Dual Filter Bank Research Articles

Augmenting Wireless Time-of-Arrival Positioning with Terrain Elevation Measurements for Navigation

The integration of time-of-arrival positioning techniques with terrain-referenced navigation is described within the framework of Bayesian estimation theory. In this approach, two banks of nonlinear filters are used in a multiple-model adaptive configuration. One filter bank represents different terrain elevation bias values, whereas the other bank represents noise parameters used to model non-line-of-sight bias for time-of-arrival positioning. Information is only periodically exchanged between filter banks to limit the overall computational complexity while allowing estimation of time-varying parameters. Monte Carlo simulations of an integrated time-of-arrival and terrain-navigation positioning problem demonstrate the advantages of the dual filter bank under conditions of significant non-line-of-sight bias.

Piecewise-linear subband coding scheme for fast image decomposition

Transform coding methods play a very important role in the development of diverse multimedia technologies. The discrete cosine and wavelet transforms are frequently used in the field of image processing and set up a basis for contemporary image compression standards (JPEG, MPEG). In this paper a novel two-channel piecewise-linear subband coding scheme (PL-SBC) is introduced. Its most important advantage are exceptionally fast and easy for implementation computational algorithms combined with good reconstruction quality. The proposed PL-SBC system is based on the dual filter bank consisting of a single filter at the decomposition stage and a single one at the reconstruction stage. For the presented PL-SBC scheme, the conditions of perfect reconstruction and the piecewise-linear approximation filter bank have been defined. The compression properties of a new subband coding scheme have been analysed for different categories of images and in comparison with well-known signal transforms, such as cosine, piecewise-linear, piecewise-constant and wavelet transforms. The research includes a comparison of the reconstruction error both in objective as well as subjective approach.

Hilbert Transform Pairs of Tight Frame Wavelets with Integer Dilation Factor

This paper aims to design a pair of tight frame wavelets with dilation $$M$$ M , where all the generators form Hilbert transform pairs. To ensure the primal and dual filterbanks satisfy the perfect reconstruction condition simultaneously, the periods of phase functions should be $$\frac{2\pi }{M}$$ 2 ? M based on our results. According to the sufficient and necessary condition of phase functions, we not only give a linear phase solution for them but also establish their formulae. Moreover, by analyzing the symmetric properties of the dual tight frame, it is shown that as long as their primal tight frames are symmetric those duals are symmetric as well. Finally, we construct an optimization model with minimizing the error to search for the optimal filter coefficients. A design example is given to illustrate the results.

Dual-Tree Cosine-Modulated Filter Bank With Linear-Phase Individual Filters: An Alternative Shift-Invariant and Directional-Selective Transform

Dual-tree transforms have recently received much attention for the properties of shift-invariance and directional-selectivity. However, their designs generally encounter fractional-delay constraints, and become more complicated for providing linear-phase (LP) individual filters and flexible directional-selectivity, two important properties in image processing. In this paper, we propose an alternative shift-invariant and directional-selective transform-the dual-tree cosine-modulated filter bank (DTCMFB). In the proposed DTCMFB, its primal and dual filter banks are derived by cosine-modulating one LP prototype filter, and thus its design involves no fractional-delay constraints. Meanwhile, the derived modulation technique guarantees each individual filter to be LP and the LP condition is satisfied without any constraint on the prototype filter. By separable operations, the DTCMFB is extended to two-dimensions. The resulting 2D DTCMFB can provide much more flexible directional-selectivity. Finally, several simulations are given to verify the proposed DTCMFB, and the experiments on nonlinear approximation and image denoising are presented to demonstrate its potential in image processing.

