chapter 1 통계이론의 기초
1.1 용어 설명 ························································································· 14
1.2 모집단과 표본 ·················································································· 15
1.3 분산 평가 ························································································· 27
1.4 통계적 추정(statistical estimation) ····················································· 30
1.5 측정불확도 포함 ·············································································· 32
연습문제 ································································································ 34

chapter 2 확률변수와 확률분포함수
2.1 연속확률분포 ··················································································· 36
2.2 Q function의 정의 ············································································· 37
2.3 이항분포(binominal distribution) ····················································· 41
2.4 표준정규분포 ··················································································· 43
2.5 student"s 분포 ··················································································· 47
2.6 균등분포(uniform distribution) 및 삼각형 분포 ·································· 55
2.7 F-분포 ······························································································ 57
2.8 중심극한 정리(central limit theorem) ················································· 59
연습문제 ································································································ 62

chapter 3 자유도 해석
3.1 개 요 ································································································ 66
3.2 표본의 크기에 대한 자유도 ······························································· 68
3.3 표본 변수의 자유도 ········································································ 70
3.4 회귀와 영(null) 모델 자유도 ···························································· 72
3.5 정규 모집단의 통계량 분포와 자유도 ················································ 72
3.6 수학에서의 자유도 ·········································································· 74
3.7 역학계의 자유도 ·············································································· 76
3.8 화학계 및 물리계의 자유도 ······························································ 78
연습문제 ································································································ 80

chapter 4 신호 해석을 위한 함수론 응용
4.1 센서의 직선성과 감도 ······································································ 82
4.2 테일러급수(Taylor series) ······························································· 86
4.3 오일러(Euler"s) 공식 ········································································ 89
4.4 직교 함수 (orthogonal function) ······················································ 92
4.5 계단 함수와 임펄스 함수 ································································· 96
4.6 sinc 함수와 샘플(Sa) 함수 ····························································· 100
4.7 푸리에 급수(fourier series) ····························································· 102
4.8 푸리에 변환(fourier transform) ······················································· 110
4.9 중첩 적분 ······················································································ 118
4.10 라플라스 변환 ·············································································· 123
4.11 퍼스발의 정리(parseval"s theorem) ··············································· 126
4.12 전달함수(transfer function) ··························································· 129
4.13 힐버트 변환(Hilbert transform) ····················································· 136
4.14 베셀 함수 (Bessel function) ·························································· 138
4.15 확률(probability) ·········································································· 143
4.16 표본화(Sampling)와 보간법(interpolation) ···································· 146
4.17 랜덤 펄스열의 자기상관 함수 ······················································ 152
4.18 정합 필터 (matched filter) ···························································· 156
4.19 상관 함수 (correlation function) ···················································· 161
4.20 2차 시스템 해석(Analysis of 2nd order system) ···························· 166
4.21 백색 잡음 (additive white gaussian noise) ····································· 169
연습문제 ······························································································ 172

chapter 5 미분 방정식과 해석함수
5.1 개요 ······························································································ 176
5.2 상미분 방정식 ··············································································· 176
5.3 벡터의 미분 ·················································································· 184
5.4 선 적분 과 면 적분 ········································································ 187
5.5 편미분 방정식 ··············································································· 190
5.6 복소함수 ······················································································· 193
5.7 유수 정리(Residue Theorem) ·························································· 197
연습문제 ······························································································ 203

chapter 6 이산신호 처리
6.1 개 요 ···························································································· 208
6.2 이산신호 ························································································ 210
6.3 이산시간 푸리에 분석 ···································································· 214
6.4 이산 푸리에 변환 ··········································································· 220
6.5 이산시스템의 응답 ········································································ 227
6.6 z변환 ····························································································· 235
6.7 이산시스템 표현과 분석 ································································ 246
6.8 디지털 필터 구조 ··········································································· 251
연습문제 ······························································································ 259

chapter 7 선형 연산자와 동적 시스템의 수학적 표현
7.1 개 요 ···························································································· 262
7.2 선형 연산자 ··················································································· 262
7.3 시스템의 수학적 표현 ···································································· 273
7.4 선형 동적방정식과 임펄스 행렬 ··················································· 276
7.5 비선형 수학적 모델의 선형화 ························································ 281
연습문제 ······························································································ 283

