IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 9, SEPTEMBER 1998 2541 Multiresolution Wavelet Decomposition of the Seismocardiogram William Sandham, David Hamilton, Anthony Fisher, Wei Xu, and Michael Conway Abstract— The seismocardiogram (SCG) is a complex, nonstationary signal used for pathological analysis of cardiac vibratory activity. This correspondence reports the results of multiresolution wavelet decomposi- tion of SCG’s for a normal male subject, pertaining to three different physiological conditions. Marked differences in certain sub-bands are discernible, which are undetectable in the time-domain alone. I. INTRODUCTION Seismocardiography is an emerging, noninvasive technique de- veloped for recording and analyzing cardiac vibratory activity as a measure of cardiac contractile performance [1], [2]. The seis- mocardiogram (SCG) is a signal recording obtained by placing an ultra low-frequency acceleration transducer on the sternum of human subjects. A single channel electrocardiogram (ECG) is recorded simultaneously to provide a timing reference for signal processing and analysis. Fig. 1 shows a recording of the (raw) SCG and ECG for a healthy subject at rest. The QRS complex in the ECG and analogous W com- plex in the SCG are clearly evident. Recent studies have demonstrated the potential of SCG’s for predicting the onset of coronary artery disease, monitoring congestive heart failure, and evaluating patient response to various cardiological drug therapies [3]–[5]. Current indications are that seismocardiography offers superior clinical diag- nostibility compared with other forms of displacement cardiography, such as apexcardiography, kinetocardiography, ballistocardiography, and cardiokymography, all of which have limitations due to technical difficulty, cost, and/or uncertain clinical applicability. An additional application for SCG’s is their use in enhancing the diagnostic performance of the associated ECG’s [3]. Previous studies of signal processing applied to SCG’s have involved the application of classification and signal averaging al- gorithms to reduce noise and respiratory artifacts. Classification is carried out using cross-correlation information, and the class containing the largest number of SCG beats is retained to produce a representative average SCG waveform [5]. Automatic analysis and interpretation of the (exercise) SCG, using artificial neural networks, has also been investigated and indicates the potential of the method for the early detection of heart disease [6], [7]. These previous studies have all investigated the characteristics of SCG’s in the time-domain alone, thus limiting the technique. How- ever, very little is known regarding the frequency characteristics of SCG’s, which could potentially yield important clinical information. Frequency analysis, based on classical spectrum estimation methods, Manuscript received March 3, 1997; revised October 16, 1998. The as- sociate editor coordinating the review of this paper and approving it for publication was Prof. Keshab Parhi. W. Sandham, D. Hamilton, and W. Xu are with the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, U.K. A. Fisher is with the Department of Clinical Engineering, Royal Liverpool University Hospital, Liverpool, U.K. M. Conway is with the Department of Pharmacology and Therapeutics, Trinity Centre for Health Sciences, St James’s Hospital, Dublin, Ireland. Publisher Item Identifier S 1053-587X(98)05968-6. Fig. 1. Typical seismocardiogram (SCG) beats and simultaneously recorded electrocardiogram (ECG) beats. Fig. 2. Decomposition of a discrete approximation into an approximation at a coarser resolution and the signal detail at that resolution. The full multiresolution wavelet decomposition at resolution levels is obtained through repeated application of the algorithm. is inadequate for complex, nonstationary signals such as SCG’s, whose statistical characteristics change considerably with time. In recent years, joint time–frequency representations (TFR’s) and time-scale representations (TSR’s) have emerged that enable the rep- resentation of signal characteristics jointly in terms of time–frequency or time-scale, respectively, and extend the fundamental concept of “spectrum” to include nonstationary signals and facilitate time- varying “spectrum estimation” [8], [9]. The wavelet transform (WT), which is a TSR based on multiresolution signal decomposition, was chosen for the work reported here since it has the ability to localize the frequency changes of a nonstationary signal and is free of any assumptions regarding the statistical characteristics of the signal. Previous applications of the WT have shown it to be a useful tool for biomedical signal analysis [10], [11]. II. MULTIRESOLUTION WAVELET DECOMPOSITION Multiresolution wavelet decomposition (MRWD) developed by Meyer [12], Daubechies [13], and Mallat [14], [15] was adopted for the work reported here. Important definitions and implementation details essential to this correspondence are summarized below. A. Definitions 1) denotes the vector space of measurable, square- integrable one-dimensional (1-D) functions . 1053–587X/98$10.00  1998 IEEE