Half-band Filters Research Articles

LOW POWER DIGITAL DECIMATION FILTER FOR RF WIRELESS COMMUNICATIONS

In this paper, we present a unique low power decimation filter architecture for RF wireless applications. To implement the low power decimation filter, we considered low power design techniques such as multi-rate, multi-stage signal processing, proper selection of decimation factor, one multiplier realization of 1/3-band filters, and poly-phase 1/2-band filters. We have designed three conventional decimation filter architectures using a single-stage FIR filter, a three-stage FIR filter, and a three-stage half-band FIR filter. Compared to the 55-tap comb-FIR filter architecture, the proposed decimation filter has only 13 taps, and requires 76% less hardware and consumes 64% less power.

Design of Halfband Filters for Orthogonal Wavelets via Sum of Squares Decomposition

This letter is concerned with design of halfband product filters for orthogonal wavelets. We first remark that the recent zero-pinning technique for orthogonal wavelet design cannot always guarantee the nonnegativity of the filter. We then propose to use sum of squares (SOS) decomposition to ensure its nonnegativity. The use of SOS decomposition also allows us to solve two optimization problems on the halfband filter via semidefinite programming. For a given length with pre-specified number of zeros at , we obtain halfband filters with maximal passband width. Design examples are provided.

STENCIL COEFFICIENT COMPUTATIONS FOR THE MULTIRESOLUTION TIME DOMAIN METHOD - A FILTERBANK APPROACH

Multiresolution Time Domain (MRTD) techniques based on wavelet expansions can be used for adaptive refinement of computations to economize the resources in regions of space and time where the fields or circuit parameters or their derivatives are large. Hitherto, standard wavelets filter coefficients have been used with the MRTD method but the design of such filter itself may enable to incorporate desired properties for different applications. Towards this, in this paper, a new set of stencil coefficients in terms of scaling coefficients starting from a half band filter, designed by window method and deriving a physically realizable filter by spectral factorization using cepstral technique, for the MRTD method is presented. These stencil coefficients for the MRTD are found to give good agreement with similar MRTD schemes such as those obtained using Daubechies orthogonal wavelets.

On the Design of FIR Wavelet Filter Banks Using Factorization of a Halfband Polynomial

A classic method of designing two-channel biorthogonal wavelet FIR filter banks is by the factorization of a halfband polynomial. Most of the popular biorthogonal filter banks are designed by the factorization of the Lagrange halfband polynomial, which has the maximum number of zeros at z = -1. However, the Lagrange halfband polynomial does not have any parameter, and thus, there is no direct control over the frequency response of the filters obtained by factorization. In this letter, our aim is have some control over the frequency response of the filters designed by factorization. To achieve this, we start with a general halfband filter (not the Lagrange halfband filter) whose coefficients are parameters to be designed. We then impose the regularity constraint by imposing zeros at z = -1. The number of zeros we impose is less than the maximum possible. Imposing the zeros gives a set of constraints on the coefficients of the halfband polynomial. We then factorize the halfband polynomial by expressing it in terms of the independent (free) parameters after imposing the regularity constraints. We use the free parameters to control the frequency response of the filters. We present design examples to illustrate this method.

Discrete Lattice Wavelet Transform

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The discrete wavelet transform (DWT) has gained a wide acceptance in denoising and compression coding of images and signals. In this work we introduce a discrete lattice wavelet transform (DLWT). In the analysis part, the lattice structure contains two parallel transmission channels, which exchange information via two crossed lattice filters. For the synthesis part we show that the similar lattice structure yields a perfect reconstruction (PR) property. The PR condition can be used to design half-band filters, which effectively eliminate aliasing in decimated tree structured wavelet transform. The DLWT can be implemented directly to any of the existing DWT algorithms. </para>

Directional filter bank-based segmentation for improved evaluation of nondestructive evaluation images

This paper introduces a directional filter bank (DFB) for segmentation of NDE images containing directional information. The DFB is used to split an image into a desired number of sub-band images with each sub-band image containing features belonging only to a given angular range. The DFB is a two-channel decomposition employing the Quincunx sampling matrix and the diamond half band filter pair. The DFB is also designed to incorporate the property of perfect reconstruction or alias free reconstruction. Applications of the DFB towards segmenting C-scan images of fiber-reinforced composites, magnetic flux leakage (MFL) images of seamless tubes, IR images of solar cell panels and optical images for the computation of area coverage in a shot-peening process are discussed.