A SUFFICIENT AND NECESSARY CONDITION FOR CONSTRUCTION OF 3-BAND DUAL TREE COMPLEX WAVELET

To desire expectable applications in image processing, the construction of 3-band dual tree complex wavelet is a meaningful and constructive topic. In this paper, a sufficient and necessary condition 2π/3-periodic of phase difference between the prime and dual filter banks is proposed. With this condition, it is proposed that the phase function θl(ω) of wavelet filters can be uniquely determined by the phase function θ0(ω) of the scaling filters. Imposed on a necessary constraint to θ0(ω), phase function θl(ω) can be obtained which results in the analytical of the 3-band dual tree complex wavelet. Furthermore, the complex filter banks are obtained using the wavelet matrix factorization approach. Then the dual tree 3-band complex wavelet is analytical that indicates approximately shift invariance property. In addition, it also has more direction selectivity because there are more sub-bands than dyadic wavelet transform is frequency domain.

Fabrication strategies for filter banks based on microring resonators

Wavelength-division demultiplexers are a fundamental component needed for many proposed integrated photonic systems. By using filter banks based on microring resonators it is possible to create demultiplexers that are two orders of magnitude smaller and achieve better performance than the discrete component demultiplexers currently used. To create a filter bank out of microring resonators the resonant-frequency spacing must be controlled to within 1GHz. This is achieved by controlling the electron-dose during scanning-electron-beam lithography in order to change the average ring waveguide width on the tens of picometer scale. Using this method a second-order twenty-channel dual filter bank (80 microrings) is fabricated with a average channel spacing of 83GHz demonstrating the capability to make changes in the average ring waveguide width with an accuracy of 75pm. It is shown that any frequency errors that remain after fabrication can be corrected using thermal tuning with integrated microheaters. The amount of power needed to correct for all frequency errors in the fabricated filter banks is 0.09W, compared to the 2.4W that is needed if no attempt is made to control the frequency spacing during fabrication. Also a temperature stabilization circuit is demonstrated that can stabilize the temperature of the filters to 80mK (280MHz).

Sampled-Data Design of FIR Dual Filter Banks for Dual-Tree Complex Wavelet Transforms via LMI Optimization

Starting from a given finite-impulse-response (FIR) primal filter bank, we design a dual filter bank such that the complex wavelets associated with the dual-tree filter bank are (almost) analytic. The dual filter bank is required to be FIR and have a prescribed number of zeros at . We formulate a sampled-data optimization problem based on the half-sample delay condition on scaling filters. A discrete-time filter is introduced in the formulation to specify the number of the zeros. The optimization problem is converted into an equivalent discrete-time control problem; the latter is further reduced to an LMI optimization problem. We then present a procedure for design of FIR dual filter banks. Illustrative examples are provided; the results compare favorably to early designs.

Modified distributed arithmetic based architecture for discrete wavelet transforms

A highly area-efficient multiplier-less filterbank architecture for one- and two-dimensional discrete wavelet transforms (DWT) is presented. The look-up table (LUT) structure in traditional distributed arithmetic (DA)-based filter structures has been dissolved to implement a LUT-less DA-DWT with dual filterbanks, which permits the reuse of the same circuitry for both highpass and lowpass filters.

Characterization and Sampled-Data Design of Dual-Tree Filter Banks for Hilbert Transform Pairs of Wavelet Bases

Characterization and design of dual-tree filter banks for forming Hilbert transform pairs of wavelet bases are studied. The characterization extends the existing results for quadrature mirror filter banks to general prefect reconstruction filter banks that satisfy only a mild technical assumption regarding the ratio of determinants of the two filter banks. We establish equivalent relationships of Hilbert transform pairs on scaling filters, wavelet filters, or scaling functions. The design of scaling filters of a dual filter bank is formulated as a sampled-data H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> optimization problem. The wavelet filters are then determined using the relationship on the determinants of the filter banks. We convert the sampled-data problem into an equivalent discrete-time H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> control problem, which can be solved by standard H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> control theory. An analytical solution to the sampled-data design problem is obtained for a special case. The sampled-data design approach usually gives infinite impulse response filter. In the case where the primal filter bank is of finite impulse response (FIR), we may truncate the impulse responses to get FIR approximations. They also lead to approximate Hilbert transform pairs. Design examples are presented