Abstract
In this paper, a novel methodology is proposed to implement the Morlet wavelet transform in an analog circuit. Under the proposed scheme, the impulse response of the linear time-invariant system is used to approximate the Morlet wavelet function. The approximation accuracy is guaranteed by the constrained L 2 -norm method, which reduces the approximation error by decreasing free parameters in searching routines. Due to the complex wavelet function, a common-pole strategy is presented for filter construction. With the common poles in real and imaginary parts, partial components can be shared during the analog implementation of the wavelet transform. With the reasonably good approximation for Morlet wavelet function, an analog continuous-time filter is designed based on the Gm-C integrator and orthonormal ladder topology. Application examples are introduced to illustrate the superior performance of the proposed filter. It is shown that the designed analog filter approximates the ideal Morlet wavelet function well in both time and frequency.
Highlights
Morlet wavelet transform (MWT) has been recognized as an efficient tool in many areas of interest, including signal or image denoising [1], [2], transients detection [3], [4] and feature extraction [5], [6]
An accurate analog implementation for MWT is achieved by the Gm-C filter
Due to the complex waveform of Morlet wavelet function, we provide the common-pole strategy to construct the analog filter, such that partial components can be shared during the analog implementation
Summary
Morlet wavelet transform (MWT) has been recognized as an efficient tool in many areas of interest, including signal or image denoising [1], [2], transients detection [3], [4] and feature extraction [5], [6]. In some specific applications, namely lowpower front-ends in wearable devices, digital implementation for MWT is impractical due to the high power consumption and large chip area associated with the required A/D converters [9], [10]. For wearable devices, the requirement in miniaturization limits the available battery size and power draw, and will absolutely limit the applications in long-term monitoring Taking these issues into account, in this paper, the continuous wavelet transform is implemented in an integrated low-power Gm-C filter, which is well suited for the application in wearable devices. The constrained L2-norm method is proposed to improve the performance in wavelet function approximation Such that a more accurate implementation for wavelet transform is achieved.
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