SIGNALDEPENDENT ORTHOGONAL TRANSFORM FOR ECG SIGNAL ANALYSIS

1、专业文档，值得珍藏！signal-dependent orthogonal transform for ecg signal analysis优秀文档，值得收藏！h. baali, r. akmeliawati and m.j.e. salamidepartment of mechatronics engineering, international islamic university malaysia (iium) jalan gombak, 53100 kuala lumpur, malaysia .baalihayahoo.frabstract: linear prediction i

2、s formulated to develop a real valued, signal dependent orthogonal transform with good energy compaction property. in order to appreciate the effectiveness of the technique, applications to electrocardiographic (ecg) signals compression and interpolation are discussed and benchmarked against the sta

3、te-of-the-art dct transform. results show that the technique achieves competitive results. an insight is given to use the technique for model order selection. keywords: ecg, period normalization, linear prediction, signal-dependent transform, svd. introductionlinear prediction (lp) has been extensiv

4、ely used for signal and spectral analysis 1. the idea of lp is to consider the observed signal as the output of an all pole filter of order p excited by some unknown input. the best prediction coefficients are found by the minimization of the sum-of-squared error (sse) between the original and the p

5、redicted signal with respect to the lpc coefficients.the original signal can be recovered by using: y=he, where y and e are respectively the n1 columns vectors of the observed signal samples and the residual error, while h is the nn impulse response matrix of the synthesis filter (also called lpc fi

6、lter) whose entries are completely determined by the linear prediction coefficients. h is a lower triangular and toeplitz matrix of the form:h=1h1.hn-1 01.hn-2 . . . . 00.1 (1)applying the singular values decomposition (svd) to h gives: y=udvte , (2)where u and v are nn orthogonal matrices, and d is

7、 a real valued nn diagonal matrix with the singular values of h on its diagonal, tdenotes the transpose. the aforementioned decomposition has been adopted for accurate representation of the excitation signal applied to speech signal in 2 and for ecg period normalization in 3. in this work, the decom

8、position is used to build an orthogonal transform that can be applied in a wide range of areas.we define the forward and inverse transforms respectively as follows: =uty and y=u .from (2), each component of the residual signal (e) is mapped onto the space spanned by v and then weighted by the corres

9、ponding singular value. knowing that the singular values are always decaying, one can expect that the transform coefficients vector would be sparse.ecg signal compression once the transform coefficients are calculated and sorted in descending order, a compression ratio(cr) n:m is achieved using the

10、proposed transform by keeping the largest m-p coefficients while the remaining n-m+p are discarded (p lp coefficients are saved as side information to form the matrix h) . the same cr is achieved using the dct by maintaining the m largest transform coefficients 4. the time domain signal retrieval is

11、 accomplished by inserting zeros in the transform domain to replace the discarded coefficients followed by the application of the inverse transforms. when both dct and the proposed transform are applied to an ecg signal as shown in fig. 1, most of the signal energy is packed in a few coefficients wh

12、ere the shape is damped sinusoidal as shown in fig. 1(b). fig. 1 transform based ecg compression(a) original and reconstructed ecgs, (b) transform domain vector and dct coefficients vector the performance of the two techniques are evaluated on signals with large waveform characteristics variations n

13、amely, normal sinus rhythm (n) and premature ventricular contraction (pvc). the data is taken from the mit-bih arrhythmia database. the widely used percent root mean square difference (prd%) is employed to measure the distortion between the original and reconstructed signal ( y ), that is,prd%=y-yty

14、-yyty100 (3)different compression ratios are tested using different model orders and the corresponding prds obtained after signal reconstruction are summarized in table 1. results when the lp coefficients are not taken into account when computing the cr are also reported in table i.in the case where

15、 the lp coefficients are not taken into account, the proposed technique outperforms the dct for high cr. however, for low cr, dct achieves better prd for normal rhythm. when the lp coefficients are taken into account dct achieves slightly better results with exception to cr 3:1 for pvc rhythm. for b

16、oth transforms, compression performances are better for pvc rhythm when compared to the normal sinus rhythm.table i. compression performances for different compression ratios compared to the state-of-the-art dct techniquecrprd3:14.5:16:19:1normal sinus rhythmdct0.9609 3.0815 7.5394 22.5177proposed (

