Log-domain wavelet bases

Abstract

A novel procedure to approximate Wavelet bases using analog circuitry is presented. First, an approximation is introduced to calculate the transfer function of the filter, whose impulse response is the required Wavelet. Next, for low-power low-voltage applications, we optimize dynamic range, minimize sensitivity and fulfill sparsity requirements. The filter design that follows is based on an orthonormal ladder structure with log-domain integrators as main building blocks. Simulations demonstrate an excellent approximation of the required Wavelet base (i.e. Morlet). The circuit operates from a 1.2-V supply and a bias current of 1.2µA.

Designing Delay Lines Based on the SD/DE Algorithm for Transmitted-Reference Ultra-Wideband Systems

“…The reason to apply Padé approximation is that it immediately yields a rational Fig. 3 Group delay response of the Bessel-Thomson filter with n = 8 and w 0 = 2πf 0 = 4.8356e9 rad/s expression, which is convenient for implementation [15,16]. Here, the method is applied in the Laplace transformed domain, and the objective function is H (s) = e −T d s .…”

“…The coefficients of P m (s) and Q n (s), which are determined by the first (m + n + 1) coefficients of the Taylor series, can be calculated following [16]. And, then, the result is transformed into the Fourier domain aŝ…”

“…In particular, the Bessel-Thomson approximation based on Bessel polynomials [18] is widely used, which however leads to a low-pass delay function. Padé approximation [2,16,17], on the other hand, is a common approach using a truncated Taylor expansion of the ideal transfer function around one point. The main drawbacks of these common methods are: (1) they often depend on the designer's intuition or experience and thus do not provide a generic procedure, for which actually a trial-and-error process is unavoidable in most designs; (2) the designer has to reconstruct the whole hardware architecture once there are any changes in design parameters such as the order parameter.…”

Detection of Cardiac Signal Characteristic Point Using Log-Domain Wavelet Transform Circuits

“…Reducing the power consumption and the size have been the two major challenges in designing implantable pacemakers to make them more durable and less invasive. In order to achieve the low-power requirement in pacemakers, some approaches for implementing the WT in an analog way by means of the dynamic translinear circuit technique [6,[8][9][10][11][12][13]30] have been reported. In these methods, the circuits for implementing the WT consist of analog filters whose impulse response is the first derivative of the Gaussian.…”

“…In [12,13], complex first order systems (CFOSs) were used to implement analog wavelet filters. In [6,11], Padé approximation [2] was used to calculate the transfer function of wavelet filters, and the Padé method proved to be more successful than the method using the CFOS. However, there are also some disadvantages which limit the practical applicability of Padé approximation [3].…”