Wave digital filters with minimum multiplier for discrete Hilbert transformer realization

This paper describes the design of wave digital filters for discrete Hilbert transformer realization. A method for designing real and complex half-band wave digital filters (WDFs) with a minimum number of multipliers is afforded where the multiplier coefficients for the adaptors are calculated directly from the digital domain transfer functions. This technique uses the equations derived for a class of infinite impulse response (IIR) filter and hence avoids the conventional technique of synthesizing a WDF from an analogue reference filter. The selection of the adaptor configuration is determined from the multiplier coefficient values. A minimum multiplier realization of real half-band WDFs can be obtained to meet the low-pass digital filter magnitude specifications. By applying a transformation equation, a complex half-band WDF suitable for the realization of the discrete Hilbert transformer with a minimum number of multiplier is obtained.

Low-power decimator design using approximated linear-phase N-band IIR filter

This correspondence presents a new design of a low-power decimation filter, which consists of a poly-phase finite-impulse-response (FIR)-4 comb filter, an approximate linear-phase one-third-band infinite-impulse-response (IIR) filter, and a half-band FIR filter. A poly-phase FIR-4 comb filter architecture was designed, which consumes 75% less power than the recursive comb filter architecture. New general equations were derived for the design of 1/N-band IIR filters, and these equations were used to design a novel approximate linear-phase one-third-band IIR filter. The decimation filter is designed using Simulink and DSP Blockset, and Matlab simulations are performed to verify the phase linearity and magnitude response of the designed filter. The group delay for the passband region of one-third-band IIR filter has a negligible error of 0.009%. The resulting decimation filter has 60% less hardware and consumes 67% less power than the comb-FIR-FIR decimation filter.

Efficient Implementation of Real and Complex Linear-Phase FIR and Minimum-Phase IIR Halfband Filters for Sample Rate Alteration

Efficient Implementation of Real and Complex Linear-Phase FIR and Minimum-Phase IIR Halfband Filters for Sample Rate Alteration

Optimum masking levels and coefficient sparseness for Hilbert transformers and half-band filters designed using the frequency-response masking technique

Hilbert transformers and half-band filters are two very important special classes of finite-impulse response filters often used in signal processing applications. Furthermore, there exists a very close relationship between these two special classes of filters in such a way that a half-band filter can be derived from a Hilbert transformer in a straightforward manner and vice versa. It has been shown that these two classes of filters may be synthesized using the frequency-response masking (FRM) technique resulting in very efficient implementation when the filters are very sharp. While filters synthesized using the FRM technique has been characterized for the general low-pass case, Hilbert transformers and half-band filters synthesized using the FRM technique have not been characterized. The characterization of the two classes of filter is a focus of this paper. In this paper, we re-develop the FRM structure for the synthesis of Hilbert transformer from a new perspective. This new approach uses a frequency response correction term produced by masking the frequency response of a sparse coefficient filter, whose frequency response is periodic, to sharpen the bandedge of a low-order Hilbert transformer. Optimum masking levels and coefficient sparseness for the Hilbert transformers are derived; corresponding quantities for the half-band filters are obtained via the close relationship between these two classes of filters.

Synthesis of very sharp Hilbert transformer using the frequency-response masking technique

Frequency translation of audio signals requires the use of very sharp Hilbert transformer if the low frequency components are to be faithfully translated. Unfortunately, the order of a very sharp Hilbert transformer is very high, resulting in very high arithmetic complexity. The frequency-response masking (FRM) technique has been used very successfully for greatly reducing the complexity of extremely sharp halfband filters. There is a very close relationship between a halfband filter and a Hilbert transformer. In this correspondence, we propose to synthesize a very sharp Hilbert transformer using the FRM technique via the synthesis of a very sharp halfband filter.

A multicarrier QAM modulator for WCDMA base-station with on-chip D/A converter

In this paper, design and implementation of a multicarrier quadrature amplitude modulation (QAM) modulator for a wideband code division multiple access (WCDMA) base-station with a 14-bit on-chip D/A converter is described. The modulator is capable of modulating four carriers with four independent in phase (I) and quadrature (Q) data streams. The proposed modulator structure consists of an interpolation chain for data streams and four digital frequency synthesizer/modulators, which are based on a coordinate rotation digital computer (CORDIC) vector rotation algorithm. The interpolation chain consists of a root-raised cosine pulse shaping filter and three half-band filters for image filtering. The modulated carriers are combined to form a multicarrier WCDMA signal. The SINC-attenuation effect of a digital/analog (D/A) converter is canceled by an inverse-SINC predistortion filter. The multicarrier signal is converted to the analog domain with a 14-bit current steering D/A converter, which is integrated on the same silicon chip. The modulator is implemented with a 0.35-mum BiCMOS process with CMOS transistors only

SNR-maximizing interpolation filters for band-limited signals with quantization

As an interpolation filter for sampling rate transformation, a half-band filter with a reduced amount of computation is often used. Due to the restrictions on its amplitude characteristic, it is not possible to sufficiently reduce the quantization noise of the transition region of the filter. In this paper, the output SNR of the L-interpolator filter is analyzed with a quantized band-limited signal as the input. A design method is proposed for the linear phase FIR filter maximizing the output SNR. For the design, both the SNR maximizing design within the Type I FIR filters and one supplemented with the restriction of the L-th band filter are presented. Each design is reduced to derivation of the solution of a system of linear equations with a coefficient matrix represented analytically. The filter based on the proposed method can attain an SNR not attainable under the sacrifice of the order in the conventional filter taking into account only the passband and the stopband. ©2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(1): 31–46, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20178

Multiple resolution analysis for robust automatic speech recognition

This paper investigates the potential of exploiting the redundancy implicit in multiple resolution analysis for automatic speech recognition systems. The analysis is performed by a binary tree of elements, each one of which is made by a half-band filter followed by a down sampler which discards odd samples. Filter design and feature computation from samples are discussed and recognition performance with different choices is presented. A paradigm consisting in redundant feature extraction, followed by feature normalization, followed by dimensionality reduction is proposed. Feature normalization is performed by denoising algorithms. Two of them are considered and evaluated, namely, signal-to-noise ratio-dependent spectral subtraction and soft thresholding. Dimensionality reduction is performed with principal component analysis. Experiments using telephone corpora and the Aurora3 corpus are reported. They indicate that the proposed paradigm leads to a recognition performance with clean speech, measured in word error rate, marginally superior to the one obtained with perceptual linear prediction coefficients. Nevertheless, performance of the proposed analysis paradigm is significantly superior when used with noisy data and the same denoising algorithm is applied to all the analysis methods, which are compared.

Synthesis of Optical Wavelet Filters

The goal of the next generation of core and access optical networks is not the only the optical time and frequency signal multiplexing, but also the entire data processing performed in the optical domain, without any electrical-to-optical-to-electrical conversion. In a recent paper, we presented innovative planar lightwave circuit devices that perform the discrete wavelet transform and the wavelet packets decomposition of a data signal in the optical domain. The same filtering procedure was used to design optical encoders-decoders that generate-process a set of orthogonal optical code simultaneously. The aim of this letter is to furnish the synthesis guidelines for two-port lattice-form optical wavelet filters, starting from the half-band filters architecture presented by Jinguji et al.

Design of IIR half‐band filters with arbitrary flatness and its application to filter banks

AbstractHalf‐band filters are important for applications to multirate signal processing and wavelets. Previously, FIR half‐band filters have mainly been treated. However, it should be recognized that the IIR filter can produce frequency characteristics similar to those of the FIR filter with a low order. Also, in the applications of filter banks and wavelets, design of a half‐band filter is needed in which the degree of flatness can be specified arbitrarily. In the present paper, a new design method is proposed for an IIR half‐band filter with an arbitrary degree of flatness. In the present design method, the analytical solution of the filter coefficients is given in the case of a maximally flat filter. Also, in the case of a specified degree of flatness, the amplitude error in the stopband can be specified in the design. Further, the stability of the filter is studied and then the minimum group delay for causal stability is clarified. Finally, the IIR half‐band filter is applied to the design of a two‐channel filter bank and the effectiveness of the present design method is proven. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 10–18, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10114

Tree-structured IIR/FIR uniform-band and octave-band filter banks with very low-complexity analysis or synthesis filters

This paper introduces new tree-structured uniform-band and octave-band digital filter banks (FBs). These FBs make use of half-band IIR filters in the analysis FBs and FIR filters in the synthesis FBs. The resulting FBs are asymmetric in the sense that the analysis FB has a very low arithmetic complexity whereas that in the synthesis FB is higher. However, compared with other asymmetric FBs, the proposed ones have in many cases a lower overall arithmetic complexity and delay. The proposed FBs have magnitude distortion but no phase distortion; further, the aliasing components are either zero (uniform-band case) or approximately zero (octave-band case). The FBs are designed using linear and nonlinear programming. Design examples are included demonstrating the properties of the proposed filters banks.

Closed-form design of maximally flat IIR half-band filters

Half-band (HB) filters are of great importance and are often used in multirate digital signal processing systems, filter banks and wavelets. In this paper, a new closed-form expression for the transfer function of the maximally flat (MF) infinite-impulse response (IIR) HB filters is presented. The filter coefficients are directly obtained by solving a linear system of Vandermonde equations that are derived from the maximal flatness conditions. The proposed IIR half-band filters are more general than the existing half-band filters, because they include the conventional finite-impulse response (FIR) half-band filters with exactly linear phase, the generalized FIR half-band filters with approximately linear phase and the all-pass-based IIR half-band filters, as special cases. Furthermore, the causal stable IIR HB filters and the IIR HB filters with exactly linear phase can be realized also. Finally, some design examples are presented to demonstrate the effectiveness of the proposed IIR HB filters.

Design of High-Performance Wavelets for Image Coding Using a Perceptual Time Domain Criterion

This paper presents a new biorthogonal linear-phase wavelet design for image compression. Instead of calculating the prototype filters as spectral factors of a half-band filter, the design is based on the direct optimization of the lowpass analysis filter using an objective function directly related to a perceptual criterion for image compression. This function is defined as the product of the theoretical coding gain and an index called the peak-to-peak ratio, which was shown to have high correlation with perceptual quality. A distinctive feature of the proposed technique is a procedure by which, given a “good” starting filter, “good” filters of longer lengths are generated. The results are excellent, showing a clear improvement in perceptual image quality. Also, we devised a criterion for constraining the coefficients of the filters in order to design wavelets with minimum ringing.

A k-space method for coupled first-order acoustic propagation equations.

A k-space method for large-scale simulation of ultrasonic pulse propagation is presented. The present method, which solves the coupled first-order differential equations for wave propagation in inhomogeneous media, is derived in a simple form analogous to previous finite-difference methods with staggered spatial and temporal grids. Like k-space methods based on second-order wave equations, the present method is exact for homogeneous media, unconditionally stable for "slow" [c(r) < or = c0] media, and highly accurate for general weakly scattering media. In addition, unlike previous k-space methods, the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer (PML) nonreflecting boundary conditions. Numerical examples illustrate the capabilities of the present k-space method. For weakly inhomogeneous media, accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite-difference and pseudospectral methods. The low dispersion of the k-space method allows accurate representation of frequency-dependent attenuation and phase velocity associated with relaxation absorption. A technique for reduction of Gibbs phenomenon artifacts, in which compressibility and exponentially scaled density functions are smoothed by half-band filtering, is introduced. When employed together with this smoothing technique, the k-space method provides high accuracy for media including discontinuities, high-contrast inhomogeneities, and scattering structures smaller than the spatial grid resolution.