Cosine-modulated Filter Banks Research Articles

On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards

The Dolby Digital (Plus) AC-3 audio coding standards are currently the key enabling technologies for high-quality compression and decompression of digital audio signals. The Dolby Digital (Plus) AC-3 audio coding standards have adopted the modified discrete cosine transform (MDCT) for the time/frequency transformation of an audio data block. Besides a long transform being the MDCT, the AC-3 defines additional two variants of cosine-modulated filter banks called the first and second short transforms. Based on the matrix representation of AC-3 filter banks, by a systematic investigation of their properties and relations among transform matrices, a relation between the frequency coefficients of the long (MDCT) and those of two short transforms is derived. Frequency coefficients of two short transforms in AC-3 can be simply obtained from the given frequency coefficients of the long (MDCT) transform via a conversion matrix. Since the conversion matrix after proper scaling is an orthonormal matrix with very regular general structure, the frequency coefficients of the short transforms can be converted to the frequency coefficients of the long (MDCT) transform via the transposed conversion matrix. Consequently, the current implementation of AC-3 filter banks for the time/frequency transformation of an audio data block can be simplified in the encoder and the forward long (MDCT) transform computation is required only. Further, it is shown that there exists a simple relation between the time domain aliased data sequence recovered by the backward long (MDCT) and those of two short transforms. Consequently, the current implementation of AC-3 filter banks can be also simplified in the decoder and the backward long (MDCT) transform computation is required only. Thus, the computation of two short transforms in both the AC-3 encoder and decoder can be completely eliminated. Moreover, due to the existence of both relations between transform coefficients and time domain aliased data sequences, the conversion matrix in the AC-3 encoder and decoder may not be used at all.

Robust Detection and Analysis of Power System Oscillations Using the Teager-Kaiser Energy Operator

Critical to real-time oscillations monitoring is early detection when otherwise dormant natural modes become a serious threat to grid stability. The next urgent issue is to determine the frequency and damping of the problematic modes when the signal is embedded in noise and the system contains closely spaced natural modes. The present paper addresses the detection issue using the Teager-Kaiser energy operator (TKEO) which has shown to be a fast predictor of the instability onset time when applied to the output signals of an orthogonal filter bank. In the system stability context, linear filter decomposition (LFD) is preferred rather than empirical mode decomposition (EMD), well known for its tendency to generate artificial modes with no physical meaning. A narrowband LFD with a less than 0.2-Hz bandwidth is achieved in the range 0.05 to 3 Hz through a cosine-modulated filter bank design. The effectiveness of the scheme in accurately detecting and tracking the frequency and damping of oscillatory modes is demonstrated using Monte Carlo simulations of three closely spaced modes and a detailed analysis of an actual event recorded by Hydro-Quebec's WAMS in 2006.

A simple design method for the cosine-modulated filter banks using weighted constrained least square technique

This paper presents a simple and efficient design method for cosine-modulated filter banks with prescribed stopband attenuation , passband ripple , and channel overlap. The method casts the design problem as a linear minimization of filter coefficients such that their value at ω = π /2 M is 0.707, which results in a simpler, more direct design procedure. The weighted constrained least squares technique is exploited for designing the prototype filter for cosine modulation (CM) filter banks. Several design examples are included to show the increased efficiency and flexibility of the proposed method over the exiting methods. An application of the proposed method is considered in the area of sub-band coding of the ECG and speech signals.

An Improved and Simplified Approach for Designing Cosine Modulated Filter Bank Using Window Technique

An improved and simplified approach is presented for design of nearly perfect reconstructed cosine-modulated (CM) filter banks with prescribed stopband attenuation and channel overlapping. The method employs Kaiser window technique to design the prototype filter for filter banks with the novelty of exploiting spline functions in the transition band of the ideal filter instead of using the conventional brick-wall filter based on linear optimization of filter coefficients such that their value at frequency (??=??/2M) is 0.707. The simulation results illustrate the proposed method and its improvement over other existing methods in terms of amplitude distortion (e am ), number of iterations (NOI), aliasing distortion (e a ) and computation time (CPU time).

Cosine Modulated Non-Uniform Filter Banks

Traditional designs for non-uniform filter bank (NUFB) are usually complex; involve complicated nonlinear optimization with a large number of parameters and lack of linear phase ([LP) property. In this paper, we describe a simple design method for multirate near perfect reconstruction (NPR) cosine modulated filter banks with non-uniform frequency spacing and linear phase property that involves optimization of only single parameter. 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. Compared to other design methods our method provides very good design and converges very rapidly but the method is applicable, only if the upper band edge frequency of each non-uniform filter is an integral multiple of the bandwidth of the corresponding band. The design examples are presented to show the superiority of the proposed method over existing one.

