Cosine-modulated Filter Banks Research Articles

Review Article on Designing of Pseudo Quadratue Mirror Filter Bank

This paper presents the review of the Pseudo-QMF bank which is one of the most important subclass of the Multi-rate filter banks. It deals with the advantages of Pseudo-QMF bank over the other filter banks such as fewer complexes in designing and easy to implement. Various design techniques of pseudo-QMF have been discussed here, so that this paper would help other researchers to work in this very important field of digital signal processing. Keywords: Cosine modulated filter bank, Kaiser window approach (KWA), Pseudo-QMF, Non-uniform sub- band filter bank, Spectral factorization approach.

On Efficient Design of High-Order Filters With Applications to Filter Banks and Transmultiplexers With Large Number of Channels

This paper proposes a method for designing high-order linear-phase finite-length impulse response (FIR) filters which are required as, e.g., the prototype filters in filter banks (FBs) and transmultiplexers (TMUXs) with a large number of channels. The proposed method uses the Farrow structure to express the polyphase components of the desired filter. Thereby, the only unknown parameters, in the filter design, are the coefficients of the Farrow subfilters. The number of these unknown parameters is considerably smaller than that of the direct filter design methods. Besides these unknown parameters, the proposed method needs some predefined multipliers. Although the number of these multipliers is larger than the number of unknown parameters, they are known a priori. The proposed method is generally applicable to any linear-phase FIR filter irrespective of its order being high, low, even, or odd as well as the impulse response being symmetric or antisymmetric. However, it is more efficient for filters with high orders as the conventional design of such filters is more challenging. For example, to design a linear-phase FIR lowpass filter of order 131071 with a stopband attenuation of about 55 dB, which is used as the prototype filter of a cosine modulated filter bank (CMFB) with 8192 channels, our proposed method requires only 16 unknown parameters. The paper gives design examples for individual lowpass filters as well as the prototype filters for fixed and flexible modulated FBs.

Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation

Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated–frequency-modulated (AM-FM) signals using a signal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor’s AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

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.

An optimized cosine-modulated nonuniform filter bank design for subband coding of ECG signal

A simple iterative technique for the design of nonuniform cosine modulated filter banks (CMFBS) is presented in this paper. The proposed technique employs a single parameter for optimization. The nonuniform cosine modulated filter banks are derived by merging the adjacent filters of uniform cosine modulated filter banks. The prototype filter is designed with the aid of different adjustable window functions such as Kaiser, Cosh and Exponential, and by using the constrained equiripple finite impulse response (FIR) digital filter design technique. In this method, either cut off frequency or passband edge frequency is varied in order to adjust the filter coefficients so that reconstruction error could be optimized/minimized to zero. Performance and effectiveness of the proposed method in terms of peak reconstruction error (PRE), aliasing distortion (AD), computational (CPU) time, and number of iteration (NOI) have been shown through the numerical examples and comparative studies. Finally, the technique is exploited for the subband coding of electrocardiogram (ECG) and speech signals.

An Efficient Method for Designing of Modulated Filter Banks with Causal-Stable IIR Filters

This paper proposes an efficient method for the design of a class of causal-stable infinite impulse response (IIR) cosine modulated filter banks (CMFBs) and a class of IIR modified discrete Fourier transform filter banks (MDFT FBs) with a very low system delay. Instead of designing the frequency magnitude responses of the IIR prototype filters, the power spectrums of the desired filters are designed so as to reformulate the design problems as a quasi-convex optimization problem which can be solved by CVX software. When the solutions are found, the IIR prototype filters can be obtained by a spectral factorization technique. By using a bisection search, IIR FBs obtained are nearly perfect reconstruction (NPR) and which can be used as effective initial guess to some constrained nonlinear optimizer for further optimization to design perfect reconstruction (PR) IIR FBs with a very low system delay.

