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In this paper, we describe a QRS complex detector based on the dyadic wavelet transform (Dy WT) which is robust to time-varying QRS complex morphology and to noise. We design a spline wavelet that is suitable for QRS detection. The scales of this wavelet are chosen based on the spectral characteristics of the electrocardiogram (ECG) signal. We illustrate the performance of the Dy WT-based QRS detector by considering problematic ECG signals from the American Heart Association (AHA) data base. Seventy hours of data was considered. We also compare the performance of Dy WT-based QRS detector with detectors based on Okada, Hamilton-Tompkins, and multiplication of the backward difference algorithms. From the comparison, results we observed that although no one algorithm exhibited superior performance in all situations, the Dy WT-based detector compared well with the standard techniques. For multiform premature ventricular contractions, bigeminy, and couplets tapes, the Dy WT-based detector exhibited excellent performance.

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The time-frequency (TF) version of the wavelet transform and the "affine" quadraticlbilinear TF representations can be used for a TF analysis with constant-Q characteristic. This paper considers a new approach to constant-Q TF analysis. A specific TF warping transform is applied to Cohen's class of quadratic TF representations, which results in a new class of quadratic TF representations with constant-Q characteristic. The new class is related to a "hyperbolic TF geometry" and is thus called the hyperbolic class (HC). Two prominent TF representations previously considered in the literature, the Bertrand Po distribution and the Altes-Marinovic Q-distribution, are members of the new HC. We show that any hyperbolic TF representation is related to both the wideband ambiguity function and a "hyperbolic ambiguity function." It is also shown that the HC is the class of all quadratic TF representations which are invariant to "hyperbolic time-shifts" and TF scalings, operations which are important in the analysis of Doppler-invariant signals and self-similar random processes. The paper discusses the definition of the HC via constant-Q warping, some signal-theoretic fundamentals of the "hyperbolic TF geometry,'' and the description of the HC by 2-D kernel functions. Several members of the HC are considered, and a list of desirable properties of hyperbolic TF representations is given together with the associated kernel constraints. I. INTRODUCTION UADRATIC time-frequency representations (QTFR's) are useful in the analysis of nonstationary signals [l]. This paper discusses a new class of "constant-Q" QTFR's. By way of introduction, and to establish the notation used, we first give a brief review of two basic QTFR classes. In the following, let x (t) be a signal with Fourier transform X (f) = jYm x(t)e-'2*fr dt.