R (page.25) 812 0 R (page.26) 822 0 R (page.27) 832 0 R (page.3) 497 0 R] -/Limits [(page.23) (page.3)] +/Names [(equation.5.6) 789 0 R (equation.5.6a) 790 0 R (equation.5.6b) 791 0 R (equation.5.6c) 792 0 R (equation.5.7) 798 0 R (equation.5.8) 799 0 R] +/Limits [(equation.5.6) (equation.5.8)] >> endobj 915 0 obj << -/Names [(page.4) 530 0 R (page.5) 535 0 R (page.6) 548 0 R (page.7) 567 0 R (page.8) 578 0 R (page.9) 598 0 R] -/Limits [(page.4) (page.9)] +/Names [(equation.5.9) 800 0 R (equation.6.1) 829 0 R (equation.6.1a) 830 0 R (equation.6.1b) 831 0 R (equation.6.1c) 832 0 R (equation.6.2) 833 0 R] +/Limits [(equation.5.9) (equation.6.2)] >> endobj 916 0 obj << -/Names [(section*.3) 450 0 R (section.1.1) 6 0 R (section.1.2) 18 0 R (section.1.3) 30 0 R (section.1.4) 46 0 R (section.1.5) 50 0 R] -/Limits [(section*.3) (section.1.5)] +/Names [(equation.6.3) 834 0 R (equation.6.4) 839 0 R (equation.6.4a) 840 0 R (equation.6.4b) 841 0 R (equation.6.4c) 842 0 R (equation.6.4d) 843 0 R] +/Limits [(equation.6.3) (equation.6.4d)] >> endobj 917 0 obj << -/Names [(section.1.6) 62 0 R (section.1.7) 74 0 R (section.2.1) 102 0 R (section.2.2) 114 0 R (section.3.1) 134 0 R (section.3.2) 138 0 R] -/Limits [(section.1.6) (section.3.2)] +/Names [(equation.6.4e) 844 0 R (equation.6.4f) 845 0 R (equation.6.4g) 846 0 R (page.0) 404 0 R (page.1) 416 0 R (page.10) 611 0 R] +/Limits [(equation.6.4e) (page.10)] >> endobj 918 0 obj << -/Names [(section.3.3) 150 0 R (section.3.4) 170 0 R (section.3.5) 182 0 R (section.3.6) 194 0 R (section.4.1) 226 0 R (section.4.2) 254 0 R] -/Limits [(section.3.3) (section.4.2)] +/Names [(page.11) 620 0 R (page.12) 629 0 R (page.13) 645 0 R (page.14) 661 0 R (page.15) 676 0 R (page.16) 687 0 R] +/Limits [(page.11) (page.16)] >> endobj 919 0 obj << -/Names [(section.4.3) 262 0 R (section.4.4) 278 0 R (section.5.1) 294 0 R (section.5.2) 322 0 R (section.5.3) 342 0 R (section.6.1) 370 0 R] -/Limits [(section.4.3) (section.6.1)] +/Names [(page.17) 710 0 R (page.18) 727 0 R (page.19) 740 0 R (page.2) 452 0 R (page.20) 749 0 R (page.21) 773 0 R] +/Limits [(page.17) (page.21)] >> endobj 920 0 obj << -/Names [(section.6.2) 382 0 R (subsection.1.1.1) 10 0 R (subsection.1.1.2) 14 0 R (subsection.1.2.1) 22 0 R (subsection.1.2.2) 26 0 R (subsection.1.3.1) 34 0 R] -/Limits [(section.6.2) (subsection.1.3.1)] +/Names [(page.22) 780 0 R (page.23) 797 0 R (page.24) 810 0 R (page.25) 818 0 R (page.26) 828 0 R (page.27) 838 0 R] +/Limits [(page.22) (page.27)] >> endobj 921 0 obj << -/Names [(subsection.1.3.2) 38 0 R (subsection.1.3.3) 42 0 R (subsection.1.5.1) 54 0 R (subsection.1.5.2) 58 0 R (subsection.1.6.1) 66 0 R (subsection.1.6.2) 70 0 R] -/Limits [(subsection.1.3.2) (subsection.1.6.2)] +/Names [(page.3) 500 0 R (page.4) 535 0 R (page.5) 540 0 R (page.6) 553 0 R (page.7) 572 0 R (page.8) 583 0 R] +/Limits [(page.3) (page.8)] >> endobj 922 0 obj << -/Names [(subsection.1.7.1) 78 0 R (subsection.1.7.2) 82 0 R (subsection.1.7.3) 86 0 R (subsection.1.7.4) 90 0 R (subsection.1.7.5) 94 0 R (subsection.2.1.1) 106 0 R] -/Limits [(subsection.1.7.1) (subsection.2.1.1)] +/Names [(page.9) 603 0 R (section*.3) 454 0 R (section.1.1) 6 0 R (section.1.2) 18 0 R (section.1.3) 30 0 R (section.1.4) 46 0 R] +/Limits [(page.9) (section.1.4)] >> endobj 923 0 obj << -/Names [(subsection.2.1.2) 110 0 R (subsection.2.2.1) 118 0 R (subsection.2.2.2) 122 0 R (subsection.2.2.3) 126 0 R (subsection.3.2.1) 142 0 R (subsection.3.2.2) 146 0 R] -/Limits [(subsection.2.1.2) (subsection.3.2.2)] +/Names [(section.1.5) 50 0 R (section.1.6) 62 0 R (section.1.7) 74 0 R (section.2.1) 102 0 R (section.2.2) 114 0 R (section.3.1) 138 0 R] +/Limits [(section.1.5) (section.3.1)] >> endobj 924 0 obj << -/Names [(subsection.3.3.1) 154 0 R (subsection.3.3.2) 158 0 R (subsection.3.3.3) 162 0 R (subsection.3.3.4) 166 0 R (subsection.3.4.1) 174 0 R (subsection.3.4.2) 178 0 R] -/Limits [(subsection.3.3.1) (subsection.3.4.2)] +/Names [(section.3.2) 142 0 R (section.3.3) 154 0 R (section.3.4) 174 0 R (section.3.5) 186 0 R (section.3.6) 198 0 R (section.4.1) 230 0 R] +/Limits [(section.3.2) (section.4.1)] >> endobj 925 0 obj << -/Names [(subsection.3.5.1) 186 0 R (subsection.3.5.2) 190 0 R (subsection.3.6.1) 198 0 R (subsection.3.6.2) 202 0 R (subsection.3.6.3) 206 0 R (subsection.3.6.4) 210 0 R] -/Limits [(subsection.3.5.1) (subsection.3.6.4)] +/Names [(section.4.2) 258 0 R (section.4.3) 266 0 R (section.4.4) 282 0 R (section.5.1) 298 0 R (section.5.2) 326 0 R (section.5.3) 346 0 R] +/Limits [(section.4.2) (section.5.3)] >> endobj 926 0 obj << -/Names [(subsection.3.6.5) 214 0 R (subsection.3.6.6) 218 0 R (subsection.4.1.1) 230 0 R (subsection.4.1.2) 234 0 R (subsection.4.1.3) 238 0 R (subsection.4.1.4) 242 0 R] -/Limits [(subsection.3.6.5) (subsection.4.1.4)] +/Names [(section.6.1) 374 0 R (section.6.2) 386 0 R (subsection.1.1.1) 10 0 R (subsection.1.1.2) 14 0 R (subsection.1.2.1) 22 0 R (subsection.1.2.2) 26 0 R] +/Limits [(section.6.1) (subsection.1.2.2)] >> endobj 927 0 obj << -/Names [(subsection.4.1.5) 246 0 R (subsection.4.1.6) 250 0 R (subsection.4.2.1) 258 0 R (subsection.4.3.1) 266 0 R (subsection.4.3.2) 270 0 R (subsection.4.3.3) 274 0 R] -/Limits [(subsection.4.1.5) (subsection.4.3.3)] +/Names [(subsection.1.3.1) 34 0 R (subsection.1.3.2) 38 0 R (subsection.1.3.3) 42 0 R (subsection.1.5.1) 54 0 R (subsection.1.5.2) 58 0 R (subsection.1.6.1) 66 0 R] +/Limits [(subsection.1.3.1) (subsection.1.6.1)] >> endobj 928 0 obj << -/Names [(subsection.4.4.1) 282 0 R (subsection.4.4.2) 286 0 R (subsection.5.1.1) 298 0 R (subsection.5.1.2) 302 0 R (subsection.5.1.3) 306 0 R (subsection.5.1.4) 310 0 R] -/Limits [(subsection.4.4.1) (subsection.5.1.4)] +/Names [(subsection.1.6.2) 70 0 R (subsection.1.7.1) 78 0 R (subsection.1.7.2) 82 0 R (subsection.1.7.3) 86 0 R (subsection.1.7.4) 90 0 R (subsection.1.7.5) 94 0 R] +/Limits [(subsection.1.6.2) (subsection.1.7.5)] >> endobj 929 0 obj << -/Names [(subsection.5.1.5) 314 0 R (subsection.5.1.6) 318 0 R (subsection.5.2.1) 326 0 R (subsection.5.2.2) 330 0 R (subsection.5.2.3) 334 0 R (subsection.5.2.4) 338 0 R] -/Limits [(subsection.5.1.5) (subsection.5.2.4)] +/Names [(subsection.2.1.1) 106 0 R (subsection.2.1.2) 110 0 R (subsection.2.2.1) 118 0 R (subsection.2.2.2) 122 0 R (subsection.2.2.3) 126 0 R (subsection.2.2.4) 130 0 R] +/Limits [(subsection.2.1.1) (subsection.2.2.4)] >> endobj 930 0 obj << -/Names [(subsection.5.3.1) 346 0 R (subsection.5.3.2) 350 0 R (subsection.5.3.3) 354 0 R (subsection.5.3.4) 358 0 R (subsection.5.3.5) 362 0 R (subsection.6.1.1) 374 0 R] -/Limits [(subsection.5.3.1) (subsection.6.1.1)] +/Names [(subsection.3.2.1) 146 0 R (subsection.3.2.2) 150 0 R (subsection.3.3.1) 158 0 R (subsection.3.3.2) 162 0 R (subsection.3.3.3) 166 0 R (subsection.3.3.4) 170 0 R] +/Limits [(subsection.3.2.1) (subsection.3.3.4)] >> endobj 931 0 obj << -/Names [(subsection.6.1.2) 378 0 R (subsection.6.2.1) 386 0 R (subsection.6.2.2) 390 0 R (subsubsection*.10) 750 0 R (subsubsection*.4) 573 0 R (subsubsection*.5) 579 0 R] -/Limits [(subsection.6.1.2) (subsubsection*.5)] +/Names [(subsection.3.4.1) 178 0 R (subsection.3.4.2) 182 0 R (subsection.3.5.1) 190 0 R (subsection.3.5.2) 194 0 R (subsection.3.6.1) 202 0 R (subsection.3.6.2) 206 0 R] +/Limits [(subsection.3.4.1) (subsection.3.6.2)] >> endobj 932 0 obj << -/Names [(subsubsection*.6) 673 0 R (subsubsection*.7) 684 0 R (subsubsection*.8) 709 0 R (subsubsection*.9) 744 0 R] -/Limits [(subsubsection*.6) (subsubsection*.9)] +/Names [(subsection.3.6.3) 210 0 R (subsection.3.6.4) 214 0 R (subsection.3.6.5) 218 0 R (subsection.3.6.6) 222 0 R (subsection.4.1.1) 234 0 R (subsection.4.1.2) 238 0 R] +/Limits [(subsection.3.6.3) (subsection.4.1.2)] >> endobj 933 0 obj << -/Kids [884 0 R 885 0 R 886 0 R 887 0 R 888 0 R 889 0 R] -/Limits [(Doc-Start) (equation.1.5a)] +/Names [(subsection.4.1.3) 242 0 R (subsection.4.1.4) 246 0 R (subsection.4.1.5) 250 0 R (subsection.4.1.6) 254 0 R (subsection.4.2.1) 262 0 R (subsection.4.3.1) 270 0 R] +/Limits [(subsection.4.1.3) (subsection.4.3.1)] >> endobj 934 0 obj << -/Kids [890 0 R 891 0 R 892 0 R 893 0 R 894 0 R 895 0 R] -/Limits [(equation.1.5b) (equation.3.21)] +/Names [(subsection.4.3.2) 274 0 R (subsection.4.3.3) 278 0 R (subsection.4.4.1) 286 0 R (subsection.4.4.2) 290 0 R (subsection.5.1.1) 302 0 R (subsection.5.1.2) 306 0 R] +/Limits [(subsection.4.3.2) (subsection.5.1.2)] >> endobj 935 0 obj << -/Kids [896 0 R 897 0 R 898 0 R 899 0 R 900 0 R 901 0 R] -/Limits [(equation.3.22) (equation.4.4)] +/Names [(subsection.5.1.3) 310 0 R (subsection.5.1.4) 314 0 R (subsection.5.1.5) 318 0 R (subsection.5.1.6) 322 0 R (subsection.5.2.1) 330 0 R (subsection.5.2.2) 334 0 R] +/Limits [(subsection.5.1.3) (subsection.5.2.2)] >> endobj 936 0 obj << -/Kids [902 0 R 903 0 R 904 0 R 905 0 R 906 0 R 907 0 R] -/Limits [(equation.4.4a) (equation.5.6)] +/Names [(subsection.5.2.3) 338 0 R (subsection.5.2.4) 342 0 R (subsection.5.3.1) 350 0 R (subsection.5.3.2) 354 0 R (subsection.5.3.3) 358 0 R (subsection.5.3.4) 362 0 R] +/Limits [(subsection.5.2.3) (subsection.5.3.4)] >> endobj 937 0 obj << -/Kids [908 0 R 909 0 R 910 0 R 911 0 R 912 0 R 913 0 R] -/Limits [(equation.5.6a) (page.22)] +/Names [(subsection.5.3.5) 366 0 R (subsection.6.1.1) 