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Considerind ca este asteptata aparitia, intr-o celula de timp data, a unui semnal s(t) (cu suportul mai mic decit durata celulei), pot aparea doua situatii (care formeaza un sistem complet de evenimente):
A1 - semnalul s(t) a aparut;
A0 - semnalul s(t) nu a aparut.
In raport cu aceste situatii se pot lua deciziile:
A1 - decizie de aparitie a semnalul s(t);
A0 - decizie de neaparitie.
care formeaza, de asemenea, un sistem complet de evenimente.
Din combinarea celor doua sisteme rezulta un nou sistem complet de evenimente:
DESCOPERIREA JUSTA - semnalul a aparut si s-a luat decizia de aparitie
PIERDEREA SEMNALULUI - semnalul a aparut si s-a luat decizia de neaparitie
ALARMA FALSA - semnalul nu a aparut si s-a luat decizia de aparitie
NEDESCOPERIREA JUSTA - semnalul nu a aparut si s-a luat decizia de neaparitie
Intre acesti indicatori se stabilesc relatiile:
(1)
Daca se asteapta aparitia semnalului intr-un interval de timp T format din n celule si se accepta ideea ca valoarea alarmei false este mult mai mica decit 1/n, probabilitatea nedescoperirii juste in acest interval este:
iar probabilitatea alarmei false:
Aplicatie:
Se considera semnalul la receptie x(i):;
unde: n(i) este zgomotul iar y(i) semnalul util
se genereaza un set de i 500 de valori aleatoare, u;
daca acestea sint distribuite uniform in intevalul [0÷1] se trece la o alta variabila, care ar putea fi n:
coeficientul de scara k va in intervalul [0,8÷1,2]
Se genereaza o secventa continind 50 de valori 1 si 450 de valori 0, intr-o ordine aleatoare, reprezentind semnalul util, y(i)
Se sumeaza secventele n(i) si y(i) pentru a se obtine semnalul receptionat, x(i).
Se fixeaza un nivel de prag x0 si se compara cu secventa x(i), luind decizia de existenta, A1*, si respectiv de nonexistenta A0*, a semnalului util.
Se genereaza o secventa cuprinzind starile posibile, conforme cu relatia:
Se calculeaza valorile statistice ale indicatorilor descoperirii.
Se verifica indeplinirea cerintelor exprimate de relatia 1.
Am generat 500 de valori aleatoare
0.38241 |
0.029843 |
0.064326 |
0.69344 |
0.770182 |
0.90125 |
0.743656 |
0.386752 |
0.725888 |
0.607964 |
0.359773 |
0.279148 |
0.338552 |
0.789842 |
0.169586 |
0.388003 |
0.952844 |
0.074553 |
0.237144 |
0.503062 |
0.328482 |
0.164635 |
0.647487 |
0.549406 |
0.829449 |
0.481109 |
0.331586 |
0.219846 |
0.970067 |
0.349733 |
0.551415 |
0.432721 |
0.901184 |
0.973858 |
0.112311 |
0.968549 |
0.479036 |
0.430787 |
0.371789 |
0.493328 |
0.045194 |
0.895609 |
0.677325 |
0.687886 |
0.427772 |
0.275069 |
0.479022 |
0.584067 |
0.539197 |
0.988236 |
0.211129 |
0.823225 |
0.456322 |
0.089502 |
0.758738 |
0.76481 |
0.138424 |
0.018558 |
0.204399 |
0.497712 |
0.481051 |
0.834375 |
0.35671 |
0.202182 |
0.016183 |
0.548961 |
0.62883 |
0.69195 |
0.36174 |
0.579467 |
0.341212 |
0.49067 |
0.70672 |
0.72544 |
0.730177 |
0.345828 |
0.468812 |
0.375803 |
0.905477 |
0.836666 |
0.364997 |
0.084734 |
0.830251 |
0.886065 |
0.822481 |
0.65528 |
0.253336 |
0.303371 |
0.260959 |
0.72373 |
0.463203 |
0.230288 |
0.602312 |
0.811141 |
0.122393 |
0.776009 |
0.978721 |
0.972592 |
0.07643 |
0.549899 |
0.361031 |
0.780738 |
0.229861 |
0.828006 |
0.414169 |
0.86381 |
0.012105 |
0.447755 |
0.574117 |
