Search results for "wavelet packet decomposition"
showing 10 items of 33 documents
Periodic Discrete and Discrete-Time Splines
2018
Periodic discrete splines with different periods and spans are introduced in Sect. 3.4 of Volume I (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [2]. In this chapter, we regard periodic discrete splines as a base for the design of periodic discrete-time wavelets, wavelet packets and wavelet frames. Therefore, only the discrete splines whose spans are 2 are outlined. These discrete splines are linear combinations of the discrete B-splines. So also, the so-called discrete-time splines are discussed in the chapter that are linear combinations of the discrete-time B-splines. The discrete-time B-s…
Wavelet Frames Generated by Spline Based p-Filter Banks
2014
This chapter presents a design scheme to generate tight and so-called semi-tight frames in the space of discrete-time periodic signals. The frames originate from oversampled perfect reconstruction periodic filter banks. The filter banks are derived from discrete-time and discrete periodic splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pass filter, whose magnitude response mirrors that of a low-pass filter. In addition, these filter banks comprise a number of band-pass filters. In this chapter, frames generated by four-channel filter banks are briefly outlined (see Chap. 17 in [2] for details) and tight frames generated by six-…
Block-Based Inversion of the Heat Equations
2014
This chapter presents robust methods, which refine the algorithms, in Sect. 7.2, for inversion of the heat equations. The idea behind the algorithms is to solve the inversion problem separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions that minimize some parameterized quadratic functionals, are derived as linear combinations of the wavelet packets. Choice of parameters, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. The Spline Harmonic Analysis (SHA) technique provides a unified computational scheme for the fast implementation of the algorithm and an explicit r…
Periodic Orthogonal Wavelets and Wavelet Packets
2018
In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal wavelets and wavelet packets from discrete and discrete-time splines outlined in Chap. 3. These wavelets and wavelet packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The wavelet and wavelet packet transforms are implemented in a fast way using the FFT.
Two-Dimensional Orthogonal Wavelets and Wavelet Packets
2018
This chapter extends the design of spline-based orthogonal discrete-time wavelets and wavelet packets to two-dimensional case. The corresponding transforms are implemented by using the 2D FFT.
Discrete-Time Periodic Wavelet Packets
2014
Direct and inverse wavelet and wavelet packet transforms of a spline are implemented by filtering the spline’s coordinates by two-channel critically sampled p-filter banks. In this chapter, those p-filter banks are utilized for processing discrete-time signals. The p-filter banks generate discrete-time wavelets and wavelet packets in the spaces of 1D and 2D periodic signals.
Interference excision algorithm for frequency hopping spread spectrum based on undecimated wavelet packet transform
2002
An algorithm for reducing narrowband interference effects in frequency hopping spread spectrum is presented. The method is based on the undecimated wavelet packet transform. It improves the performance obtained by other methods. Experimental results demonstrate the suitability of the algorithm.
Block Based Deconvolution Algorithm Using Spline Wavelet Packets
2010
This paper presents robust algorithms to deconvolve discrete noised signals and images. The idea behind the algorithms is to solve the convolution equation separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions are derived as linear combinations of the wavelet packets that minimize some parameterized quadratic functionals. Parameters choice, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. This technique, which id called Spline Harmonic Analysis, provides a unified computational scheme for the design of orthonormal spline wavelet packets, fast implementation of the…
Detection of Incipient Bearing Fault in a Slowly Rotating Machine Using Spline Wavelet Packets
2018
This chapter describes a successful application of spline-based wavelet packet transforms (WPTs) described in Chap. 4 to a complicated problem of detection of incipient defects in rolling element bearings by the analysis of recorded vibration signals. The methodology presented in this chapter is applied to the analysis of vibration data recorded from large bearings working in real unfavorable operation conditions in presence of strong noise and vibrations from multiple internal and external sources. It relies on properties of discrete spline-based wavelet packets such as orthogonality, near-rectangular spectra, transient oscillating shapes of testing waveforms and fast implementation of tra…
Hydro-Acoustic Target Detection
2014
This chapter presents an example of utilization of the discrete–time wavelet packets, which are described in Sect. 9.1, to classification of acoustic signals and detection of a target. The methodology based on wavelet packets is applied to a problem of detection of a boat of a certain type when other background noises are present. The solution is obtained via analysis of boat’s hydro-acoustic signature against an existing database of recorded and processed hydro-acoustic signals. The signals are characterized by the distribution of their energies among blocks of wavelet packet coefficients.