378 0 R (subsection.6.1.2) 382 0 R (subsection.6.2.1) 390 0 R (subsection.6.2.2) 394 0 R (subsubsection*.10) 756 0 R] +/Limits [(subsection.5.3.5) (subsubsection*.10)] >> endobj 938 0 obj << -/Kids [914 0 R 915 0 R 916 0 R 917 0 R 918 0 R 919 0 R] -/Limits [(page.23) (section.6.1)] +/Names [(subsubsection*.4) 578 0 R (subsubsection*.5) 584 0 R (subsubsection*.6) 679 0 R (subsubsection*.7) 690 0 R (subsubsection*.8) 715 0 R (subsubsection*.9) 750 0 R] +/Limits [(subsubsection*.4) (subsubsection*.9)] >> endobj 939 0 obj << -/Kids [920 0 R 921 0 R 922 0 R 923 0 R 924 0 R 925 0 R] -/Limits [(section.6.2) (subsection.3.6.4)] +/Kids [890 0 R 891 0 R 892 0 R 893 0 R 894 0 R 895 0 R] +/Limits [(Doc-Start) (equation.1.5a)] >> endobj 940 0 obj << -/Kids [926 0 R 927 0 R 928 0 R 929 0 R 930 0 R 931 0 R] -/Limits [(subsection.3.6.5) (subsubsection*.5)] +/Kids [896 0 R 897 0 R 898 0 R 899 0 R 900 0 R 901 0 R] +/Limits [(equation.1.5b) (equation.3.20)] >> endobj 941 0 obj << -/Kids [932 0 R] -/Limits [(subsubsection*.6) (subsubsection*.9)] +/Kids [902 0 R 903 0 R 904 0 R 905 0 R 906 0 R 907 0 R] +/Limits [(equation.3.21) (equation.4.3c)] >> endobj 942 0 obj << -/Kids [933 0 R 934 0 R 935 0 R 936 0 R 937 0 R 938 0 R] -/Limits [(Doc-Start) (section.6.1)] +/Kids [908 0 R 909 0 R 910 0 R 911 0 R 912 0 R 913 0 R] +/Limits [(equation.4.4) (equation.5.5c)] >> endobj 943 0 obj << -/Kids [939 0 R 940 0 R 941 0 R] -/Limits [(section.6.2) (subsubsection*.9)] +/Kids [914 0 R 915 0 R 916 0 R 917 0 R 918 0 R 919 0 R] +/Limits [(equation.5.6) (page.21)] >> endobj 944 0 obj << -/Kids [942 0 R 943 0 R] -/Limits [(Doc-Start) (subsubsection*.9)] +/Kids [920 0 R 921 0 R 922 0 R 923 0 R 924 0 R 925 0 R] +/Limits [(page.22) (section.5.3)] >> endobj 945 0 obj << -/Dests 944 0 R +/Kids [926 0 R 927 0 R 928 0 R 929 0 R 930 0 R 931 0 R] +/Limits [(section.6.1) (subsection.3.6.2)] >> endobj 946 0 obj << -/Type /Catalog -/Pages 882 0 R -/Outlines 883 0 R -/Names 945 0 R -/PageMode/UseOutlines/PageLabels<>1<>]>> -/OpenAction 393 0 R +/Kids [932 0 R 933 0 R 934 0 R 935 0 R 936 0 R 937 0 R] +/Limits [(subsection.3.6.3) (subsubsection*.10)] >> endobj 947 0 obj << +/Kids [938 0 R] +/Limits 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[ ] >> startxref -286820 +287787 %%EOF diff --git a/document.tex b/document.tex index 0b9218b..f68d43f 100644 --- a/document.tex +++ b/document.tex @@ -22,7 +22,7 @@ \title{Stochastische Signale und Systeme} \subtitle{Zusammenfassung Formeln} -\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.8.3 - 24.09.2012} +\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.8.4 - 24.09.2012} \maketitle \newpage @@ -231,6 +231,12 @@ ACHTUNG: Dieser zusammenhang ist in SSS etwas anders im gegensatz zu dem Hilfsbl \begin{equation} \omega = \Omega T_s \end{equation} + +\subsection{Dirac-Kamm} +\begin{equation} +\eta (\omega) = \sum\limits_{l=-\infty}^\infty \delta(\omega +2\pi l) +\end{equation} + \subsection{Berechnen einer bertragungsfunktion im zeitdiskreten Fall} \begin{enumerate} \item Zeitkontinuierliches $H\freq=\frac{Y\freq}{X\freq}$ berechnen