An Improved Quality Adaptive Rate Filtering Technique Based on the Level Crossing Sampling

Mostly the systems are dealing with time varying signals. The Power efficiency can be achieved by adapting the system activity according to the input signal variations. In this context an adaptive rate filtering technique, based on the level crossing sampling is devised. It adapts the sampling frequency and the filter order by following the input signal local variations. Thus, it correlates the processing activity with the signal variations. Interpolation is required in the proposed technique. A drastic reduction in the interpolation error is achieved by employing the symmetry during the interpolation process. Processing error of the proposed technique is calculated. The computational complexity of the proposed filtering technique is deduced and compared to the classical one. Results promise a significant gain of the computational efficiency and hence of the power consumption. Keywords—Level Crossing Sampling, Activity Selection, Rate Filtering, Computational Complexity, Interpolation Error. I. CONTEXT OF THE STUDY HIS work is a contribution in the development of smart mobile systems. The goal is to reduce their size, cost, processing noise, electromagnetic emission and especially power consumption as they are remotely powered by batteries. This can be done by smartly reorganizing their associated signal processing theory and architecture. The idea is to combine the signal event driven processing with the asynchronous circuit design in order to reduce the system processing activity. Most of the real life signals like speech, seismic, Doppler and biological signals are time varying in nature. The spectral contents of these signals vary with time, which is a direct consequence of the signal generation process [5]. Classical systems are based on the Nyquist signal processing architectures. They do not take advantage of the input signal local variations. These systems are highly constrained due to the Shannon theory especially in the case of low activity sporadic signals like electrocardiogram, phonocardiogram, seismic signals etc. It causes a large number of samples without any relevant information, a useless increase of the system activity and so a useless increase of the power consumption. Saeed Mian Qaisar is a PhD candidate in Laboratory TIMA, CNRS UMR 5159, 46 Avenue Felix-Viallet, 38031 Grenoble Cedex, France (phone: +33-476574646; fax: +33-476574981; e-mail: saeed.mian-qaisar@ imag.fr). Laurent Fesquet is an associate professor at INPG and is working with Laboratory TIMA, CNRS UMR 5159, 46 Avenue Felix-Viallet, 38031 Grenoble Cedex, France (e-mail: laurent.fesquet@imag.fr). Marc Renaudin is a professor at INPG and is working with Laboratory TIMA, CNRS UMR 5159, 46 Avenue Felix-Viallet, 38031 Grenoble Cedex, France (e-mail: marc.renaudin@imag.fr). This problem is resolved by employing a signal driven sampling scheme, which is sensitive to the input signal local variations [12, 17]. It is based on the principle of “levelcrossing” that provides a non-uniform time repartition of the samples [1], consequently it is named as the LCSS (level crossing sampling scheme). This sampling scheme drastically reduces the activity of the post processing chain because it only captures the relevant information [11, 13]. In this context, analog to digital converters based on the LCSS have been developed [2, 4, 18]. Algorithms for processing [3, 11, 13] and analysis [8, 12, 19] of the nonuniformly spaced out in time sampled data obtained with the LCSS have also been developed. The focus of this work is to develop an efficient online FIR (Finite Impulse Response) filtering technique. The idea is to extract the input signal local features and then use them to improve the quality and to reduce the computational load of the post processing chain. An efficient solution is proposed by combining the features of both non-uniform and uniform signal processing tools. II. LCSS (LEVEL CROSSING SAMPLING SCHEME) In the case of LCSS, a sample is captured only when the input analog signal x(t) crosses one of the predefined threshold levels [1]. The samples are not uniformly spaced in time because they depend on x(t) variations as it is clear from Fig. 1. Thus, the non-uniformity in the sampling process reflects the local characteristics of x(t) [12]. According to [1], the sampling instants of a non-uniformly sampled signal obtained with the LCSS are defined by Equation 1. tn = tn-1 + dtn . (1) dtn = tn – tn-1 . (2) Where tn is the current sampling instant, tn-1 is the previous one and dtn is the time delay between the current and the previous sampling instants (cf. Equation 2).