예제: 선형 추세 제거

함수 > 신호 가공 > 시계열 분석 > 예제: 선형 추세 제거

예제: 선형 추세 제거

detrend 함수를 사용하여 최소자승적합선을 사용한 데이터에서 선형 추세를 근사화한 후 제거합니다.

1. 지수 신호를 정의합니다.

2. 지수 신호를 도표화합니다.

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3. whiten 함수를 사용하여 신호에 백색 노이즈를 추가합니다.

4. 원래 신호와 노이즈가 추가된 신호를 도표화합니다.

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5. detrend 함수를 노이즈가 추가된 신호에 적용합니다.

6. 원래 함수와 추세 제거된 함수를 도표화합니다.

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선형 추세가 사라지는 것은 추세 제거 전과 후의 최소자승선을 살펴보면 더 자세히 확인할 수 있습니다.

7. slope 및 intercept 함수를 사용하여 추세 제거 전과 후의 기울기 및 절편을 계산합니다.

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이 계산은 항상 필요합니다. detrend의 출력은 최소자승선이 원점을 통과하는 수평선인 벡터입니다. 즉, 기울기와 절편 모두 0에 근접합니다.

detrend의 효과는 추세 제거 전과 후의 DC 항에서 알 수 있는 것처럼 입력 데이터에서 평균이 제거된다는 것입니다.

8. dft 함수를 사용하여 추세 제거 전과 후의 DC(첫 번째) 항을 계산합니다.

detrend 함수는 간단한 "전처리" 작업을 수행하며, 대개 이 작업은 평활화 연산 전에 수행됩니다. 위에서 설명한 것처럼, 추세 제거는 스펙트럼 추정의 첫 단계로 자주 사용됩니다.