0.775879 |
0.744588 |
0.404484 |
0.179867 |
0.142366 |
0.26943 |
0.154097 |
0.843909 |
0.640321 |
0.345112 |
0.299921 |
0.026533 |
0.660806 |
0.87903 |
0.100713 |
0.39298 |
0.412466 |
0.157612 |
0.665228 |
0.607647 |
0.981385 |
0.553677 |
0.723875 |
0.670998 |
0.115778 |
0.610702 |
0.286404 |
0.464684 |
0.381863 |
0.005744 |
0.874291 |
0.100647 |
0.647998 |
0.057844 |
0.124842 |
0.171298 |
0.395258 |
0.787584 |
0.191264 |
0.694528 |
0.1143 |
0.935509 |
0.054855 |
0.862613 |
0.887751 |
0.804423 |
0.915412 |
0.350986 |
0.341125 |
0.716468 |
0.93261 |
0.044252 |
0.10443 |
0.491158 |
0.296432 |
0.549072 |
0.906959 |
0.435528 |
0.211597 |
0.398062 |
0.608826 |
0.440637 |
0.531919 |
0.041001 |
0.923415 |
0.310734 |
0.649141 |
0.239338 |
0.182579 |
0.934173 |
0.081234 |
0.3788 |
0.037932 |
0.448581 |
0.572827 |
0.380129 |
0.382879 |
0.96841 |
0.098011 |
0.114384 |
0.599913 |
0.141203 |
0.353672 |
0.935331 |
0.583486 |
0.059264 |
0.07437 |
0.695455 |
0.004678 |
0.016093 |
0.260884 |
0.233571 |
0.83289 |
0.663221 |
0.977186 |
0.262252 |
0.826791 |
0.100699 |
0.652502 |
0.833046 |
0.847106 |
0.290149 |
0.324037 |
0.617838 |
0.721624 |
0.27246 |
0.16319 |
0.223951 |
0.539829 |
0.634094 |
0.329765 |
0.13238 |
0.634472 |
0.617975 |
0.967485 |
0.915192 |
0.130158 |
0.434711 |
0.115836 |
0.908021 |
0.677696 |
0.048284 |
0.795944 |
0.340248 |
0.597676 |
0.209147 |
0.13869 |
0.171777 |
0.082938 |
0.668604 |
0.989757 |
0.001738 |
0.959421 |
0.337096 |
0.652591 |
0.970428 |
0.394724 |
0.346068 |
0.604088 |
0.703174 |
0.266591 |
0.129797 |
0.935906 |
0.968603 |
0.74074 |
0.712095 |
0.577277 |
0.030784 |
0.140617 |
0.507861 |
0.314079 |
0.160025 |
0.68474 |
0.799944 |
0.462458 |
0.913186 |
0.244167 |
0.138199 |
0.587385 |
0.397644 |
0.898968 |
0.531296 |
0.058938 |
0.17697 |
0.181047 |
0.31998 |
0.086773 |
0.821772 |
0.610592 |
0.338299 |
0.833332 |
0.809592 |
0.363621 |
0.31061 |
0.754967 |
0.94283 |
0.504889 |
0.012946 |
0.526841 |
0.824167 |
0.604556 |
0.801013 |
0.970779 |
0.257344 |
0.126545 |
0.034122 |
0.477386 |
0.274691 |
0.587499 |
0.807048 |
0.76439 |
0.062027 |
0.268965 |
0.669092 |
0.148933 |
0.482645 |
0.885239 |
0.02322 |
0.763399 |
0.6562 |
0.623303 |
0.275102 |
0.541998 |
0.983386 |
0.382219 |
0.707798 |
0.471363 |
0.415252 |
0.50935 |
0.967985 |
0.428076 |
0.569498 |
0.573555 |
0.230895 |
0.15423 |
0.519956 |
0.199309 |
0.679857 |
0.329358 |
0.466482 |
0.938564 |
0.001208 |
0.88149 |
0.637074 |
0.367194 |
0.283008 |
0.12067 |
0.728483 |
0.917063 |
0.523791 |
0.099162 |
0.237005 |
0.477552 |
0.477393 |
0.44257 |
0.543178 |
0.149041 |
0.724596 |
0.511708 |
0.500655 |
0.362574 |
0.228721 |
0.023482 |
0.766223 |
0.788997 |
0.923336 |
0.663225 |
0.151305 |
0.730517 |
0.148883 |
0.225803 |
0.476028 |
0.952273 |
0.73889 |
0.605844 |
0.429509 |
0.891953 |
0.692207 |
0.317474 |
0.905379 |
0.614729 |
0.66975 |
0.478099 |
0.265716 |
0.787102 |
0.72336 |
0.231143 |
0.47709 |
0.778335 |
0.854252 |
0.41651 |
0.480258 |
0.340195 |
0.441018 |
0.726315 |
0.035568 |
0.121337 |
0.228277 |
0.435472 |
0.241711 |
0.719924 |
0.355719 |
0.310518 |
0.970368 |
0.439101 |
0.468604 |
0.682221 |
0.60498 |
0.140025 |
0.573233 |
0.021314 |
0.120719 |
0.479589 |
0.177402 |
0.426387 |
0.999144 |
0.685522 |
0.423917 |
0.715666 |
0.911765 |
0.926702 |