Use of first‐ and second‐order sigma–delta quantisers in context of odd‐stacked cosine modulated filter banks

The use of sigma–delta (ΣΔ) quantisers in the context of an oversampled odd-stacked cosine modulated filter bank (CMFB) is investigated. Shown is that the exploitation of the ΣΔ quantisers jointly with the CMFB ensures significant robustness of the transmitted signal against transmission errors. In this context, an upper bound of the minimum squares error of the reconstructed signal is derived and it is proved that it decreases as (1/r 2), where r denotes the CMFB frame redundancy, for the first- and the second-order ΣΔ quantisers.

Design of Multiplier-less Cosine Modulated Filter Banks with Sharp Transition using Evolutionary Algorithms

This paper proposes a totally multiplier-less approximate reconstruction cosine modulated filter bank. The prototype filter is designed to obtain acomputationally efficient,sharp transitionwidth, finite impulse response (FIR) filter using the frequency response masking (FRM) approach combined with the canonic signed digit (CSD)representation ofthe coefficients.Meta-heuristic algorithms are deployed to optimize the performance of the filter bank. The algorithms are modified to suit the optimization problem, inwhich the objective function isnon linear and the search space consists of integers.

Two Dimensional <i>M</i>-Channel Non-separable Filter Banks Based on Cosine Modulated Filter Banks with Diagonal Shifts

Two Dimensional <i>M</i>-Channel Non-separable Filter Banks Based on Cosine Modulated Filter Banks with Diagonal Shifts

A Fast Design Method for Perfect-Reconstruction Uniform Cosine-Modulated Filter Banks

In this correspondence, we present a new and fast design algorithm for perfect-reconstruction (PR), maximally decimated, uniform, cosine-modulated filter banks. Perfect reconstruction is obtained within arithmetic machine precision. The new design does not need numerical optimization routines and is significantly faster than a competing method based on second-order cone programming (SOCP). The proposed design algorithm finds the optimum solution by iteratively solving a quadratic programming problem with linear equality constraints. By a special modification of the basic algorithm, we obtain PR filter banks with high stopband attenuations. In addition, fast convergence is verified by designing PR filter banks with up to 128 channels.

Fast Conversion Algorithm for the Dolby Digital (Plus) AC-3 Audio Coding Standards

The Dolby Digital (AC-3) and the Dolby Digital Plus or Enhanced AC-3 (E-AC-3) systems are currently the key enabling technologies for high-quality compression of digital audio signals. For the time-to-frequency transformation of an audio data block and vice versa, both systems have adopted a long transform being the modified discrete cosine transform (MDCT). The AC-3 additionally defines two variants of cosine-modulated filter banks called the first and second short transforms. A fast conversion algorithm is presented to convert the frequency coefficients of the long (MDCT) transform to those of two short transforms and vice versa, directly in the frequency domain. It is based on a block sparse matrix factorization of a conversion matrix. The fast conversion algorithm is efficient in terms of the structural simplicity, arithmetic complexity and memory requirements compared to the obvious conversion methods. Moreover, the existing AC-3 fast computational modules may be simply re-used in the conversion procedures. Consequently, the E-AC-3 to AC-3 bit stream conversion and the AC-3 to E-AC-3 bit stream transcoding can be realized in a simplified and efficient way, thus minimizing the amount of partial decoding/encoding and memory requirements during the conversion and transcoding processes.

