ANALOG WAVELET TRANSFORM EMPLOYING DYNAMIC TRANSLINEAR CIRCUITS FOR CARDIAC SIGNAL CHARACTERIZATION Sandro A. P. Haddad 1 , Richard Houben 2 and Wouter A. Serdijn 1 1 Electronics Research Laboratory, Faculty of Information Technology and Systems, Delft University of Technology Mekelweg 4, 2628 CD Delft, The Netherlands Email:{s.haddad,w.a.serdijn}@its.tudelft.nl 2 Bakken Research Center Medtronic Endepolsdomein 5,6229 GW Maastricht, The Netherlands Email: richard.houben@medtronic.com ABSTRACT An analog QRS complex detection circuit, for pacemaker applications, based on the Wavelet Transform (WT) is presented. The system detects the wavelet modulus maxima of the QRS complex. It consists of a wavelet transform filter, an absolute value circuit, a peak detector and a comparator. In order to achieve the low-power requirement in pacemakers, we propose a new method for implementing the WT in an analog way by means of the Dynamic Translinear (DTL) circuit technique. Simulations indicate a good performance of the Wavelet Transform and the QRS complex detection. The resulting circuit operates from a 2-V supply voltage, dissipates at most 55nW per scale and can be fully integrated. Keywords – Wavelet transform, dynamic translinear circuits, ECG characterization, analog electronics 1. INTRODUCTION In [1], we proposed a method for implementing the WT in an analog way. An analog Gabor transform filter was proposed, of which the impulse response is an approximated Gaussian window function. This analog Gabor Transform filter, subsequently, was implemented with Complex First Order Systems (CFOS). Since the Gaussian function is perfectly local in both time and frequency domains and is infinitely differentiable, a derivative of any order n of the Gaussian function may be a Wavelet Transform (WT). For cardiac signal characterization we are interested in the first derivative Gaussian wavelet function [2]. In this paper we propose a method for implementing the first derivative Gaussian Wavelet function by means of dynamic translinear circuits. Also we describe an algorithm an its circuit implementation based on local modulus maxima (i.e., both positive and negative peaks) point detection for ECG characterization. Section 2 treats the characteristics of the QRS complex detection algorithm. Next, Section 3 describes the circuit design. Some results provided by simulations are shown in Section 4. Finally, Section 5 presents the conclusions. 2. QRS DETECTION ALGORITHM QRS complex detection is important for cardiac signal characterization [3]. Many systems have been designed in order to perform this task. In [4] it was shown that, in spite of the existence of different types, a basic structure is common for many algorithms. This common structure is given in Fig. 1a. It is divided into a filtering stage (comprising linear and/or nonlinear filtering) and a decision stage (comprising peak detection and decision logic). The Wavelet has been shown to be a very efficient tool for local analysis of nonstationary and fast transient signals due to its good estimation of time and frequency localizations. This feature can be used to distinguish cardiac signal points from severe noise and interferences. Therefore, the algorithm detection of the QRS complex presented here is based on modulus maxima of the wavelet transform. The two maximas with opposite signs of the WT correspond to the complex QRS and are illustrated in Fig. 1b. Filtering Stage Peak detection Linear and/or nonlinear filter Decision Stage Decision algorithm Cardiac signal Event detection (a) Ventricular signal Wavelet Transform (b) Fig. 1. (a)Block diagram of the basic structure of the QRS detectors [4]. (b) Cardiac signal and the modulus maxima of the WT The main idea of the WT is to look at a signal at various windows and analyze it with various resolutions. It depends upon two parameters, being scale a and position τ. For smaller values of a, the wavelet is contracted in the time domain and gives information about the finer details of the signal. In the same way, a global view of the signal is obtained by larger values of this scale factor. Furthermore, in order to avoid redundancy, the scale I-121 0-7803-7762-1/03/$17.00 ©2003 IEEE