0.66511 |
0.423224 |
0.008637 |
0.561271 |
0.158187 |
0.131752 |
0.288279 |
0.922769 |
0.265272 |
0.892881 |
0.874329 |
0.894539 |
0.204363 |
0.556417 |
0.023931 |
0.332624 |
0.238183 |
0.939465 |
0.644659 |
0.307552 |
0.835652 |
0.167848 |
0.917964 |
0.833088 |
0.495106 |
0.141823 |
0.306185 |
0.740582 |
0.89836 |
0.067725 |
0.881734 |
0.75749 |
0.092864 |
0.576388 |
0.685278 |
0.229253 |
0.395957 |
0.328106 |
0.141415 |
0.391471 |
0.214576 |
0.710699 |
0.758949 |
0.288477 |
0.293823 |
0.742243 |
0.360127 |
0.324114 |
0.034778 |
0.381236 |
0.509427 |
0.933988 |
0.678674 |
0.377113 |
0.810055 |
0.379712 |
0.567339 |
0.289073 |
0.80952 |
0.558468 |
0.369242 |
0.459507 |
0.93249 |
0.696321 |
0.510316 |
0.926185 |
0.214488 |
0.152375 |
0.336432 |
0.545083 |
0.444331 |
0.211605 |
0.713329 |
0.778066 |
0.89126 |
0.894084 |
0.640109 |
0.143576 |
0.784927 |
0.071818 |
0.163082 |
0.70337 |
0.659648 |
0.099243 |
0.740526 |
0.031136 |
0.398874 |
0.449674 |
0.199443 |
0.230046 |
Calculez
-0.29675 |
-1.27651 |
-1.16935 |
0.492074 |
0.69571 |
1.065761 |
0.62447 |
-0.2857 |
0.577283 |
0.272263 |
-0.35458 |
-0.56398 |
-0.40912 |
0.749181 |
-0.86158 |
-0.28252 |
1.222257 |
-1.13824 |
-0.67593 |
0.007691 |
-0.43513 |
-0.87551 |
0.373198 |
0.124208 |
0.858877 |
-0.04746 |
-0.4271 |
-0.72276 |
1.276222 |
-0.38034 |
0.129269 |
-0.16926 |
1.065564 |
1.288226 |
-1.02579 |
1.271427 |
-0.05267 |
-0.17414 |
-0.32384 |
-0.01676 |
-1.22836 |
1.049079 |
0.450169 |
0.477603 |
-0.18175 |
-0.57475 |
-0.05271 |
0.211674 |
0.098513 |
1.334184 |
-0.74653 |
0.84145 |
-0.10979 |
-1.09328 |
0.664852 |
0.6812 |
-0.95005 |
-1.31238 |
-0.76496 |
-0.00575 |
-0.04761 |
0.872722 |
-0.36243 |
-0.77105 |
-1.31998 |
0.123089 |
0.325424 |
0.48819 |
-0.34954 |
0.200043 |
-0.40226 |
-0.02344 |
0.526807 |
0.576098 |
0.588637 |
-0.39038 |
-0.07837 |
-0.3136 |
1.078313 |
0.879176 |
-0.3412 |
-1.10756 |
0.861128 |
1.021033 |
0.839372 |
0.393228 |
-0.6325 |
-0.5004 |
-0.61218 |
0.571579 |
-0.09248 |
-0.69444 |
0.257907 |
0.807825 |
-0.99636 |
0.711495 |
1.303693 |
1.284212 |
-1.13256 |
0.12545 |
-0.35135 |
0.724344 |
-0.69559 |
0.854831 |
-0.21614 |
0.956465 |
-1.33309 |
-0.13136 |
0.186523 |
0.711142 |
0.626958 |
-0.24067 |
-0.83282 |
-0.93874 |
-0.58968 |
-0.90531 |
0.899652 |
0.354818 |
-0.39222 |
-0.50941 |
-1.28699 |
0.407464 |
1.000502 |
-1.05995 |
-0.26986 |
-0.22045 |
-0.89534 |
0.418872 |
0.271459 |
1.3122 |
0.134965 |
0.57196 |
0.433783 |
-1.01564 |
0.279226 |
-0.54487 |
-0.08875 |
-0.29815 |
-1.35363 |
0.986733 |
-1.06014 |
0.374508 |
-1.18922 |
-0.98925 |
-0.85678 |
-0.26408 |
0.743008 |
-0.80116 |
0.494914 |
-1.01996 |
1.168847 |
-1.19843 |
0.953024 |
1.025973 |
0.789243 |
1.107995 |
-0.37712 |
-0.40249 |
0.552424 |
1.160001 |
-1.23129 |
-1.04896 |
-0.02221 |
-0.51855 |
0.123369 |
1.082724 |
-0.16218 |
-0.74525 |
-0.25696 |
0.274454 |
-0.1493 |
0.080208 |
-1.24144 |
1.132096 |
-0.4812 |
0.377445 |
-0.67003 |
-0.82527 |
1.164767 |
-1.11807 |
-0.30595 |
-1.25104 |
-0.12928 |
0.183266 |
-0.30257 |
-0.29556 |
1.270989 |
-1.06795 |
-1.01972 |
0.251821 |
-0.94208 |
-0.37022 |
1.168304 |
0.210204 |
-1.18486 |
-1.1388 |
0.497331 |
-1.35709 |
-1.32027 |
-0.61237 |
-0.68557 |
0.868543 |
0.413692 |
1.298803 |
-0.60874 |
0.851425 |
-1.05999 |
0.386082 |
0.86898 |