Efficient Cosine Modulated Filter Bank Using Multiplierless Masking Filter and Representation of Prototype Filter Coefficients Using CSD

This paper presents a design of low complexity multichannel Nearly Perfect Reconstruction (NPR) Cosine Modulated Filter Bank (CMFB). CMFBs are used extensively because of ease realization and the inherent advantage of high stop-band attenuation. But, when the number of channel becomes large, it leads to certain limitations as it would require large number of filter coefficients to be optimized and hence longer CPU time; e.g. 32-band or 64-band CMFB. Large number of filter coefficients would also mean that computational complexity of the prototype filter is extremely increased that tends to slow down the convergence to best possible solution. Here, the prototype filter is designed using modified Interpolated Finite Impulse Response (IFIR) technique where masking filter is replaced by multiplier free cascaded structure and coefficients of model filter are converted to nearest Canonical Signed Digit (CSD). The interpolation factor is chosen in such a way that computational cost of the overall filter and different error parameters are reduced. The proposed approach thus leads to reduction in stop-band energy as well as high Side-Lobe-Fall-off-Rate (SLFOR). Three examples have been included to demonstrate the effectiveness of the proposed technique over the existing design methods and savings in computational complexity is also highlighted.

Zero-crossing approach to high-resolution reconstruction in frequency-domain optical-coherence tomography

We address the problem of high-resolution reconstruction in frequency-domain optical-coherence tomography (FDOCT). The traditional method employed uses the inverse discrete Fourier transform, which is limited in resolution due to the Heisenberg uncertainty principle. We propose a reconstruction technique based on zero-crossing (ZC) interval analysis. The motivation for our approach lies in the observation that, for a multilayered specimen, the backscattered signal may be expressed as a sum of sinusoids, and each sinusoid manifests as a peak in the FDOCT reconstruction. The successive ZC intervals of a sinusoid exhibit high consistency, with the intervals being inversely related to the frequency of the sinusoid. The statistics of the ZC intervals are used for detecting the frequencies present in the input signal. The noise robustness of the proposed technique is improved by using a cosine-modulated filter bank for separating the input into different frequency bands, and the ZC analysis is carried out on each band separately. The design of the filter bank requires the design of a prototype, which we accomplish using a Kaiser window approach. We show that the proposed method gives good results on synthesized and experimental data. The resolution is enhanced, and noise robustness is higher compared with the standard Fourier reconstruction.

A design of IFIR prototype filter for Cosine Modulated Filterbank and Transmultiplexer

This paper proposes a computational efficient approach for the design of M-band Cosine Modulated Filterbank (CMFB) and Transmultiplexer (TMUX) in Near Perfect Reconstruction (NPR) condition. The required prototype filter is formulated by using interpolated FIR (IFIR) technique. Suitable stretch factor is used for the reduction in computation cost and obtained minimum value of distortion parameters. The minimization of these parameters has been achieved by applying a single variable bisection type optimization technique. Design examples are included to prove superiority of performance over the existing work.

Design and performance analysis of adjustable window functions based cosine modulated filter banks

In this paper, design and comparative analysis of adjustable window functions based cosine modulated filter banks are analyzed. Four adjustable windows, viz., Kaiser window, Saramaki window, ultraspherical windows and [email protected]?s transitional window are used to design prototype filters. Reconstruction error, which is used as an objective function, is minimized by optimizing the cutoff frequency of designed prototype filters. The gradient based iterative optimization algorithm is used. These optimized filters are later cosine modulated to obtain filter banks. The performances of filter banks are compared on the basis of reconstruction error and aliasing error.

Near-Perfect Reconstruction Oversampled Nonuniform Cosine-Modulated Filter Banks Based on Frequency Warping and Subband Merging

Near-Perfect Reconstruction Oversampled Nonuniform Cosine-Modulated Filter Banks Based on Frequency Warping and Subband MergingA novel method for designing near-perfect reconstruction oversampled nonuniform cosine-modulated filter banks is proposed, which combines frequency warping and subband merging, and thus offers more flexibility than known techniques. On the one hand, desirable frequency partitionings can be better approximated. On the other hand, at the price of only a small loss in partitioning accuracy, both warping strength and number of channels before merging can be adjusted so as to minimize the computational complexity of a system. In particular, the coefficient of the function behind warping can be constrained to be a negative integer power of two, so that multiplications related to allpass filtering can be replaced with more efficient binary shifts. The main idea is accompanied by some contributions to the theory of warped filter banks. Namely, group delay equalization is thoroughly investigated, and it is shown how to avoid significant aliasing by channel oversampling. Our research revolves around filter banks for perceptual processing of sound, which are required to approximate the psychoacoustic scales well and need not guarantee perfect reconstruction.

