Hakan GÜRKAN, Sıddık YARMAN, Ali Nur GÖNÜLEREN

Elektrokardiyogram (EKG) işaretlerinin temel tanım ve zarf fonksiyonları ile modellenmesi

Bu çalışmada, EKG işaretlerinin Temel Tanım ve Zarf Fonksiyonları ile modellenmesine yönelik yeni bir yöntem sunulmaktadır. Sunulan yöntem, herhangi bir EKG işaretine ilişkin $X_i(t)$ çerçeve fonksiyonunu $X_i(t) = C_ialpha_K(t)varphi_R(t)$ biçiminde modellemektedir. Bu modelde, $varphi_R(t)$, Temel Tanım Fonksiyonu olarak adlandırılmakta ve bir $C_i$ katsayısı ile X, çerçeve vektörünün en yüksek enerjisini taşımaktadır. $alpha_K(t)$, Zarf Fonksiyonu olarak adlandırılmakta ve $X_i$ çerçeve vektörünün zarfını oluşturmaktadır.$C_i$ katsayısı da Çerçeve Ölçekleme Katsayısı olarak adlandırılmaktadır. Temel Tanım ve Zarf Fonksiyonları iletim bandının herbir düğümüne yerleştirilerek EKG işaretinin iletimi, Temel Tanım ve Zarf Vektör Bankasının R ve K indislerinin ve $C_i$ katsayısının iletimine indirgenerek önemli bir sıkıştırma oranı gerçeklenmiştir.

Modeling electrocardiogram (ECG) signals via signature and envelope functions

In this paper, a new method to model ECG signals by means of "Signature and Envelope Functions" is presented. In this work, on a frame basis, any ECG signal $X_i(t)$ is modeled by the form of $X_i(t) = C_ialpha_K(t)varphi_R(t)$. In this model, $varphi_R(t)$ is defined as the Signature function since it carries almost maximum energy of the frame vector $X_i$ with a constant $C_ialpha_K(t)$ is referred to as Envelope Function since it matches the envelope of $C_ivarphi_R(t)$ to the original frame vector $X_i$; and $C_i$ is called the Frame-Scaling Coefficient. It has been demonstrated that the sets $Phi={varphi_R(t)}$ and A=${alpha_K(t)}$ constitute a "Signature and Envelope Functional Banks" to describe any measured ECG signal. Thus, ECG signal for each frame is described in terms of the two indices "R" and "K" of Signature and Envelope Functional Banks and the frame-scaling coefficient $C_i$. It has been shown that the new method of modeling provides significant data compression with low level reconstruction error while preserving diagnostic information in the reconstructed ECG signal. Furthermore, once Signature and Envelope Functional Banks are stored on each communication node, transmission of ECG signals reduces to the transmission of indexes "R" and "K" of $[alpha_K(t),varphi_R(t)]$ pairs and the coefficient $C_i$, which also result in considerable saving in the transmission band.

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