0.908722 |
-0.53502 |
-0.44664 |
0.297386 |
0.566017 |
-0.58165 |
-0.87958 |
-0.7116 |
0.100102 |
0.338877 |
-0.43181 |
-0.96744 |
0.339846 |
0.297736 |
1.268072 |
1.107334 |
-0.97386 |
-0.16424 |
-1.01547 |
1.085889 |
0.451132 |
-1.21875 |
0.765903 |
-0.40475 |
0.246147 |
-0.75195 |
-0.94928 |
-0.85544 |
-1.11295 |
0.427594 |
1.339086 |
-1.36665 |
1.242756 |
-0.41287 |
0.386312 |
1.277364 |
-0.26543 |
-0.38976 |
0.262418 |
0.517514 |
-0.59721 |
-0.9749 |
1.170062 |
1.271599 |
0.616699 |
0.540919 |
0.194508 |
-1.27353 |
-0.94375 |
0.019746 |
-0.47249 |
-0.88852 |
0.46942 |
0.776898 |
-0.09435 |
1.101323 |
-0.65705 |
-0.95069 |
0.220071 |
-0.25802 |
1.059003 |
0.078641 |
-1.18586 |
-0.84091 |
-0.82953 |
-0.45716 |
-1.10144 |
0.837393 |
0.278946 |
-0.40977 |
0.869786 |
0.803531 |
-0.34472 |
-0.48152 |
0.654726 |
1.191298 |
0.012282 |
-1.33038 |
0.06744 |
0.844084 |
0.263607 |
0.779843 |
1.278473 |
-0.6218 |
-0.98431 |
-1.26301 |
-0.05682 |
-0.57575 |
0.22036 |
0.796493 |
0.680068 |
-1.17639 |
-0.59091 |
0.428855 |
-0.91999 |
-0.0436 |
1.018616 |
-1.29751 |
0.677397 |
0.395597 |
0.311317 |
-0.57467 |
0.105562 |
1.318604 |
-0.29724 |
0.529633 |
-0.07196 |
-0.2134 |
0.023487 |
1.269649 |
-0.18099 |
0.174861 |
0.185103 |
-0.6928 |
-0.90493 |
0.050137 |
-0.77895 |
0.456736 |
-0.43286 |
-0.08423 |
1.178198 |
-1.36837 |
1.007668 |
0.346503 |
-0.33558 |
-0.5538 |
-1.00137 |
0.58415 |
1.112952 |
0.059774 |
-1.06454 |
-0.67631 |
-0.0564 |
-0.0568 |
-0.14442 |
0.108531 |
-0.91968 |
0.573868 |
0.029412 |
0.001644 |
-0.3474 |
-0.69868 |
-1.29668 |
0.685012 |
0.746869 |
1.131855 |
0.413702 |
-0.91324 |
0.589538 |
-0.92013 |
-0.70658 |
-0.06023 |
1.220484 |
0.611775 |
0.266877 |
-0.17737 |
1.03831 |
0.488858 |
-0.46367 |
1.078021 |
0.289469 |
0.430556 |
-0.05502 |
-0.59953 |
0.74169 |
0.570602 |
-0.69213 |
-0.05756 |
0.717809 |
0.929073 |
-0.21022 |
-0.0496 |
-0.40488 |
-0.14834 |
0.578412 |
-1.25846 |
-0.99943 |
-0.69988 |
-0.16232 |
-0.66365 |
0.56153 |
-0.36497 |
-0.48176 |
1.277174 |
-0.15317 |
-0.07889 |
0.462873 |
0.264683 |
-0.94545 |
0.18429 |
-1.30358 |
-1.00123 |
-0.05128 |
-0.8397 |
-0.18525 |
1.36952 |
0.471452 |
-0.19149 |
0.550312 |
1.097068 |
1.142043 |
0.418568 |
-0.19324 |
-1.34427 |
0.154105 |
-0.89371 |
-0.96925 |
-0.53993 |
1.130143 |
-0.60071 |
1.041041 |
0.986844 |
1.045924 |
-0.76506 |
0.14187 |
-1.29525 |
-0.42442 |
-0.67314 |
1.180959 |
0.365939 |
-0.48949 |
0.876318 |
-0.86647 |
1.115662 |
0.869098 |
-0.01229 |
-0.9403 |
-0.49305 |
0.616278 |
1.057205 |
-1.15898 |
1.008379 |
0.661498 |
-1.08325 |
0.19226 |
0.470817 |
-0.69724 |
-0.2623 |
-0.4361 |
-0.94147 |
-0.2737 |
-0.73711 |
0.537251 |
0.66542 |
-0.53941 |
-0.52538 |
0.620703 |
-0.35367 |
-0.44644 |
-1.26095 |
-0.29975 |
0.023682 |
1.164204 |
0.453666 |
-0.31026 |
0.804815 |
-0.30363 |
0.169411 |
-0.53785 |
0.803334 |
0.147039 |
-0.33035 |
-0.10177 |
1.159635 |
0.499593 |
0.025914 |
1.140478 |
-0.73735 |
-0.9102 |
-0.41459 |
0.113326 |
-0.13999 |
-0.74523 |
0.544163 |
0.71708 |
1.036273 |
1.044582 |
0.354275 |
-0.93528 |
0.735755 |
-1.14653 |
-0.87989 |
0.518027 |
0.404479 |
-1.0643 |
0.616129 |
-1.27242 |
-0.2549 |
-0.12653 |
-0.77859 |
-0.69509 |
Generam o secventa continand 50 de valori de 1 si 450 de valori de 0,care reprezinta semnalul util y(i).
