A new approach to the design of critically sampled M-channeluniform-band perfect-reconstruction linear-phase FIR filter banks

A new approach is presented for the design of uniform-band M-channel perfect-reconstruction (PR) FIR filter banks employing linear-phase analysis and synthesis filters. The technique designs on the impulse responses of the analysis filters directly. The design problem is formulated as an optimization program. The filter bank's PR feature can either be implicitly enforced through a set of mathematical relationships among the analysis filters' coefficients or through a set of constraints in the optimization program. The former approach results in a filter bank whose PR feature's dependency on hardware and software is eliminated or, at least, minimized. The synthesis filters are then obtained by a set of relationships that describe each synthesis filter as a function of the analysis filters. The criterion for optimality is “least-squares,” where the square of the difference between the ideal and actual frequency responses is integrated over the appropriate frequency bands for all M analysis filters and minimized     

Perfect-reconstruction filter banks having linear-phase FIR filterswith equiripple response

The design of equiripple linear-phase analysis and synthesis FIR filters of two-channel perfect-reconstruction (PR) filter banks is formulated as the minimization of a weighted peak-error under both linear inequality (arising from the desired responses of the analysis filters) and nonlinear equality (PR) constraints. The effectiveness of a proposed method to solve the design problem (a modified dual-affine scaling variant of Karmarkar's (1989) algorithm and an approximation scheme) is illustrated through several design examples     

Time-domain design of FIR multirate filter banks

A new time-domain methodology for designing FIR multirate filter banks is proposed. The conditions for perfect reconstruction systems can only be met by a limited number of systems, and consequently one of the major problems is to design analysis and synthesis filters which reduce the reconstruction error to a minimum. A recursive technique is proposed which uses the synthesis filters from one iteration to update the analysis filters for the next. The Letter shows that this is computationally simpler than previously proposed time-domain methods and produces filter banks in which the reconstruction error is reduced to practically acceptable levels.<>     

Minimax design of two-channel nonuniform-division FIR filter banks

The paper deals with the minimax design of two-channel nonuniform-division filter (NDF) banks. Based on a linearisation scheme, the design problem is formulated as an optimisation problem with linear constraints. The authors present a method to design a two-channel NDF bank using a modified dual-affine scaling variant of Karmarkar's (1984) algorithm. This method provides the optimal results that the linear-phase FIR analysis and synthesis filters have equiripple stopband response and the resulting NDF bank also shows equiripple reconstruction error behaviour. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

Low delay FIR filter banks: design and evaluation

The subject of this paper is the design of low and minimum delay, exact reconstruction analysis-synthesis systems based on filter banks. It presents a time domain approach to the problem of designing FIR filter banks with adjustable reconstruction delays. It is shown that using a time domain formulation for the analysis-synthesis systems, the system delay can be considered to be relatively independent of the length of the analysis and synthesis filters. After a summary of the time domain analysis and design framework, the design of low and minimum delay systems is considered in detail. Several design examples are provided in the paper to demonstrate the performance of the design algorithm     

On the design of FIR analysis-synthesis filter banks with highcomputational efficiency

Presents an effective design algorithm for analysis-synthesis filter banks with computationally efficient structures. Although a wide variety of implementation structures can be accommodated, the focus of the paper is on cosine modulated filter banks. The design procedure is based on a time domain formulation of analysis-synthesis filter banks in which each individual channel filter is constrained to be a cosine modulated versions of a baseband filter. The resulting filter banks are very efficient in terms of computational requirements and are relatively easy to design. A unique feature of this approach is that relatively low reconstruction delays can be imposed on the system. A discussion of the associated computational properties of the designed systems and some design examples are included     

FIR principal component filter banks

Two-dimensional (2-D) principal component filter banks (PCFBs) of finite impulse response (FIR) are proposed. For 2-D signals, among all uniform paraunitary FIR analysis/synthesis filter banks, the FIR PCFBs have the most energy compaction and maximize the arithmetic mean to geometric mean ratio (AM/GM ratio) of subband variances, which is the theoretic coding gain (TCC) of the systems under proper assumptions. The theoretic proof and design techniques are provided. Several special cases are discussed. Experimental results show the potential power of the FIR PCFBs     

