Perfect-reconstruction analysis/synthesis filter bank system with high computational efficiency

1996 ◽  
Vol 32 (21) ◽  
pp. 1978
Author(s):  
C.P. Liu
Keyword(s):  
Computational Efficiency ◽  
Filter Bank ◽  
Perfect Reconstruction ◽  
Synthesis Filter ◽  
Bank System ◽  
High Computational Efficiency

Multi-Rate Filter Banks

2021 ◽  
pp. 853-873
Author(s):  
Stevan Berber
Keyword(s):  
Signal Processing ◽  
Filter Bank ◽  
Filter Banks ◽  
Theoretical Description ◽  
Perfect Reconstruction ◽  
Time Signal ◽  
Quadrature Mirror Filter ◽  
Analysis And Synthesis ◽  
Synthesis Filter ◽  
Channel Filter

This chapter presents the theoretical description and the principle of the operation of analysis and synthesis filter banks. This is essential material for understanding the modern design of transceivers that are based on discrete-time signal processing. The structure of a quadrature mirror filter bank is presented and the operation of the analysis and synthesis component filters is explained. The condition for a perfect reconstruction of a two-channel filter bank is derived. Based on a two-channel quadrature mirror filter bank, the procedure of making a multichannel quadrature mirror filter bank is presented. A brief description of multilevel filter banks with equal or unequal passband widths is given.

Examples of Multirate Filter Banks

2009 ◽  
pp. 347-384
Author(s):  
Ljiljana Milic
Keyword(s):  
Filter Bank ◽  
Filter Banks ◽  
Signal Reconstruction ◽  
Sampling Rate ◽  
Perfect Reconstruction ◽  
Original Signal ◽  
Multichannel Filter ◽  
Analysis And Synthesis ◽  
Synthesis Filter ◽  
Channel Filter

The purpose of this chapter is to illustrate by means of examples the construction of the analysis and synthesis filter banks with the use of FIR and IIR two-channel filter banks as the basic building blocks. In Chapter VIII, we have discussed the design and properties of several types of complementary filter pairs, and in Chapters IX and X we have shown how those filter pairs are used in the synthesis of digital filters with sharp spectral constraints. In this chapter, we demonstrate the application of the complementary filter pairs as two-channel filter banks used to decompose the original signal into two channel signals and to reconstruct the original signal from the channel signals. Signal decomposition is referred to as the signal analysis, whereas the signal reconstruction is referred to as the signal synthesis. Thereby, the filter bank used for the signal decomposition is called the analysis filter bank, and the bank used for signal reconstruction is called the synthesis filter bank. The two-channel filter bank is usually composed of a pair of lowpass and highpass halfband filters, which satisfy some complementary properties. The bandwidth that occupies each of two channel signals is a half of the original signal bandwidth. Hence, the channel signals can be processed with the sampling rate which is a half of the original signal sampling rate. At the output of the analysis bank, the channel signals are down-sampled-by-two and then processed at the lower sampling rate. For the signal reconstruction, each of two channel signals has to be up-sampled-by-two first, and then fed into the synthesis bank. The sampling rate alteration in the two-channel filter bank causes the unwanted effects: the downsampling produces aliasing, and the up-sampling produces imaging. The essential feature of the two-channel filter bank is that the aliasing produced in the analysis side can be compensated in the synthesis side. This is achieved by choosing the proper combination of filters in the analysis and synthesis banks. The elimination of aliasing opens the possibility of the perfect (and nearly perfect) reconstruction of the original signal. The perfect reconstruction means that the signal at the output of the cascade connection of the analysis and synthesis bank is a delayed replica of the original input signal. Constructing perfect reconstruction and nearly perfect reconstruction analysis/synthesis filter banks is an unbounded area of research. An important and widely used application of the two-channel filter banks is the construction of multichannel filter banks based on the tree-structures where the two-channel filter bank is used as a building block. In this way, a multilevel multichannel filter bank can be obtained with either uniform or nonuniform separation between the channels. The two-channel filter banks are particularly useful in generating octave filter banks. Depending on applications, the filter bank can be requested to provide frequency-selective separation between the channels, or to preserve the original waveform of the signal. The example applications of the frequency-selective filter banks are audio and telecommunication applications. The importance of preserving the original waveform is related with the images. In the case of the discrete-time wavelet banks, the frequency-selectivity is less important. The main goal is to preserve the waveform of the signal. The purpose of this chapter is to illustrate by means of MATLAB examples the signal analysis and synthesis based on the two-channel filter banks. We give first a brief review of the properties of the two-channel filter banks with the conditions for aliasing elimination. We discuss the perfect reconstruction and nearly perfect reconstruction properties and show the solutions based on FIR and IIR QMF banks and the orthogonal two-channel filter banks. In the sequel, the tree-structured multichannel filter banks are considered. The process of signal decomposition and reconstruction is illustrated by means of examples.

