Multi-objective approximation of IIR by FIR digital filters

This paper studies the mixed-norm approximation of IIR digital flters by FIR digital flters. Effective methods using LMIs are presented to solve the approximation problem. The effectiveness is demonstrated by examples

Construction of tight filter bank frames

In this paper, we present an explicit and numerically efficient formulae to construct a tight (paraunitary) FB frame from a given un-tight (non-paraunitary) FB frame. The derivation uses the well developed techniques from modern control theory, which results in the unified formulae for generic IIR and FIR FBs. These formulae involve only algebraic matrix manipulations and can be computed efficiently and reliably without the approximation required in the existing literature

Frame-theory-based analysis and design of oversampled filter banks : direct computational method

This paper studies the frames corresponding to oversampled filter banks (FBs). For this class of FB frames, we present a state-space parameterization of perfect reconstruction FB frames and explicit and numerically efficient formulas to compute the tightest frame bounds, to obtain the dual FB frame, and to construct a tight (paraunitary) FB frame from a given untight (nonparaunitary) FB frame. The derivation uses well-developed techniques from modern control theory, which results in the unified formulas for generic infinite-impulse-response (IIR) and finite-impulse-response (FIR) FBs. These formulas involve only algebraic manipulations of real matrices and can be computed efficiently, reliably, and exactly without the approximation required in the existing methods for generic FBs. The results provide a unified framework for frame-theory-based analysis and systematic design of oversampled filter banks

On frames with stable oversampled filter banks

This paper studies the frames corresponding to stable oversampled filter banks (FBs). For this class of frames, we present explicit and numerically efficient formulae to compute the tightest frame bounds, to obtain the dual frame and to construct a paraunitary FB for a given non-paraunitary FB. The derivation uses the well developed techniques from modern control theory, which results in the formulae that involve only algebraic matrix manipulation and can be performed efficiently and reliably without the approximation required in the existing methods

Improving frame-bound-ratio for frames generated by oversampled filter banks

This paper presents a simple method to improve the frame-bounds-ratio of perfect reconstruction (PR) oversampled filter banks (FBs) by adjusting the gain of each subband filter. For a given analysis PRFB, a finite convex optimization algorithm is presented to redesign the subband gains such that the frame-bounds-ratio of the FB is minimized.The algorithm also provides an effective way to compute the frame bounds. Examples show the effectiveness of the presented method

Bound ratio minimization of filter bank frames

This paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction (PR) filter banks (FBs). For a given analysis PRFB, a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel. The redesign minimizes the frame bound ratio of the FB while maintaining its original properties and performance. The obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing. The optimal solution is applied to subband noise suppression and tree structured FB gain optimization, resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement. Effectiveness of the optimal solution is demonstrated by extensive numerical examples

Noise reduction design of perfect reconstruction oversampled filter banks

This paper studies the noise reduction design problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former method caters for the noise with known power spectral density (PSD) and the latter one for the noise with unknown PSD. Explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs

Optimal noise reduction in oversampled PR filter banks

This paper studies the optimal noise reduction problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD) and the latter for the noise with unknown PSD. State-space based explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs, and the relations between different cases are analyzed and revealed. Extensive numerical examples are provided to illustrate the proposed design methods and to show their effectivenes

Efficient computation of frame bounds using LMI-based optimization

This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method

From IIR to FIR digital MIMO models : a constructive Hankel norm approximation method

This paper presents a constructive method to (sub)optimal finite impulse response (FIR) approximation of a given infinite impulse response (IIR) MIMO model. The method minimizes the Hankel norm of approximation error by using the explicit solution of norm-preserve dilation problem. It has the advantage over the existing methods that it provides an explicitly constructive solution and allows the trade-off between the Chebyshev and least square criteria. The lower and upper bounds on the H2 and H∞ norms of approximation error are given. The algorithm for approximating non-causal IIR filters by causal FIR filters is also formulated and solved. The effectiveness and properties of the proposed algorithm are demonstrated through two examples