17、p =1)1.2999 3.2173 8.2514 24.1802p=1, lpc not maintained1.2754 3.1279 7.7170 23.0390proposed ( p =2)1.6787 3.5586 8.3577 24.8113p=2, lpc not maintained1.6276 3.3526 7.5413 22.3715proposed ( p =3)1.9316 4.0540 8.2409 23.6260p=3, lpc not maintained1.8421 3.6212 7.2555 19.7117proposed ( p =4)1.7023 4.1

18、814 9.2708 25.3171p=4, lpc not maintained1.5814 3.5539 7.6041 20.5481pvcdct0.6142 1.0441 1.6895 4.3642proposed ( p =1)0.6262 1.0949 1.8725 4.4706p =1,lpc not maintained0.6213 1.0755 1.8275 4.2998proposed (p =2)0.6054 1.1357 1.9606 4.7059p =2, lpc not maintained0.5969 1.0890 1.8532 4.3381proposed ( p

19、 =3)0.6089 1.1590 2.0187 4.9107p =3, lpc not maintained0.5962 1.0867 1.8518 4.3391proposed ( p =4)0.6016 1.1429 2.1006 5.1777p =4, lpc not maintained0.5835 1.0497 1.8816 4.4091ecg signal interpolation in the special case of first order linear prediction, time compression and stretching can be accomp

20、lished using the following steps:1) compute the left singular vectors of the impulse response matrix h to construct an orthonormal transform (matrix u). 2) map the ecg period (y) from the time domain to the svd domain (the transform domain) by using: =uty . 3) zero pad (when the signal is to be stre

21、tched) or truncate (when the signal is to be shrunk) the transformed ecg vector () to match the desired length (n*). the resulting vector is called (nz).4) multiply (nz) by the matrix unz to form a normalized ecg period (ynz). note that hnz represents the impulse response matrix of the desired size

22、n*n* and is given by (4), and unz is its left singular vectors matrix. hnz=1h1.hn*-1 01.hn*-2 . . . . 00.1 (4)5) apply reverse steps to recover the heartbeats with their original lengths. the recovered signal is shown in fig. 2 along with the residual error (this last step might be needed in some ap

23、plications but not always). similarly to the dct, the method is reversible when the signal is expended (all the transformations are isometric). on the other hand, the distortion due to time compression (shrinking) of the signal is minimized due the energy packing eciency of the technique. the basis

24、functions of the transform matrix u can be found analytically as follows:ujk=asin jk , for k = 1, ., n and j = 1, ., n.the constant a is chosen so that the norm of uk is unity.k, k = 1,., n, are the solutions of the equation:asin n-sin n+1=0 , (5) a is the lp coefficient similarly, the bases functio

25、ns of unz are given by:ujknz=bsin jknz , for k = 1,., n* and j = 1, ., n*. the constant b is chosen so that the norm of uknz is unity.knz k = 1,.,n*, are the solutions of the equation:asin n*knz -sin n*+1knz =0 (6)fig. 2 distortion-free recovering of a normal signal (stretched by 50% of its original

26、 length)model order selection (mos)accurate mos has been a challenging problem in many areas of signal processing where several approaches have been reported in the literature 5. for ecg signals, the reported prediction orders varies between one and four 67. using the proposed transformation, it is

27、observed that the transform efficiency keeps improving when the model order increases from one to three then decreases for a model order of four as shown in fig. 3. this observation holds for both normal and pvc rhythms analyzed in this paper. consequently, the proposed technique provides an alterna

28、tive solution to mos which would be further investigated in our future research work. the transform efficiency is defined as the ratio between the energy retained in the first mth transform coefficients and the energy of the entire ecg period (or equivalently all the transform coefficients).fig. 3 t

29、ransform efficiency for pvc rhythmacknowledgments this work was supported by the ministry of higher education (mohe) of malaysia under the fundamental research grant scheme frgs.conclusiona signal dependent transform that has the ability to adjust to the signal characteristics is introduced and appl

30、ied to some fundamental signal processing problems. the overhead side information needed to generate the basis functions is reduced when compared to other signal dependent transforms. an analytical model has been developed to generate basis functions in the case of first order linear prediction.references1. vaidyanathan, p. p, “the theory of linear prediction” : morgan & claypool, london, u.k, 2008.2. atal,b., “a