1 |
0 |
2 |
0 |
3 |
0 |
4 |
0 |
5 |
0 |
6 |
0 |
7 |
0 |
8 |
0 |
9 |
0 |
10 |
0 |
11 |
0 |
12 |
0 |
13 |
0 |
14 |
0 |
15 |
0 |
16 |
1 |
17 |
0 |
18 |
0 |
19 |
0 |
20 |
0 |
21 |
0 |
22 |
0 |
23 |
0 |
24 |
0 |
25 |
0 |
26 |
0 |
27 |
0 |
28 |
0 |
29 |
1 |
30 |
0 |
31 |
0 |
32 |
0 |
33 |
0 |
34 |
0 |
35 |
0 |
36 |
0 |
37 |
0 |
38 |
0 |
39 |
1 |
40 |
0 |
41 |
0 |
42 |
0 |
43 |
0 |
44 |
0 |
45 |
1 |
46 |
0 |
47 |
0 |
48 |
0 |
49 |
0 |
50 |
0 |
51 |
1 |
52 |
0 |
53 |
0 |
54 |
0 |
55 |
0 |
56 |
0 |
57 |
0 |
58 |
0 |
59 |
0 |
60 |
0 |
61 |
0 |
62 |
0 |
63 |
0 |
64 |
0 |
65 |
0 |
66 |
0 |
67 |
0 |
68 |
0 |
69 |
0 |
70 |
0 |
71 |
0 |
72 |
0 |
73 |
0 |
74 |
0 |
75 |
0 |
76 |
0 |
77 |
0 |
78 |
0 |
79 |
0 |
80 |
1 |
81 |
0 |
82 |
0 |
83 |
0 |
84 |
0 |
85 |
0 |
86 |
0 |
87 |
0 |
88 |
0 |
89 |
0 |
90 |
0 |
91 |
1 |
92 |
0 |
93 |
0 |
94 |
0 |
95 |
0 |
96 |
0 |
97 |
0 |
98 |
1 |
99 |
0 |
100 |
0 |
101 |
0 |
102 |
0 |
103 |
1 |
104 |
0 |
105 |
0 |
106 |
0 |
107 |
0 |
108 |
0 |
109 |
0 |
110 |
1 |
111 |
0 |
112 |
0 |
113 |
0 |
114 |
0 |
115 |
0 |
116 |
0 |
117 |
0 |
118 |
1 |
119 |
0 |
120 |
0 |
121 |
0 |
122 |
0 |
123 |
0 |
124 |
0 |
125 |
0 |
126 |
0 |
127 |
0 |
128 |
0 |
129 |
0 |
130 |
0 |
131 |
0 |
132 |
0 |
133 |
0 |
134 |
0 |
135 |
0 |
136 |
0 |
137 |
0 |
138 |
0 |
139 |
0 |
140 |
0 |
141 |
0 |
142 |
0 |
143 |
0 |
144 |
1 |
145 |
0 |
146 |
0 |
147 |
0 |
148 |
0 |
149 |
0 |
150 |
1 |
151 |
0 |
152 |
0 |
153 |
0 |
154 |
0 |
155 |
1 |
156 |
0 |
157 |
0 |
158 |
0 |
159 |
0 |
160 |
0 |
161 |
0 |
162 |
0 |
163 |
0 |
164 |
0 |
165 |
0 |
166 |
1 |
167 |
0 |
168 |
0 |
169 |
1 |
170 |
0 |
171 |
0 |
172 |
0 |
173 |
0 |
174 |
0 |
175 |
1 |
176 |
0 |
177 |
0 |
178 |
0 |
179 |
0 |
180 |
0 |
181 |
0 |
182 |
0 |
183 |
1 |
184 |
0 |
185 |
0 |
186 |
0 |
187 |
0 |
188 |
0 |
189 |
0 |
190 |
0 |
191 |
0 |
192 |
0 |
193 |
0 |
194 |
0 |
195 |
0 |
196 |
0 |
197 |
0 |
198 |
1 |
199 |
0 |
200 |
0 |
201 |
0 |
202 |
0 |
203 |
0 |
204 |
0 |
205 |
0 |
206 |
0 |
207 |
0 |
208 |
0 |
209 |
1 |
210 |
0 |
211 |
0 |
212 |
0 |
213 |
0 |
214 |
0 |
215 |
0 |
216 |
0 |
217 |
0 |
218 |
0 |
219 |
0 |
220 |
1 |
221 |
0 |
222 |
0 |
223 |
0 |
224 |
0 |
225 |
0 |
226 |
0 |
227 |
0 |
228 |
0 |
229 |
0 |
230 |
0 |
231 |
1 |
232 |
0 |
233 |
0 |
234 |
0 |
235 |
0 |
236 |
0 |
237 |
0 |
238 |
0 |
239 |
1 |
240 |
0 |
241 |
0 |
242 |
0 |
243 |
0 |
244 |
0 |
245 |
0 |
246 |
0 |
247 |
0 |
248 |
0 |
249 |
0 |
250 |
0 |
251 |
0 |
252 |
0 |
253 |
0 |
254 |
0 |
255 |
1 |
256 |
0 |
257 |
0 |
258 |
0 |
259 |
0 |
260 |
0 |
261 |
0 |
262 |
0 |
263 |
0 |
264 |
0 |
265 |
0 |
266 |
0 |
267 |
0 |
268 |
0 |
269 |
1 |
270 |
0 |
271 |
0 |
272 |
0 |
273 |
0 |
274 |
0 |
275 |
0 |
276 |
0 |
277 |
0 |
278 |
0 |
279 |
0 |
280 |
0 |
281 |
0 |
282 |
0 |
283 |
0 |
284 |
0 |
285 |
0 |
286 |
1 |
287 |
0 |
288 |
0 |
289 |
0 |
290 |
0 |
291 |
0 |
292 |
0 |
293 |
0 |
294 |
0 |
295 |
0 |
296 |
0 |
297 |
0 |
298 |
1 |
299 |
0 |
300 |
0 |