Cosine Modulated Non-Uniform Filter Bank with Improved Computational Efficiency

In this correspondence, a simple design method for multirate near perfect reconstruction (NPR) integer decimated filter bank with non-uniform frequency spacing and linear phase property, that involves optimization of only single parameter, is proposed. It is derived from the uniform cosine modulated filter bank (CMFB) by merging some relevant band pass filters. The design procedure and the structure of the uniform CMFB are mostly preserved in the non-uniform implementation. The parent filter of the filter bank is formulated as an interpolated finite impulse response (IFIR) filter. The IFIR digital filters permit efficient hardware implementations due to less number of multiplier coefficients. Design examples show that the proposed approach provides good performance with less computational complexity at the cost of slight increase in system delay.

Design of M-channel cosine modulated filter bank using modified Exponential window

In this paper, an improved Exponential window is developed for designing M-channel cosine-modulated pseudo QMF banks. The Exponential window is modified by adding third parameter (ρ), which improves the spectral characteristic of a window in terms of smaller ripple ratio, wider main lobe width with improved side lobe roll-off ratio. When it is exploited for designing multi-channel cosine modulated filter banks, the modified Exponential window gives better performance for higher band as compared to lower band. In addition to this, the modified Exponential window performs better performance at lower stopband attenuation. When compared with modified Cosh and Kaiser windows, the modified Exponential windows performs better in terms of amplitude distortion, aliasing distortion (AD) and computational time (CPU time) for the same design specifications. Several examples are included to illustrate the effectiveness of this window in the field multirate systems designing.

Design perfect reconstruction cosine-modulated filter bank by variable neighbourhood search-least-mean-square error

In multirate digital signal processing, cosine-modulated filter banks (CMFB) satisfying perfect reconstruction (PR) or near-perfect reconstruction (NPR) property are of great interest owing to their extensive applications in data compression, feature detection and extraction and signal transmultiplexing. And the key to PR CMFB design is to design a PR prototype filter (PF). However, designing optimal PR and NPR PF is essentially a constrained non-linear programming. It is generally modelled as a non-convex quadratically constrained quadratic optimisation problem. So far, this kind of optimisation is still a very difficult class of optimisation and no practical but few metaheuristic algorithm is availabe for finding its global optimal solution. The study proposed a two-stage method for designing PR PF. In the first stage, a metaheuristic algorithm based on variable neighbourhood search is proposed for designing lower-ordered PR PF, that is the corresponding PR CMFB has less channels. Then a least-mean-square error approach is introduced to increase the length of the designed lower-ordered PF with the PR property unchanged. Design examples are given to illustrate the proposed algorithm outperforms the existing one in reconstruction error and stopband attenuation.

Retained energy-based coding for EEG signals

The recent use of long-term records in electroencephalography is becoming more frequent due to its diagnostic potential and the growth of novel signal processing methods that deal with these types of recordings. In these cases, the considerable volume of data to be managed makes compression necessary to reduce the bit rate for transmission and storage applications. In this paper, a new compression algorithm specifically designed to encode electroencephalographic (EEG) signals is proposed. Cosine modulated filter banks are used to decompose the EEG signal into a set of subbands well adapted to the frequency bands characteristic of the EEG. Given that no regular pattern may be easily extracted from the signal in time domain, a thresholding-based method is applied for quantizing samples. The method of retained energy is designed for efficiently computing the threshold in the decomposition domain which, at the same time, allows the quality of the reconstructed EEG to be controlled. The experiments are conducted over a large set of signals taken from two public databases available at Physionet and the results show that the compression scheme yields better compression than other reported methods.