Minimax design of adjustable-bandwidth linear-phase FIR filters

This paper considers the design of digital linear-phase finite-length impulse response (FIR) filters that have adjustable bandwidth(s) whereas the phase response is fixed. For this purpose, a structure is employed in which the overall transfer function is a weighted linear combination of fixed subfilters and where the weights are directly determined by the bandwidth(s). Minimax design techniques are introduced which generate globally optimal overall filters in the minimax (Chebyshev) sense over a whole set of filter specifications. The paper also introduces a new structure for bandstop and bandpass filters with individually adjustable upper and lower band edges, and with a substantially lower arithmetic complexity compared to structures that make use of two separate adjustable-bandwidth low-pass and high-pass filters in cascade or in parallel. Design examples are included in the paper.     

Boundary operation of 2-D nonseparable linear-phase paraunitary filter banks

This paper proposes a boundary operation technique of 2-D nonseparable linear-phase paraunitary filter banks (NS-LPPUFBs) for size limitation. The proposed technique is based on a lattice structure consisting of the 2-D separable block discrete cosine transform and nonseparable support-extension processes. The bases are allowed to be anisotropic with the fixed critically subsampling, overlapping, orthogonal, symmetric, real-valued, and compact-support properties. First, the blockwise implementation is developed so that the basis images can be locally controlled. The local control of basis images is shown to maintain orthogonality. This property leads a basis termination (BT) technique as a boundary operation. The technique overcomes the drawback of NS-LPPUFBs that the popular symmetric extension method is invalid. Through some experimental results of diagonal texture coding, the significance of the BT is verified.     

Derivative-controlled design of linear-phase FIR filters via waveform moments

A new method for designing linear-phase finite impulse response (FIR) filters is proposed by using the blockwise waveform moments. The proposed method yields linear-phase FIR filters whose magnitude response and its derivatives to a certain order take the prescribed values at equally spaced frequency points. The design procedure only needs to solve a system of linear equations, whose size is slightly smaller than the degree of the resulting filter. In addition, the inversion of the linear equations can be essentially precomputed. Therefore, the proposed design method is computationally efficient. In particular, for some important cases, i.e., the maximally flat R-regular L/sup th/-band FIR filters, a closed-form formula can be obtained. It is also shown that the resulting R-regular L/sup th/-band FIR filters have the zero intersymbol interference property.     

Efficient interpolators and filter banks using multiplier blocks

We examine the use of efficient shift-and-add multiplier structures and multiplier blocks to reduce computational complexity in filter banks. This is more efficient than treating each bank filter separately. We also examine the Farrow (see Proc. Int. Symp. Circuits Syst. (ISCAS), p. 2641-2645) structure, which is used in interpolators. Applying multiplier blocks makes this structure cheaper than the more recognized Lagrange interpolator     

FIR filter banks for hexagonal data processing

Images are conventionally sampled on a rectangular lattice. Thus, traditional image processing is carried out on the rectangular lattice. The hexagonal lattice was proposed more than four decades ago as an alternative method for sampling. Compared with the rectangular lattice, the hexagonal lattice has certain advantages which include that it needs less sampling points; it has better consistent connectivity and higher symmetry; the hexagonal structure is also pertinent to the vision process. In this paper, we investigate the construction of symmetric FIR hexagonal filter banks for multiresolution hexagonal image processing. We obtain block structures of FIR hexagonal filter banks with 3-fold rotational symmetry and 3-fold axial symmetry. These block structures yield families of orthogonal and biorthogonal FIR hexagonal filter banks with 3-fold rotational symmetry and 3-fold axial symmetry. In this paper, we also discuss the construction of orthogonal and biorthogonal FIR filter banks with scaling functions and wavelets having optimal smoothness. In addition, we present a few of such orthogonal and biorthogonal FIR filters banks.     

