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

Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications

IIR Wavelet Filter Banks for ECG Signal Denoising

ElectroCardioGram (ECG) signals are widely used for diagnostic purposes. However, it is well known that these recordings are usually corrupted with different type of noise/artifacts which might lead to misdiagnosis of the patient. This paper presents the design and novel use of Infinite Impulse Response (IIR) filter based Discrete Wavelet Transform (DWT) for ECG denoising that can be employed in ambulatory health monitoring applications. The proposed system is evaluated and compared in terms of denoising performance as well as the computational complexity with the conventional Finite Impulse Response (FIR) based DWT systems. For this purpose, raw ECG data from MIT-BIH arrhythmia database are contaminated with synthetic noise and denoised with the aforementioned filter banks. The results from 100 Monte Carlo simulations demonstrated that the proposed filter banks provide better denoising performance with fewer arithmetic operations than those reported in the open literature

Hybrid IIR/FIR Wavelet Filter Banks for ECG Signal Denoising

ElectroCardioGram (ECG) signals are usually corrupted with various types of artifacts which degrade the signal quality and might lead to misdiagnosis. The wavelet denoising technique is widely studied in the artifact removal literature which employs conventional Finite Impulse Response (FIR) wavelet filter banks for decomposing, thresholding and reconstructing the noisy signal to obtain high fidelity and clean ECG signal. However, the use of high order FIR wavelet filters increases the hardware complexity and cost of the system. This paper presents novel hybrid Infinite Impulse Response (IIR)/FIR Discrete Wavelet Transform (DWT) filter banks that can be employed in ambulatory health monitoring applications for denoising purposes. The proposed systems are evaluated and compared to the conventional FIR based DWT systems in terms of the computational complexity as well as the denoising performance. The results from 100 Monte Carlo simulations demonstrated that the proposed filter banks provide better denoising performance with fewer arithmetic operations than those reported in the open literature

Designing two-channel causal stable IIR PR filter banks and wavelet bases by model order reduction and constrained optimization

In this paper, two methods for designing two-channel causal stable IIR PR filter banks are introduced. The first method makes use of model reduction and constrained optimization to obtain a causal stable IIR filter bank from the structural PR FIR filter bank proposed in [2]. It yields better frequency characteristics than the original FIR filter bank and avoids the dump at π/2 when allpass filters are used. Using the 1-D to 2-D transformation proposed in [2], two dimensional PR IIR filter bank can readily be obtained from these prototypes. The second method is based on constrained optimization technique using the general PR condition. Using this technique, filter banks with low system delay and flexible frequency characteristics can be designed. The technique can also be modified to design causal stable IIR dyadic wavelet bases with added regularity conditions. A number of design examples are used to demonstrate the usefulness of the proposed design methods.published_or_final_versio

Construction of M - Band bandlimited wavelets for orthogonal decomposition

While bandlimited wavelets and associated IIR filters have shown serious potential in areas of pattern recognition and communications, the dyadic Meyer wavelet is the only known approach to construct bandlimited orthogonal decomposition. The sine scaling function and wavelet are a special case of the Meyer. Previous works have proposed a M - Band extension of the Meyer wavelet without solving the problem. One key contribution of this thesis is the derivation of the correct bandlimits for the scaling function and wavelets to guarantee an orthogonal basis. In addition, the actual construction of the wavelets based upon these bandlimits is developed. A composite wavelet will be derived based on the M scale relationships from which we will extract the wavelet functions. A proper solution to this task is proposed which will generate associated filters with the knowledge of the scaling function and the constraints for Mband orthogonality

Efficient design of a class of multiplier-less perfect reconstruction two-channel filter banks and wavelets with prescribed output accuracy

The 11th IEEE Signal Processing Workshop on Statistical Signal Processing, Singapore, 6-8 August 2001This paper proposes a novel algorithm for the design and hardware reduction of a class of multiplier-less two-channel PR filter banks (FBs) using sum-of-powers-of-two (SOPOT) coefficient. It minimizes a more realistic hardware cost, such as adder cells, subject to a prescribe output accuracy taking into account of the rounding and overflow effects, instead of using just the SOPOT terms as in conventional method. Furthermore, by implementing the filters in the FBs using multiplier-block (MB), significant overall saving in hardware resources can be achieved. An effective random search algorithm is also proposed to solve the design problem, which is also applicable to PR IIR FBs with highly nonlinear objective functions.published_or_final_versio