Subband Vector Quantization with Trellis Coding

In this paper, a subband coding system consisting a combination of analysis filter bank, vector quantizer and trellis coding is designed. For the analysis filter bank, which decompose an input signal spectrum to bands we used a design method of cosine modulated filter bank with the perfect reconstruction. The analysis filters are obtained by cosine modulation of a prototype filter with the transfer function H(z), which optimization is performed right through the two-channel lossless lattice structure. Next block in this coding system is the vector quantizer with a full search, which perform quantization in the subband domain. The final block of the designed subband coding system is the block of trellis coding. This uses a block structured codebook of the vector quantizer with an extended set of the quantization vectors in accordance with Ungerboeck’s theory of clustering the set.

An improved closed form design method for the cosine modulated filter banks using windowing technique

This paper presents an improved closed form method for designing cosine modulated filter banks with prescribed stopband attenuation and channel overlap. The proposed method is based on optimum passband frequency, which is calculated using empirical formulas instead of using time consuming single or multivariable optimization. Different window functions are employed to design the prototype filter with the novelty of exploiting spline functions in the transition region of the ideal filter. Several design examples are included to show the increased efficiency of the proposed method over other exiting methods in terms of computation time, amplitude distortion ( e am) and aliasing distortion ( e a). An application of the proposed method is considered in the area of subband coding of the ECG and speech signals.

Analysis and Properties of Time-Varying Modified DFT Filter Banks

We provide a comprehensive analysis of the time-varying modified DFT (MDFT) filter bank based on the general time-varying filter bank theories (Wang, 2005, 2006, 2008, 2009) in both the time domain and frequency domain. We give firstly the description of the time-invariant MDFT filter bank including its perfect reconstruction (PR) condition, its mechanism of aliasing error cancellation and the relationship with the cosine-modulated filter bank in detail. Then, the time-varying MDFT filter bank is analyzed according to the time-domain description. Finally, the window switching method is introduced to design the prototype filter in the time-varying MDFT filter bank with examples. The error analysis shows that the introduced design approach is useful in practice.

A simple method for the design of cosine-modulated pseudo-QMF banks

In this paper, a simple and efficient iterative technique for designing of Cosine-Modulated (CM) filter banks with approximate reconstruction is presented. In the proposed technique, cut-off frequency is optimised to satisfy a new Perfect Reconstruction (PR) condition at frequency (ω = π/2M). Different window functions have been used to design the prototype filter for CM filter banks. The simulation results illustrate the improvement achieved through this method over other existing methods in terms of amplitude distortion (eam), Number of Iterations (NOI), aliasing distortion (ea) and computation time (CPU time). When it is exploited for subband coding of the Electrocardiogram (ECG) and speech signals, the proposed method yields good fidelity performance measuring parameters.

Design of NPR-Type Cosine Modulated Filterbank Using Combinational Window Functions

This paper presents the design of near perfect reconstruction (NPR) cosine modulated filterbank (CMFB). The prototype filter is designed by the combinational window functions. These window functions provide high side-lobe-fall-off-rate (SLFOR) with better far-end attenuation which suppresses the undesired inter-ferences occur in the filterbank. A linear optimization is used to minimize the error parameters. Design ex-amples have been included to illustrate the effectiveness of the proposed technique over the earlier reported work.

Design of M-Band NPR Cosine-Modulated Filterbank Using IFIR Technique

This paper presents a design of M-band near perfect reconstructed (NPR) cosine-modulated filterbank (CMFB). The prototype filter is formulated as an interpolated finite impulse response (IFIR) filter. Suitable stretched factor is used to provide considerable reduction in computation cost as well as minimum value of error parameters. Further minimization in errors has been achieved by applying a linear gradient optimization technique. The IFIR approach provides reduction in stopband energy as side-lobe-fall-off-rate (SLFOR) in magnitude response of the prototype filter is improved. Design examples have been included to illustrate the effectiveness of the proposed technique over the existing work.

A Class of Near Shift-Invariant and Orientation-Selective Transform Based on Delay-Less Oversampled Even-Stacked Cosine-Modulated Filter Banks

The purpose of this study is to show a class of near shift-invariant and orientation-selective transform based on even-stacked cosine-modulated filter banks (ECFBs) which originally have been proposed by Lin and Vaidyanathan. It is well-known that ECFBs can be designed by the modulation of just one prototype filter and guarantee the linear phase property. We extend this class to delay-less oversampled ECFB and show two additional attractive features; high directional selectivity and near shift-invariant property. In this paper, these properties are verified by theoretical analysis and demonstrations.

