TAILIEUCHUNG - Biosignal and Biomedical Image Processing phần 6

Tham khảo tài liệu 'biosignal and biomedical image processing phần 6', kỹ thuật - công nghệ, kĩ thuật viễn thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Wavelet Analysis 193 theoretically and practically. It is possible at least in theory to go between the two approaches to develop the wavelet and scaling function from the filter coefficients and vice versa. In fact the coefficients c n and d n in Eqs. 14 and 15 are simply scaled versions of the filter coefficients c n 2 h0 n d n 2 h1 n 25 With the substitution of c n in Eq. 14 the equation for the scaling function the dilation equation becomes tt ộ í x 2 h0 n ộ 2í - n 26 n -tt Since this is an equation with two time scales t and 2t it is not easy to solve but a number of approximation approaches have been worked out Strang and Nguyen 1997 pp. 186-204 . A number of techniques exist for solving for ộ t in Eq. 26 given the filter coefficients h1 n . Perhaps the most straightforward method of solving for Ộ in Eq. 26 is to use the frequency domain representation. Taking the Fourier transform of both sides of Eq. 26 gives i M H f 27 Note that 2t goes to f2 in the frequency domain. The second term in Eq. 27 can be broken down into H0 f 4 O ro 4 so it is possible to rewrite the equation as shown below. .JfLJmLM i M H2 H4 4jl f f f Ịto Jà 2H4 H 8 In the limit as N tt Eq. 29 becomes O ro J 28 29 30 The relationship between ộ t and the lowpass filter coefficients can now be obtained by taking the inverse Fourier transform of Eq. 30 . Once the scaling function is determined the wavelet function can be obtained directly from Eq. 16 with 2h1 n substituted for d n tt W x 2 h1 n ộ 2í - n 31 n -tt Copyright Marcel Dekker Inc. All rights reserved. Marcel Dekker Inc. 270 Madison Avenue New York New York 10016 TLFeBOOK 194 Chapter 7 Eq. 30 also demonstrates another constraint on the lowpass filter coefficients h0 n not mentioned above. In order for the infinite product to converge or any infinite product for that matter H0 w 2 must approach 1 as j . This implies that H0 0 1 a criterion that is easy to meet with a lowpass filter. While Eq. 31 provides an explicit formula for .

Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.