Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter

This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a functional inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods

Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs

An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith

Design of near allpass strictly stable minimal phase real valued rational IIR filters

In this brief, a near-allpass strictly stable minimal-phase real-valued rational infinite-impulse response filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic functional inequality constraints. To solve this problem, the nonsmooth cost function is first approximated by a smooth function, and then our previous proposed method is employed for solving the problem. Computer numerical simulation result shows that the designed filter satisfies all functional inequality constraints and achieves a small maximum absolute phase error

Linear phase paraunitary filter banks: theory, factorizations and designs

M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. In this paper, we study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. We begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, we develop a minimal factorizdion for a large class of such systems. This factorization will be proved to be complete for even M. Further, we structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. We then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory

The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks

We introduce a new approach to design FIR energy compaction filters of arbitrary order N. The optimization of such filters is important due to their close connection to the design of an M-channel orthonormal filter bank adapted to the input signal statistics. The novel procedure finds the optimum product filter Fopt(Z)=H opt(Z)Hopt(Z^-1) corresponding to the compaction filter Hopt(z). The idea is to express F(z) as D(z)+D(z^-1) and reformulate the compaction problem in terms of the state space realization of the causal function D(z). For a fixed input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum due to the convexity of the new formulation. The new design method can be solved quite efficiently and with great accuracy using recently developed interior point methods and is extremely general in the sense that it works for any chosen M and any arbitrary filter length N. Finally, obtaining Hopt(z) from F opt(z) does not require an additional spectral factorization step. The minimum phase spectral factor can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z)

Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming

This paper considers an optimum nonuniform FIR transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique and the local solution is a global minimum

Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property

Based on the concept of losslessness in digital filter structures, this paper derives a general class of maximally decimated M-channel quadrature mirror filter banks that lead to perfect reconstruction. The perfect-reconstruction property guarantees that the reconstructed signalhat{x} (n)is a delayed version of the input signal x (n), i.e.,hat{x} (n) = x (n - n_{0}). It is shown that such a property can be satisfied if the alias component matrix (AC matrix for short) is unitary on the unit circle of the z plane. The number of channels M is arbitrary, and when M is two, the results reduce to certain recently reported 2-channel perfect-reconstruction QMF structures. A procedure, based on recently reported FIR cascaded-lattice structures, is presented for optimal design of such FIR M-channel filter banks. Design examples are included

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters