Two-band Filter Research Articles

Novel Nth/2Nth Order Two-Band Bandpass Filters for Sub-6 GHz 5G Applications

In this paper, a new design method is proposed for multi-mode two-band bandpass filters based on combining a square loop resonator that has a capacitive perturbation element and short-circuited stubs. This concept is a new multi-mode two-band filter design having Nth and 2Nth order for the first and second passbands that appear in f0 and 3f0 center frequencies, respectively. It has been shown that the number of transmission modes in each passband can easily be increased by periodically cascading one unit filter cell including one square loop resonator and two short-circuited stubs. This also provides a reconfigurable filter property, namely the obtaining of two different filtering characteristics in the second passband by means of the reverse and straight placing of the cascaded unit filter cells in the horizontal axis. Two 2nd/4th order two-band bandpass filter prototypes are fabricated and tested to validate the proposed design method. The total surface areas of these fabricated prototypes are 26.0 mm × 9.0 mm and 24.4 mm × 16.8 mm, and the measured insertion losses in the first/second passband are about 0.63 dB/0.96 dB and 0.59 dB/0.83 dB. It is observed that the filter prototypes have the advantages of low insertion loss, compact size, and flexible filtering characteristics. The designed filters are suitable for operation in the 5G spectrum, which includes a range of radio frequencies sub-6 GHz.

A new approach to identify obstructive sleep apnea using an optimal orthogonal wavelet filter bank with ECG signals

Abstract Obstructive sleep apnea (OSA) is a severe sleep ailment. It manifests when a person's breathing is interrupted while sleeping due to an inadequate supply of oxygen to the brain and physical body. The detection of OSA at an early stage can provide better mitigation from severe health impairments. An accurate method to detect OSA can improve the quality of life significantly. The computer-aided diagnosis (CAD) system of OSA developed using single-channel, single-signal physiological signals can efficiently cut costs, and can be used even at home. Therefore, a simple and portable OSA-CAD system using single-channel electrocardiogram (ECG) is introduced in this paper. This study proposes the automated identification of ECG signal affected from OSA employing an optimal two-band filter bank (FB) technique. While designing the filter bank, our central objective is to minimize the spectral localization, subjected to exact regeneration and regularity criteria. The identification of OSA using ECG signals is duly based on the newly designed FB. Using the proposed FB, ECG signals were split into wavelet frequency-bands (WFBs). The fuzzy-entropy (FUEN) and the log of signal-energy (LOEN) of WFBs have been employed as the distinguishing features. The 35-fold cross-validation technique was exercised using various classifiers, namely K nearest neighbor (KNN), decision tree (DT), linear discriminant, logistic regression, and support vector machine (SVM) to separate into normal and OSA affected subjects. The proposed model has attained respective highest average accuracy (AVAC), average sensitivity (AVSE), average specificity (AVSP) and F1-score of 90.87%, 92.43% 88.33% and 92.61%. Our proposed model outperformed the existing systems developed using the same database and was found to be more efficient, robust, and easy to use.

Design of Time–Frequency-Localized Two-Band Orthogonal Wavelet Filter Banks

In this paper, we design time–frequency-localized two-band orthogonal wavelet filter banks using convex semidefinite programming (SDP). The sum of the time variance and frequency variance of the filter is used to formulate a real symmetric positive definite matrix for joint time–frequency localization of filters. Time–frequency-localized orthogonal low-pass filter with specified length and regularity order is designed. For nonmaximally regular two-band filter banks of length twenty, it is found that, as we increase the regularity order, the solution of the SDP converges to the filters with time–frequency product (TFP) almost same as the Daubechies maximally regular filter of length twenty. Unlike the class of Daubechies maximally regular minimum phase wavelet filter banks, a rank minimization algorithm in a SDP is employed to obtain mixed-phase low-pass filters with TFP of the filters as well as the scaling and wavelet function better than the equivalent two-band Daubechies filter bank.

Time–frequency localized three-band biorthogonal wavelet filter bank using semidefinite relaxation and nonlinear least squares with epileptic seizure EEG signal classification

In this paper, we design time–frequency localized three-band biorthogonal linear phase wavelet filter bank for epileptic seizure electroencephalograph (EEG) signal classification. Time–frequency localized analysis and synthesis low-pass filters (LPF) are designed using convex semidefinite programming (SDP) by transforming a nonconvex problem into a convex SDP using semidefinite relaxation technique. Three-band parameterized lattice biorthogonal linear phase perfect reconstruction filter bank (BOLPPRFB) is chosen and nonlinear least squares algorithm is used to determine its parameters values that generate the designed analysis and synthesis LPF such that the band-pass and high-pass filters are also well localized in time and frequency domain. The designed analysis and synthesis three-band wavelet filter banks are compared with the standard two-band filter banks like Daubechies maximally regular filter banks, Cohen–Daubechies–Feauveau (CDF) biorthogonal filter banks and orthogonal time–frequency localized filter banks. Kruskal–Wallis statistical test is employed to measure the statistical significance of the subband features obtained from the various two and three-band filter banks for epileptic seizure EEG signal classification. The results show that the designed three-band analysis and synthesis filter banks both outperform two-band filter banks in the classification of seizure and seizure-free EEG signals. The designed three-band filter banks and multi-layer perceptron neural network (MLPNN) are further used together to implement a signal classifier that provides classification accuracy better than the recently reported results for epileptic seizure EEG signal classification.

Two-Band Hybrid FIR–IIR Filters for Image Compression

Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity.

Filter Banks for Prediction-Compensated Multiple Description Coding

In this paper, a prediction-compensated multiple description (MD) coding framework for two-band filter banks is proposed, in which the coefficients in each subband are split into two descriptions. Each description also includes the prediction residuals of the data in the other description. The designs of the optimal orthogonal and biorthogonal filter banks are formulated in a unified framework, and both one-level and multiple-level decompositions are analyzed. Contrary to the existing MD filter banks in the literature, the optimal filter banks in the proposed scheme are quite similar to those in single description coding. Therefore, the method can be applied to systems with single-description-optimized filter banks and still attain near-optimal performance. Image coding results show that this method achieves better performance and lower complexity than the latest JPEG 2000 based MDC.

Synthesis of Flat-Top Bandpass Filters Using Two-Band Rejection Long-Period Fiber Gratings

We propose a synthesis method based on the genetic algorithm for designing flat-top bandpass filters using two-band rejection long-period fiber grating (LPFG) filters. In the proposed method, the LPFG structure constructed by concatenating the two-band rejection filters is used as the initial parameter to easily design good flat-top bandpass filters in a wavelength range.

Hilbert transform pairs of biorthogonal wavelet bases

The forming of Hilbert transform pairs of biorthogonal wavelet bases of two-band filter banks is studied in this paper. We first derive necessary and sufficient conditions on the scaling filters that render two Hilbert transform pairs: one decomposition pair and one reconstruction pair. We show that the Hilbert transform pairs are achieved if and only if the decomposition scaling filter of one filter bank is half-sample delayed from that of the other filter bank; and the reconstruction scaling filter of the former is half-sample advanced from that of the latter. Hilbert transform pairs of wavelet bases are also characterized by equivalent relationships on the wavelet filters and the scaling functions associated with the two filter banks. An illustrative example is provided.

The boundary processing of wavelet based image compression

When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported.

Analysis, design, and implementation of two-channel linear-phase filter banks: a new approach

The problem of designing two-channel perfect-reconstruction FIR filter banks with linear-phase analysis and synthesis filters is revisited. Based on a new algebraic formulation, all the possible factorized forms for this two-band filter bank are derived. We thus obtain complete and canonical solutions for the filter banks, composed of odd-order symmetric and antisymmetric filters (type-A systems) and for those built with symmetric even order filters (type-B systems). A strong characteristic of these new cascade structures, which, until now, had not been identified, is related to a defectivity property. Taking this into account is the key issue to cover all the FIR solutions and to design cascade structures being robust to the quantization of their parameters. Design examples are provided that illustrate our method.

Rugate filter manufacturing by electron cyclotron resonance plasma-enhanced chemical vapor deposition of SiN<sub><italic>x</italic></sub>

Electron cyclotron resonance plasma-enhanced chemical va- por deposition (ECR-PECVD) is used to deposit thin films of SiN x of different composition from mixtures of N2 and 30% SiH4 in Ar onto dif- ferent substrates. Measured values of the complex refractive index over the wavelength range of interest are used in the design and computer- controlled fabrication of one- and two-band rugate optical interference filters. The excursion of the continuously varying refractive index is cho- sen to be between 0.8 and 1.2, and window functions and matching layers at both sides are employed for sidelobe suppression. Measured reflection patterns of filters agreed well with simulated results. Filters designed for a center wavelength of 1000 nm and a total thickness of 2.1 mm, have a reflectance of 97% in the stopband and a bandwidth of typically 240 nm. The two-band filter is designed for stopbands at 1000 and 770 nm with reflectance of 98 and 96% and bandwidths of 150 and 120 nm, respectively. The total thickness of this filter is 3.33mm. Filters are successfully deposited on optical fiber ends using one of the fibers for in situ monitoring of the deposition process. © 1997 Society of Photo- Optical Instrumentation Engineers. (S0091-3286(97)04004-X)

Construction methods and algorithm design of wavelet bases

Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper.

Subband coding of images using asymmetrical filter banks

We address the problem of the choice of subband filters in the context of image coding. The ringing effects that occur in subband-based compression schemes are the major unpleasant distortions. A new set of two-band filter banks suitable for image coding applications is presented. The basic properties of these filters are linear phase, perfect reconstruction, asymmetric length, and maximum regularity. The better overall performances compared to the classical QMF subband filters are explained. The asymmetry of the filter lengths results in a better compaction of the energy, especially in the highpass subbands. Moreover, the quantization error is reduced due to the short lowpass synthesis filter. The undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter. The proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images, which explains the better coding performance.

On the realizability of biorthogonal, m-dimensional two-band filter banks

We show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks. The key ingredient of the approach is known in literature as Euclid's algorithm. Using this algorithm we derive some strong result on the design freedom for ladder structures. In particular we show that the dimensionality of the problem plays an important role. We end by with some conjectures concerning the extensions to multichannel and noncausal filter banks. >

Smooth wavelets, transform coding, and Markov-1 processes

This paper compares the energy compacting properties of unitary transforms from transform coders and two-band paraunitary filter banks from subband coders using a cost criterion that is proposed. Stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal, and all subband optimal processes are analytically characterized for the case of length-4 filters. It is shown analytically for length-4 filters and empirically for longer-length filters that Markov-1 processes are subband optimal and that the Daubechies (1988) maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for Markov-1 inputs.

The design of 2-D nonseparable directional perfect reconstruction filter banks

In this paper, we develop a directional 2-D nonseparable filter bank that can perfectly reconstruct the downsampled subband signals. The filter bank represents two powerful image and video processing tools: directional subband decomposition and perfect reconstruction. The directional filter banks consist of (1) the input signal and the subband signals modulation, (2) diamond shape prefilter, and (3) four different parallelogram shape prefilters. This paper addresses the design and implementation of a two-band filter bank that is proved to be able to provide perfect reconstruction of the downsampled subband signals. Finally, we use a conventional 1-D half-band filter as a prototype and then apply the McClellan transform for the specific 2-D diamond shape and parallelogram shape subfilters. This method is extremely simple in designing the analysis/synthesis subfilters for the filter bank.

Iterated filter banks with rational rate changes connection with discrete wavelet transforms

Some properties of two-band filter banks with rational rate changes ("rational filter banks") are first reviewed. Focusing then on iterated rational filter banks, compactly supported limit functions are obtained, in the same manner as previously done for dyadic schemes, allowing a characterization of such filter banks. These functions are carefully studied and the properties they share with the dyadic case are highlighted. They are experimentally observed to verify a "shift property" (strictly verified in the dyadic ease) up to an error which can be made arbitrarily small when their regularity increases. In this case, the high-pass outputs of an iterated filter bank can be very close to samples of a discrete wavelet transform with the same rational dilation factor. Straightforward extension of the formalism of multiresolution analysis is also made. Finally, it is shown that if one is ready to put up with the loss of the shift property, rational iterated filter banks can be used in the same manner as if they were dyadic filter banks, with the advantage that rational dilation factors can be chosen closer to 1.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>