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Aparitia, intr-o celula de timp data, a unui semnal





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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