Subspace approach for the design of cosine-modulated filter bankswith linear-phase prototype filter

A method for designing perfect reconstruction (PR) prototypes for paraunitary cosine-modulated filter banks is presented. The design procedure is based on a subspace approach that allows linear combinations of even-length linear-phase PR prototype filters in such a way that the resulting filter is also a linear-phase PR prototype. Within a given subspace, the weights of the optimal linear combination can easily be computed via an eigenanalysis. The filter design is carried out iteratively while the PR property is guaranteed throughout the design process. No nonlinear optimization routine is needed. As a special case, the proposed approach allows the design of discrete-coefficient prototypes, which are of great interest for efficient hardware implementations     

Two-dimensional perfect reconstruction FIR filter banks withtriangular supports

We present a theory and design of two-dimensional (2-D) perfect reconstruction (PR) filter banks (FBs) (PRFBs) in which the supports of the analysis and synthesis filters consist of two triangulars. The two-triangular FB can be realized by designing an appropriate 2-D complex prototype whose passband support is a triangle that is a half of a parallelepiped-shaped passband support defined by the sampling matrix. Then a complex prototype filter is modulated by the DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB satisfies the condition of permissibility. A necessary and sufficient condition for 2-D PRFBs is derived. Moreover, we present a design method of the 2-D PRFB that minimizes the cost function consisting of the frequency constraint and PR condition. Finally, a design example is presented to confirm the validity of the proposed method     

On Chebyshev design of linear-phase FIR filters with frequency inequality constraints

The alternation theorem is the basis of the Remez algorithm for unconstrained Chebyshev design of finite-impulse response (FIR) filters. In this paper, we extend the alternation theorem to the inequality-constrained case and present an improved Remez algorithm for the design of minimax FIR filters with inequality constraints in frequency domain. Compared with existing algorithms, the presented algorithm has faster convergence rate and guaranteed optimal solutions.     

On the design and realization of a class of uniform single rate FIR DFT filter banks

In this paper we present a computationally efficient realization of single rate uniform FIR filter banks for audio and spectral analysis applications. The channel filters in the analysis bank are represented as modulated versions of a prototype narrowband lowpass FIR filter. Using the IFIR filter design technique [23], [24], this prototype lowpass filter can be designed very efficiently as a cascade of two subfilters. The IFIR filter design is extended for the two-branch realization of uniform filter banks with overlapping channels. A generalized structure is presented which can be used for bothodd andeven stacking arrangements of the channels. The shaping filter structures for the two branches are realized from a single delay line and a single set of filter coefficients, thus conserving the total number of multipliers and delays in the overall realization. The postfilter structure, in conjunction with the Generalized DFT matrices, performs the channel selection. The Generalized DFT matrices are used to provide the necessary modulation for the postfilter coefficients so that the appropriate passbands are selected for each channel of the analysis bank. This leads to a polyphase network realization of the postfilter structure. We derive conditions so that the original input signal can be exactly reconstructed from the channel signals.This work was supported in part by the National Science Foundation under Grant MIP 85-08017 and in part by a University of California MICRO Grant with matching support from the Rockwell Corporation and the Intel Corporation.     

A new algorithm for linear-phase paraunitary filter banks with pairwise mirror-image frequency responses

Subband filter banks have attracted much attention during the past few years. In this paper, an efficient design algorithm, which leads to linear-phase paraunitary filter banks with pairwise mirror-image frequency responses, is revisited and further studied. New lattice structures are presented to extend the algorithm to the case where the number (M) of channels is odd. Design examples of filter banks with 3 and 5 channels are presented.     

Cosine-modulated FIR filter banks with linear phase and paraunitaryproperties

A new class of cosine-modulated FIR filter banks is proposed. The necessary and sufficient condition is given which ensures that the filter banks satisfy the paraunitary and linear phase properties simultaneously. The prototype filter can be designed by optimising its stopband energy on the two-channel lattice parameters, and the filter banks can be implemented efficiently using DCT and DST