301 |
0 |
302 |
1 |
303 |
0 |
304 |
0 |
305 |
0 |
306 |
0 |
307 |
0 |
308 |
0 |
309 |
0 |
310 |
0 |
311 |
1 |
312 |
0 |
313 |
0 |
314 |
0 |
315 |
0 |
316 |
0 |
317 |
0 |
318 |
0 |
319 |
1 |
320 |
0 |
321 |
0 |
322 |
0 |
323 |
0 |
324 |
1 |
325 |
0 |
326 |
0 |
327 |
0 |
328 |
0 |
329 |
0 |
330 |
0 |
331 |
0 |
332 |
0 |
333 |
1 |
334 |
0 |
335 |
0 |
336 |
1 |
337 |
0 |
338 |
0 |
339 |
0 |
340 |
0 |
341 |
0 |
342 |
0 |
343 |
0 |
344 |
0 |
345 |
0 |
346 |
0 |
347 |
1 |
348 |
0 |
349 |
0 |
350 |
0 |
351 |
0 |
352 |
0 |
353 |
0 |
354 |
0 |
355 |
0 |
356 |
1 |
357 |
0 |
358 |
0 |
359 |
0 |
360 |
0 |
361 |
0 |
362 |
0 |
363 |
0 |
364 |
1 |
365 |
0 |
366 |
0 |
367 |
0 |
368 |
0 |
369 |
0 |
370 |
0 |
371 |
0 |
372 |
0 |
373 |
0 |
374 |
0 |
375 |
0 |
376 |
1 |
377 |
0 |
378 |
1 |
379 |
0 |
380 |
0 |
381 |
0 |
382 |
0 |
383 |
0 |
384 |
0 |
385 |
0 |
386 |
0 |
387 |
0 |
388 |
0 |
389 |
0 |
390 |
1 |
391 |
0 |
392 |
0 |
393 |
0 |
394 |
0 |
395 |
0 |
396 |
0 |
397 |
0 |
398 |
0 |
399 |
0 |
400 |
0 |
401 |
1 |
402 |
0 |
403 |
0 |
404 |
0 |
405 |
1 |
406 |
0 |
407 |
0 |
408 |
0 |
409 |
0 |
410 |
0 |
411 |
0 |
412 |
0 |
413 |
0 |
414 |
0 |
415 |
0 |
416 |
1 |
417 |
0 |
418 |
0 |
419 |
1 |
420 |
0 |
421 |
0 |
422 |
0 |
423 |
0 |
424 |
0 |
425 |
0 |
426 |
0 |
427 |
0 |
428 |
0 |
429 |
0 |
430 |
0 |
431 |
0 |
432 |
0 |
433 |
0 |
434 |
0 |
435 |
0 |
436 |
0 |
437 |
0 |
438 |
0 |
439 |
1 |
440 |
0 |
441 |
0 |
442 |
0 |
443 |
0 |
444 |
0 |
445 |
0 |
446 |
1 |
447 |
0 |
448 |
0 |
449 |
0 |
450 |
0 |
451 |
0 |
452 |
0 |
453 |
0 |
454 |
0 |
455 |
0 |
456 |
0 |
457 |
1 |
458 |
0 |
459 |
0 |
460 |
0 |
461 |
0 |
462 |
0 |
463 |
0 |
464 |
1 |
465 |
0 |
466 |
0 |
467 |
0 |
468 |
0 |
469 |
0 |
470 |
0 |
471 |
0 |
472 |
0 |
473 |
0 |
474 |
0 |
475 |
0 |
476 |
0 |
477 |
0 |
478 |
0 |
479 |
0 |
480 |
0 |
481 |
1 |
482 |
0 |
483 |
0 |
484 |
0 |
485 |
0 |
486 |
0 |
487 |
0 |
488 |
0 |
489 |
1 |
490 |
0 |
491 |
0 |
492 |
0 |
493 |
0 |
494 |
0 |
495 |
0 |
496 |
0 |
497 |
1 |
498 |
0 |
499 |
0 |
500 |
0 |
Insumam secventele n(i) si y(i) pentru a obtine semnalul receptionat, rezultand x(i)
0.029071 |
1.307307 |
-0.97218 |
1.103676 |
0.189723 |
-0.34694 |
-0.25151 |
1.073888 |
-0.60422 |
-0.81765 |
-0.69237 |
0.915264 |
-0.70449 |
-1.25251 |
1.047664 |
1.915413 |
0.670051 |
0.384415 |
0.978607 |
0.416867 |
-0.15422 |
0.254841 |
-0.60476 |
-0.17969 |
1.207375 |
0.307678 |
0.066266 |
0.272204 |
1.082072 |
0.49731 |
0.312763 |
-0.62184 |
0.848831 |
0.95164 |
1.103463 |
-0.2714 |
-0.49812 |
1.218872 |
0.444236 |
0.705184 |
-1.3672 |
0.133834 |
0.961583 |
-0.48328 |
-0.26841 |
0.386809 |
-0.83405 |
-0.27325 |
1.209837 |
1.322347 |
0.179446 |
0.846449 |
-0.41676 |
0.003201 |
0.153145 |
1.18809 |
1.357346 |
0.642291 |
0.752221 |
0.087303 |
-1.26885 |
1.156307 |
0.697638 |
0.214836 |
1.127546 |
-0.6137 |
-0.3126 |
-1.11222 |
0.874582 |
0.385658 |
-1.14954 |
-0.86883 |
-0.73166 |
0.373553 |