chapter 8 측정불확도의 표현 및 평가
8.1 개 요 ····························································································· 286
8.2 측정불확도의 기초 개념 ······························································· 287
8.3 측정불확도 요소 ············································································ 288
8.4 측정불확도 전파법칙 ····································································· 289
8.5 측정불확도 평가방법 ···································································· 292
8.6 불확도 평가절차 ··········································································· 293
8.7 A형 표준불확도 평가 ····································································· 294
8.8 B형 표준불확도 평가 ····································································· 298
8.9 합성표준불확도 ·············································································· 303
8.10 확장불확도 ·················································································· 305
8.11 유효자유도 ··················································································· 306
8.12 포함인자의 결정 ··········································································· 307
8.13 불확도 보고 ················································································· 310
연습문제 ······························································································ 311

chapter 9 측정시스템의 불확도 평가 방법
9.1 측정시스템의 구성 ········································································ 314
9.2 측정시스템의 주요 오차 요소 ························································· 315
9.3 측정오차 분류 ················································································ 315
9.4 RSS 방식에 의한 불확도 평가 ·························································· 317
9.5 힘 측정시스템의 불확도 평가 ························································ 318
9.6 도플러 레이더 측정시스템의 불확도 평가 ······································ 320
9.7 솔레노이드 코일을 이용한 속도 측정시스템의 불확도 평가 ··········· 322
9.8 동구게이지 측정불확도 평가 ························································ 325
9.9 압전형 압력센서를 이용한 포구(砲腔) 내부 압력 측정불확도 평가 · 329
9.10 열전대 센서를 이용한 온도 측정시스템의 불확도 평가 ················· 331
9.11 모발 습도계의 측정불확도 평가 ··················································· 336
연습문제 ······························································································ 339

chapter 10 교정 불확도 평가
10.1 최고 측정능력(BMC : Best Measurement Capability) ····················· 358
10.2 최고 측정능력의 표현방법 ···························································· 358
10.3 최고 측정능력의 도시적 이해 ························································ 359
10.4 교정시스템의 불확도 요소 ···························································· 359
10.5 교정 대상기기의 불확도 종류 ························································ 359
10.6. 스텝 동압력 교정기기의 불확도 평가 ·········································· 362
10.7 멀티미터 교정 불확도 평가 ·························································· 368
연습문제 ······························································································ 381

chapter 11 측정불확도 평가 사례
11.1 측정불확도 평가 논문 작성 예 ······················································ 388
11.2 변형률 측정시스템의 불확도 평가 ················································ 393
11.3 압력 측정시스템의 불확도 평가 ··················································· 398
11.4 RTD 저항 및 열전대 센서를 이용한 교정시스템의 불확도 평가 ····· 401
11.5 포구속도 측정용 도플러레이더 측정불확도 평가 ······················· 405
11.6 포구속도 측정용 광 스크린시스템의 측정불확도 평가 ·················· 408
연습문제 ······························································································ 420

chapter 12 회귀분석의 결정계수 적합도 평가
12.1 개 요 ····························································································· 422
12.2. 회귀모형과 회귀방정식의 결정 ··················································· 423
12.3 최소자승법의 회귀계수 추정 ························································· 424
12.4. 회귀선의 적합도 ·········································································· 430
12.5. 회귀계수와 결정계수 계산 ··························································· 435
12.6 검토 ······························································································ 440
연습문제 ······························································································ 441

chapter 13 신호 검출용 회로 해석
13.1 브리지 회로 ·················································································· 444
13.2 원형 코일센서 ·············································································· 447
13.3 압전기 센서 ·················································································· 450
13.4 LVDT 센서 ··················································································· 452
13.5 도플러 신호 발생기 ······································································· 455
13.6 필터 회로 ······················································································ 457
연습문제 ······························································································ 462

chapter 14 오일러상수 감마
14.1 조화급수 ······················································································· 464
14.2 제타함수 ······················································································· 465
14.3 감마함수 ······················································································· 465
14.4 오일러-매클로린 합 ······································································ 467
14.5 리만의 소수 세기 ········································································· 468
14.6 테일러 전개 ················································································· 469
14.7 복소미분과 적분 ·········································································· 473
연습문제 ······························································································ 479
부 록 ···································································································· 481

참고문헌 ·································································································489
찾아보기 ·································································································491