281. Evaluation of a High-Efficiency Filter-Bank System

2005 ◽  
Author(s):  
S. Martin ◽  
E. Moyer ◽  
B. Beamer
Keyword(s):  
Filter Bank ◽  
High Efficiency ◽  
Bank System

A CONFORMING POINT INTERPOLATION METHOD (CPIM) BY SHAPE FUNCTION RECONSTRUCTION FOR ELASTICITY PROBLEMS

2010 ◽  
Vol 07 (03) ◽  
pp. 369-395 ◽  
Author(s):  
X. XU ◽  
G. R. LIU ◽  
Y. T. GU ◽  
G. Y. ZHANG
Keyword(s):  
Convergence Rate ◽  
Computational Efficiency ◽  
Shape Function ◽  
Interpolation Method ◽  
Numerical Studies ◽  
Point Interpolation Method ◽  
Elasticity Problems ◽  
Point Interpolation ◽  
Continuous Displacement ◽  
High Computational Efficiency

A conforming point interpolation method (CPIM) is proposed based on the Galerkin formulation for 2D mechanics problems using triangular background cells. A technique for reconstructing the PIM shape functions is proposed to create a continuous displacement field over the whole problem domain, which guarantees the CPIM passing the standard patch test. We prove theoretically the existence and uniqueness of the CPIM solution, and conduct detailed analyses on the convergence rate; computational efficiency and band width of the stiffness matrix of CPIM. The CPIM does not introduce any additional degrees of freedoms compared to the linear FEM and original PIM; while convergence rate of quadratic CPIM is in between that of linear FEM and quadratic FEM which results in the high computational efficiency. Intensive numerical studies verify the properties of the CPIM.

scholarly journals Modeling and Experimental Validation of the VARTM Process for Thin-Walled Preforms

Polymers ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2003
Author(s):  
Da Wu ◽  
Ragnar Larsson ◽  
Mohammad S. Rouhi
Keyword(s):  
Shell Model ◽  
Computational Efficiency ◽  
Large Scale ◽  
Strongly Coupled ◽  
Thin Walled Structures ◽  
Simulation Based ◽  
Thin Walled ◽  
High Computational Efficiency ◽  
Insight Into ◽  
Vartm Process

In this paper, recent shell model is advanced towards the calibration and validation of the Vacuum-assisted Resin Transfer Molding (VARTM) process in a novel way. The model solves the nonlinear and strongly coupled resin flow and preform deformation when the 3-D flow and stress problem is simplified to a corresponding 2-D problem. In this way, the computational efficiency is enhanced dramatically, which allows for simulations of the VARTM process of large scale thin-walled structures. The main novelty is that the assumptions of the neglected through-thickness flow and the restricted preform deformation along the normal of preform surface suffice well for the thin-walled VARTM process. The model shows excellent agreement with the VARTM process experiment. With good accuracy and high computational efficiency, the shell model provides an insight into the simulation-based optimization of the VARTM process. It can be applied to either determine locations of the gate and vents or optimize process parameters to reduce the deformation.

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