0.998501 |
-0.17805 |
-0.50618 |
-0.04097 |
-1.04919 |
0.769015 |
0.883515 |
-0.72219 |
0.037985 |
0.406867 |
0.190781 |
0.203688 |
-0.66863 |
0.713544 |
-0.39617 |
0.903498 |
0.157129 |
0.918021 |
-0.16296 |
-1.07497 |
-1.30852 |
-0.93188 |
-0.31516 |
1.418818 |
-0.19863 |
-0.10792 |
-0.57035 |
0.753334 |
0.040563 |
-0.61875 |
0.786541 |
0.761618 |
-0.85014 |
0.28436 |
-0.08084 |
1.838125 |
-0.30208 |
-0.19968 |
-0.41022 |
-0.08061 |
-1.09358 |
0.288966 |
-1.22378 |
1.57353 |
-0.70129 |
-0.40847 |
1.217662 |
-1.24659 |
-0.32256 |
-0.91548 |
0.128225 |
-0.18364 |
0.479223 |
-0.31728 |
1.306503 |
-0.60086 |
-1.22497 |
-0.18226 |
0.454245 |
-0.39068 |
-0.13209 |
-1.21912 |
0.068845 |
-0.68106 |
-1.12194 |
0.730198 |
1.246422 |
-1.05731 |
-0.22746 |
1.637362 |
0.784164 |
0.258947 |
0.885536 |
-1.0356 |
-1.26416 |
1.970262 |
0.219346 |
-1.30142 |
-0.28067 |
1.362763 |
1.411863 |
1.256881 |
0.593226 |
-0.84624 |
1.059629 |
-0.76449 |
-1.09201 |
1.116121 |
0.988323 |
1.246641 |
-0.05439 |
1.846288 |
-1.26706 |
1.072843 |
1.519946 |
-1.10241 |
-1.2332 |
0.269924 |
0.093195 |
-0.12426 |
1.616169 |
0.38547 |
1.260717 |
0.386418 |
1.236152 |
-1.12375 |
-0.63053 |
-0.96781 |
0.936027 |
0.987045 |
0.375102 |
0.375077 |
0.912125 |
-0.7773 |
-0.81619 |
0.347077 |
0.814585 |
1.36491 |
1.344215 |
1.303478 |
0.268386 |
-0.21729 |
0.973109 |
1.776623 |
-0.16124 |
0.671999 |
-0.38865 |
0.411627 |
-0.55977 |
0.260031 |
1.064446 |
0.168163 |
0.716128 |
-0.86329 |
0.892528 |
-0.14612 |
-0.33261 |
0.089743 |
-0.05661 |
0.845877 |
0.750584 |
-0.74008 |
-1.00557 |
-0.61676 |
-0.64413 |
1.233256 |
-0.21217 |
0.536955 |
-1.08937 |
-0.3948 |
-0.71328 |
-0.16688 |
-0.3451 |
0.86156 |
0.786283 |
-0.56257 |
1.969242 |
0.830474 |
1.029854 |
-0.41747 |
0.946447 |
-0.52843 |
0.490806 |
-0.62067 |
1.121775 |
0.405914 |
0.081398 |
0.50521 |
-1.18969 |
0.930401 |
0.707377 |
0.01152 |
1.171 |
0.290147 |
-0.82951 |
-0.08028 |
-0.47048 |
-0.50352 |
1.368564 |
-0.24528 |
-0.23006 |
-0.48178 |
0.727565 |
-0.95701 |
1.280494 |
-0.7393 |
0.783321 |
0.626506 |
-0.24116 |
-0.25647 |
-0.88645 |
-0.22562 |
0.650316 |
0.5456 |
-0.13808 |
-0.47477 |
0.826688 |
-0.00589 |
0.469489 |
0.259025 |
1.357987 |
0.790397 |
0.686704 |
0.867535 |
0.899534 |
0.714288 |
1.007343 |
1.273431 |
0.996549 |
-1.14032 |
-0.14249 |
0.216287 |
-0.27324 |
-1.3401 |
-0.81815 |
0.483834 |
-1.26259 |
0.216858 |
-1.25951 |
0.302414 |
-0.14717 |
-0.57963 |
-0.37465 |
0.658334 |
-0.15404 |
0.61136 |
-1.29183 |
1.739904 |
-0.49283 |
0.888311 |
0.600814 |
-0.29916 |
0.805776 |
-1.21997 |
-0.9157 |
-0.97354 |
1.11691 |
0.514128 |
0.855505 |
1.335452 |
-1.07653 |
0.116888 |
-0.80952 |
1.186275 |
2.109594 |
-0.89449 |
-1.00795 |
0.868677 |
-0.37707 |
0.963585 |
0.959436 |
-0.99816 |
-0.7475 |
-0.62981 |
-0.83866 |
-1.00127 |
1.257875 |
0.710148 |
1.056069 |
-0.51497 |
0.763636 |
1.85092 |
-0.11383 |
-0.72708 |
0.286835 |