Design of Kaiser window based optimized prototype filter for cosine modulated filter banks

In this paper, Kaiser window based design of prototype filter for cosine modulated filter banks is presented. The reconstruction error, which is used as an objective function, is minimized by optimizing the cutoff frequency of designed prototype filter. Linear search optimization algorithm is employed. The results show significant reduction in reconstruction error compared to other earlier reported works.

Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks

This paper introduces two classes of cosine-modulated causal and stable filter banks (FBs) with near perfect reconstruction (NPR) and low implementation complexity. Both classes have the same infinite-length impulse response (IIR) analysis FB but different synthesis FBs utilizing IIR and finite-length impulse response (FIR) filters, respectively. The two classes are preferable for different types of specifications. The IIR/FIR FBs are preferred if small phase errors relative to the magnitude error are desired, and vice versa. The paper provides systematic design procedures so that PR can be approximated as closely as desired. It is demonstrated through several examples that the proposed FB classes, depending on the specification, can have a lower implementation complexity compared to existing FIR and IIR cosine-modulated FBs (CMFBs). The price to pay for the reduced complexity is generally an increased delay. Furthermore, two additional attractive features of the proposed FBs are that they are asymmetric in the sense that one of the analysis and synthesis banks has a lower computational complexity compared to the other, which can be beneficial in some applications, and that the number of distinct coefficients is small, which facilitates the design of FBs with large numbers of channels.

Efficient Design of Cosine-Modulated Filter Banks via Convex Optimization

This paper presents efficient approaches for designing cosine-modulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of 2M th-band filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the nonconvex optimization problem can be cast into a semi-definite programming (SDP) problem by a convex relaxation technique. Then the reconstruction error is further minimized by an efficient iterative algorithm in which the closed-form expression is given in each iteration. Several examples are given to illustrate the effectiveness of the proposed method over the existing ones.

A Novel Design of Regular Cosine-Modulated Filter Banks for Image Coding

This paper describes a design method of cosine-modulated filter banks (CMFB's) for an efficient coding of images. Whereas the CMFB has advantages of low design and implementation cost, subband filters of the CMFB do not have linear phase property. This prevents from employing a symmetric extension in transformation process, and leads to a degradation of the image compression performance. However, a recently proposed smooth extension alleviates the problem with CMFB's. As a result, well-designed CMFB's can be expected to be good candidates for a transform block in image compression applications. In this paper, we present a novel design approach of regular CMFB's. After introducing a regularity constraint on lattice parameters of a prototype filter in paraunitary (PU) CMFB's, we also derive a regularity condition for perfect reconstruction (PR) CMFB's. Finally, we design regular 8-channel PUCMFB and PRCMFB by an unconstrained optimization of residual lattice parameters, and several simulation results for test images are compared with various transforms for evaluating the proposed image coder based on the CMFB's with one degree of regularity. In addition, we show a computational complexity of the designed CMFB's.

Efficient Design of High-Complexity Cosine Modulated Filter Banks Using $2 M$th Band Conditions

This paper presents several new properties of biorthogonal cosine modulated filter banks (CMFBs) and efficient algorithms for designing CMFBs with a very large number of subbands and very long filters. For a biorthogonal CMFB, we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete Fourier transform (DFT) analysis filter bank. By exploiting gradient information and 2M th band conditions, efficient algorithms are proposed for designing both orthogonal and biorthogonal CMFBs. In addition, an efficient matrix inversion algorithm with O(N 2 ) complexity is also presented. Several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms.

Method for signal decomposition and denoising based on nonuniform cosine-modulated filter banks

In this paper, a novel method for signal decomposition and denoising is proposed based on a nonuniform filter bank (NUFB), which is derived from a uniform filter bank. With this method, the signal is firstly decomposed into M subbands using a uniform filter bank. Then according to their energy distribution, the corresponding consecutive filters are merged to compose the nonuniform filters. With the resulting NUFB, the signal can be readily matched and flexibly decomposed according to its power spectrum distribution. As another advantage, this method can be used to detect and remove the narrow-band noise from the corrupted signal. To verify the proposed method, a simulation of extracting the main information of an audio signal and removing its glitch is given.

On the Theory and Design of a Class of PR Uniform and Recombination Nonuniform Causal-Stable IIR Cosine Modulated Filter Banks

This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> , where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly.

A Computationally Efficient Design for Prototype Filters of an M-Channel Cosine Modulated Filter Bank

A Computationally Efficient Design for Prototype Filters of an M-Channel Cosine Modulated Filter Bank