tailieunhanh - Biosignal and Biomedical Image Processing MATLAB-Based Applications Muya phần 5

Tham khảo tài liệu 'biosignal and biomedical image processing matlab-based applications muya phần 5', ngoại ngữ, anh văn thương mại phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Time-Frequency Analysis 149 window is made smaller to improve the time resolution then the frequency resolution is degraded and visa versa. This time-frequency tradeoff has been equated to an uncertainty principle where the product of frequency resolution expressed as bandwidth B and time T must be greater than some minimum. Specifically BT -1 3 4n The trade-off between time and frequency resolution inherent in the STFT or spectrogram has motivated a number of other time-frequency methods as well as the time-scale approaches discussed in the next chapter. Despite these limitations the STFT has been used successfully in a wide variety of problems particularly those where only high frequency components are of interest and frequency resolution is not critical. The area of speech processing has benefitted considerably from the application of the STFT. Where appropriate the STFT is a simple solution that rests on a well understood classical theory . the Fourier transform and is easy to interpret. The strengths and weaknesses of the STFT are explored in the examples in the section on MATLAB Implementation below and in the problems at the end of the chapter. Wigner-Ville Distribution A Special Case of Cohen s Class A number of approaches have been developed to overcome some of the shortcomings of the spectrogram. The first of these was the Wigner-Ville distribution which is also one of the most studied and best understood of the many time-frequency methods. The approach was actually developed by Wigner for use in physics but later applied to signal processing by Ville hence the dual name. We will see below that the Wigner-Ville distribution is a special case of a wide variety of similar transformations known under the heading of Cohen s class of distributions. For an extensive summary of these distributions see Boudreaux-Bartels and Murry 1995 . The Wigner-Ville distribution and others of Cohen s class use an approach that harkens back to the early use of the .

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