tailieunhanh - Biosignal and Biomedical Image Processing MATLAB-Based Applications Muya phần 6

Tham khảo tài liệu 'biosignal and biomedical image processing matlab-based applications muya phần 6', ngoại ngữ, anh văn thương mại phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 178 Chapter 7 tions could be used to probe the characteristics of a waveform but sinusoidal functions are particularly popular because of their unique frequency characteristics they contain energy at only one specific frequency. Naturally this feature makes them ideal for probing the frequency makeup of a waveform . its frequency spectrum. Other probing functions can be used functions chosen to evaluate some particular behavior or characteristic of the waveform. If the probing function is of finite duration it would be appropriate to translate or slide the function over the waveform x t as is done in convolution and the short-term Fourier transform STFT Chapter 6 s Eq. 1 repeated here tt STFT t f j x T w t - T e-yf dT 2 tt where f the frequency also serves as an indication of family member and w t T is some sliding window function where t acts to translate the window over x. More generally a translated probing function can be written as tt X t m j x T f t -T mdT 3 tt where f t m is some family of functions with m specifying the family number. This equation was presented in discrete form in Eq. 10 Chapter 2. If the family of functions f t m is sufficiently large then it should be able to represent all aspects the waveform x t . This would then allow x t to be reconstructed from X t m making this transform bilateral as defined in Chapter 2. Often the family of basis functions is so large that X t m forms a redundant set of descriptions more than sufficient to recover x t . This redundancy can sometimes be useful serving to reduce noise or acting as a control but may be simply unnecessary. Note that while the Fourier transform is not redundant most transforms represented by Eq. 3 including the STFT and all the distributions in Chapter 6 would be since they map a variable of one dimension t into a variable of two dimensions t m . THE CONTINUOUS WAVELET TRANSFORM The wavelet transform introduces an intriguing twist to the basic concept defined by Eq. 3 . In wavelet .

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