-0.22838 |
-0.11307 |
-0.62378 |
-0.12442 |
0.28916 |
0.272181 |
-1.28801 |
2.081721 |
1.268025 |
-1.11983 |
0.929948 |
0.506931 |
-0.96493 |
0.105248 |
-0.8124 |
0.103537 |
1.54131 |
0.137297 |
-0.44814 |
-0.15481 |
1.292901 |
-0.77774 |
-1.01747 |
-0.87675 |
0.269553 |
-0.60475 |
-0.44363 |
0.400948 |
-1.12074 |
0.908125 |
0.826574 |
-0.98508 |
1.318399 |
0.75393 |
-0.10383 |
-0.11134 |
-0.16879 |
-0.0879 |
-0.17881 |
1.302744 |
1.038176 |
0.592475 |
0.245584 |
-0.4399 |
0.141874 |
0.693317 |
0.753578 |
0.940309 |
-0.90993 |
1.284097 |
1.020701 |
-0.98912 |
1.306301 |
-0.95303 |
0.057231 |
-0.68749 |
0.58034 |
0.89412 |
0.233131 |
-0.3613 |
0.484485 |
0.678809 |
-0.62381 |
0.662121 |
-0.73322 |
1.375211 |
-0.71139 |
0.176363 |
-1.22437 |
-0.05341 |
-1.10159 |
-0.86066 |
0.94689 |
-0.34205 |
-0.15162 |
-0.7975 |
0.439407 |
-0.20587 |
-1.30286 |
2.167698 |
0.959342 |
0.505052 |
-0.29486 |
0.30922 |
-0.9178 |
-0.18841 |
-0.65773 |
-1.30808 |
1.117257 |
0.846035 |
-0.86388 |
0.491751 |
0.588782 |
0.69304 |
-1.17348 |
-0.081 |
-1.02318 |
0.93498 |
-0.19728 |
0.311866 |
-1.31141 |
-1.15307 |
0.523435 |
-0.42968 |
-0.53769 |
-1.10642 |
0.897693 |
1.353988 |
0.435468 |
-0.484 |
-0.01926 |
1.16798 |
-0.64278 |
0.609691 |
0.818864 |
-0.77054 |
-0.20132 |
1.305633 |
-0.7929 |
-1.26605 |
-0.56882 |
-0.09425 |
-1.1229 |
1.301885 |
0.188366 |
-1.1212 |
1.351169 |
-0.07656 |
-1.05609 |
-1.17761 |
-1.03652 |
-0.2122 |
1.344937 |
1.27829 |
-0.80729 |
-0.29648 |
0.120712 |
0.263106 |
0.80844 |
-0.59917 |
-0.07285 |
1.337626 |
-0.96007 |
0.616303 |
0.582688 |
0.749497 |
0.189337 |
0.199857 |
0.181521 |
0.603987 |
-0.28158 |
-0.09086 |
-0.87578 |
0.890871 |
-1.01448 |
1.331381 |
-0.64018 |
1.223248 |
-0.39134 |
-0.65534 |
-0.35045 |
Fixez nivelul de prag x0=0.98;
Sistemul complet de evenimente Ws este:
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
Numarul valorilor care depasesc pragul este de 46, dar iau decizia ca este semnal doar in 34 de cazuri(cand coincide cu semnalul util,este simultan cu acesta), restul de semnal pierdandu-se.
Avem :
A1=50(evenimente)
A0=450
obtin
A1*=34
A0*=16
Descoperirea justa-Semnalul a aparut si s-a luat decizia de aparitie:
Pierderea semnalului-semnalul a aparut si s-a luat decizia de neaparitie;
Alarma falsa- semnalul nu a aparut si s-a luat decizia de aparitie;
A0*=46-34=12
F=12/450=0.026 =2.66%
Nedescoperirea justa-semnalul nu a aparut si s-a luat decizia de neaparitie;
Observam ca sunt indeplinite conditiile:
Concluzii :
Pentru a putea face observa cum se semnalul se comporta in alte conditii scad nivelul de prag la x0=0.82, numarul valorilor care il depasesc este de 39, dar iau decizia ca este semnal in doar 32 de cazuri (cand coincide cu semnalul util), restul de semnal pierdandu-se.
In acest caz se observa ca daca coboram nivelul de prag creste alarma falsa.
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