Wavelet packet transform-based compression for teleoperation

This paper introduces a codec scheme for compressing the control and feedback signals in networked control and teleoperation systems. The method makes use of Wavelet Packet Transform (WPT) and Inverse Wavelet Packet Transform (IWPT) for coding and decoding operations, respectively. Data compression is carried out in low-pass filter output by reducing the sampling rate, and in high-pass filter output by truncating the wavelet coefficients. The proposed codec works on both directions of signal transmission between a master robot and a slave robot over a networked motion control architecture. Following the formulation of the compression/decompression methodology, experimental validation is conducted on a single-degree-of-freedom motion control system. In the experiments, responses from different Wavelet structures are analyzed and a comparative study is carried out considering the factors of compression rate, reconstruction power error and real-time computational complexity. It is confirmed that the controller using the proposed compression algorithm performs very close to the uncompressed one while enabling transmission of much less data over the network

Wavelet packet transform based compression for bilateral teleoperation

This paper introduces a codec scheme for compressing the control and feedback signals in bilateral control systems. The method makes use of Wavelet Packet Transform (WPT) and Inverse Wavelet Packet Transform (IWPT) for coding and decoding operations respectively. Data compression is carried out in low pass filter output by reducing the sampling rate; and in high pass filter output by truncating the wavelet coefficients. The proposed codec works on both directions of signal transmission between a master robot and a slave robot over a networked motion control architecture. Following the formulation of the compression/decompression methodology, experimental validation is conducted on a single degree of freedom (DOF) motion control system. In the experiments, responses from different Wavelet structures are analyzed and a comparative study is carried out considering the factors of compression rate, reconstruction power error and real time computational complexity. It is confirmed that the controller using the proposed compression algorithm performs very close to the uncompressed one while enabling transmission of much less data over network

Necessary and sufficient conditions for the wave packet frames on positive half-line

In this paper, we consider wave packet systems as special cases of generalized shift-invariant systems, a concept studied by Hern´andez, Lebate and Weiss. The objective of the paper is to construct wave packet frames on positive half line. We establish necessary and sufficient conditions for the wave packet frames on positive half-line using Walsh-Fourier transform.Publisher's Versio

Orthonormal bases of regular wavelets in spaces of homogeneous type

Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpolation and reproducing properties as the linear splines in Euclidean spaces. They also have H\"older regularity. This is used to build an orthonormal basis of H\"older-continuous wavelets with exponential decay in any space of homogeneous type. As in the classical theory, wavelet bases provide a universal Calder\'on reproducing formula to study and develop function space theory and singular integrals. We discuss the examples of $L^p$ spaces, BMO and apply this to a proof of the T(1) theorem. As no extra condition {(like 'reverse doubling', 'small boundary' of balls, etc.)} on the space of homogeneous type is required, our results extend a long line of works on the subject.Comment: We have made improvements to section 2 following the referees suggestions. In particular, it now contains full proof of formerly Theorem 2.7 instead of sending back to earlier works, which makes the construction of splines self-contained. One reference adde

Transforms, algorithms and applications

Fourier transforms and other related transforms are an essential tool in applications of science, engineering and technology. In fact, much of the work currently being done in mathematics, physics and engineering has its roots in Fourier's pioneering idea of representing an arbitrary function as the sum of a trigonometric series. The main purpose of these notes is to give a brief overview of some Fourier-related transforms, namely: continuous Fourier transform, Fourier series, discrete Fourier transform, fast Fourier transform (FFT),sine and cosine transforms, Z-transform, Laplace transform, windowed Fourier transform, continuous and discrete wavelet transforms. Our aim is simply to present a summary of these transforms and to describe their main properties and possible applications, and so most of the results are presented with no proof.References containing the proofs and other details about the transforms are always indicated