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8.2.6 Blackman Tukey. 병렬기구 로봇 연구실 김성주 - 20067166. 8.2.6 Blackman Tukey method : Periodogram smoothing. The methods of Bartlett and Welch 는 averaging periodograms and modified periodograms 에서 각각 the variance of the periodogram 를 감소 하는 방법이다.
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8.2.6 Blackman Tukey 병렬기구 로봇 연구실 김성주 -20067166 SUNG JU KIM
8.2.6 Blackman Tukey method : Periodogram smoothing The methods of Bartlett and Welch는 averaging periodograms and modified periodograms에서 각각 the variance of the periodogram를 감소 하는 방법이다. decreasing the statistical variability of the periodogram is periodogram smoothing For example, note that the estimate of r,(k) at lag k = N - 1 비록 N이 크더라도 관한 estimates의 평균은 작다. 이러한 estimate는 신뢰 할 수가 없다. In the Blackrnan-Tukey method, the variance of the periodogram는 periodogram에서 신뢰할 수 없는 estimate를 줄이기 위해 에 a window 적용 함으로서 줄여진다.
Specifically, the Blackman-Tukey spectrum estimate : a lag windowthat is applied to the autocorrelation estimate. For example, : a rectangular window extending from -M to M with M < N - 1, the estimates having the largest variance are set to zero the power spectrum estimate will have a smaller variance the frequency convolution theorem, the frequency convolution theorem, should be conjugate symmetric so that is real-yalued, the window should have a nonnegative Fourier transform, is guaranteed to be nonnegative.
the performance of the Blackman-Tukey method, We will evaluate the bias and the variance Eq. (8.23) value of the periodogram = if , the frequency convolution theorem
: is the Fourier transform of the lag window the variance of the Blackman-Tukey spectrum estimate FromEq. (8 .70) the mean-square value
Using the approximation given in Eq. (8.43) p407 Eq. (8.76) 의 first term Eq. (8.76) 의 second term
discrete-time Fourier transform of a Bartlett window, if N is large then the term in brackets may be approximated by an impulse of area 2n/N, for large N, the variance of the Blackman-Tukey estimate using Parseval's therem N >> M >> 1. Generally, it is recommended that M have a maximum value of M = N / 5 [26]
