Introduction The electrocardiogram (ECG) contains well-known PQRST(U) pattern. Its morphology has been extensively studied since the technique of recording was introduced in the beginning of the twentieth century. The use of computers for ECG recording enabled studies of dynamic properties of the ECG. In particular, two important characteristics have been revealed: amplitude and frequency modulation. 2 11 9 17 6 The amplitude characteristics and amplitude modulation received less attention, especially because the notion of the ECG amplitude is ambiguous: the heart as a source of the signal is moving and the signal is collected from the surface of the body that is moving as well. In addition, it is usually recorded as a 2-D projection. However, it has long been recognized that one of the sources of the amplitude modulation—the respiratory related movement of the thorax can be usefully used to extract the information about the respiration. 5 13 1 4 8 10 3 16 The problem to reconstruct waveform from the discrete Fourier analysis is that the biological signal has complicated properties; being non-stationary wave, including random noise and having interactive components. However, though people rarely notice, the essential problem is that there is no way to gather impartial and statistical samples. That is why samples from an unique sampling frequency are biased for spectral analysis even if fine sampling. 12 Algorithm The principle of this algorithm is the selection of three particular scale transforms. Two scales convert modulating waveforms into the periodic signal and the other converts the periodic components into a few terms. The role of the SFT is to hold sample information for any transforms. a j t u j t o j t t k a j t u j t o j t a j   a j t u j   u j τ j x t x j t x j t x a j u j a j a j t u j a j a kj t u kj a kj k  k j · k j T j o j   o j t x j t r j r j x j t τ j t 1 \documentclass[12pt]{minimal}
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$$ x'(t){\text{ }} = {\sum {u_{j} } }(\tau _{j} (t))v_{j} (\tau _{j} (t)) + \varepsilon _{m} (t)\quad (j = 1,...,m) $$\end{document} 2 t t τ j j τ j t v j t j ε m t m 2 x′ t v j τ j τ j j =  ..., m Quantity of information on the modulating signal 3 4 2 j p j  = r j /n x′ t m p r 1 r 2 r m p 1 r p 2 r ... p m rm \documentclass[12pt]{minimal}
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\begin{document}$$\dot{V}(t).$$\end{document} Fig. 3 Classified process of modulating signal of the algorithm    x t x′ j t V t V j t x j t x t ρ V j t V t 4 1 1 ρ ρ ≈ ρ ≤  4 ρ ≈  u j τ j T j Fig. 4 X Y V j t V j t V t  Table 1 ρ i V j t V j 1 t V t Cardiac stages PQ QRS ST-T Base line  Total ρ i V j t V t  ρ i 0.8328 0.8243 0.8149 0.8151  0.8244  Number of samples 13,566 12,690 33,018 43,553  102,827 Respiratory stages I  II  III  VI  V  Total ρ i V j t V t  ρ i 0.3990 0.9788 0.5772 0.9970 0.9546 0.7273  Number of samples 25,747 25,210 25,928 14,574 11,558 103,017 ρ i V j t V t  ρ i 0.9923 0.6589 0.9943 0.8032 0.7305 0.91648  Number of samples 25,286 22,816 21,163 15,155 18,077 102,497 I II III VI V V j t 2 m 5 x′ t 5 x j t 5 V j+ t 5 ε j+ t 5 ε t ε j t 5 x j t ε t 5 V t 5 u j+ t 5 . V j+ t ε j+ t V t ε j+ t V t Fig. 5 Scale classification of the four modulating signals in an electro-cardiac signal  V j t V t 4 . ρ 1 V f V j+ f ε j+ f φ f V f V j+ f 6 V f V j f ε j+ f ε j+ f V f V j+ f Fig. 6 V f V j f ε j f  V j t ε j t ε j t V j t ε j t Discussion and conclusion 2 9 n n f 11 12 t k t i t j t i t j \documentclass[12pt]{minimal}
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