Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

In this paper, a new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filterbanks are parameterized by two functions (β(z) and α(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical β(z) and α(z) was considered by Phoong et al. with the delay parameter M chosen as 2N - 1. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase constraint is relaxed, the lengths of β(z) and α(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.published_or_final_versio

New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al. The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods. © 2004 IEEE.published_or_final_versio

Low-delay perfect reconstruction two-channel FIR/IIR filter banks and wavelet bases with SOPOT coefficients

IEEE International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey, 5-9 June 2000In this paper, a new family of two-channel low-delay filter banks and wavelet bases using the PR structure in [3] with SOPOT coefficients are proposed. In particular, the functions alpha(z) and beta(z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay filter banks with flexible lengths, delays, and regularity. Several design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

Low-delay perfect reconstruction two-channel FIR/IIR filter banks and wavelet bases with SOPOT coefficients

IEEE International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey, 5-9 June 2000In this paper, a new family of two-channel low-delay filter banks and wavelet bases using the PR structure in [3] with SOPOT coefficients are proposed. In particular, the functions alpha(z) and beta(z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay filter banks with flexible lengths, delays, and regularity. Several design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio

Multiplier-less low-delay FIR and IIR wavelet filter bank with SOPOT coefficients

In this paper, a new family of multiplier-less two-channel lowdelay wavelet filter banks using the PR structure in [3] and the SOPOT(sum-of-powers-of-two) representation is proposed. In particular, the functions α (z) and β (z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay wavelet bases with flexible length, delay, and number of zero at π (or 0) in their analysis filters. Several design examples are given to demonstrate the usefulness of the proposed method.postprin

New method for designing two-channel causal stable IIR perfect reconstruction filter banks and wavelet bases

A new method for designing two-channel causal stable IIR PR filter banks and wavelet bases is proposed. It is based on the structure previously proposed by Phoong et al. (1995). Such a filter bank is parameterized by two functions α(z) and β(z), which can be chosen as an all-pass function to obtain IIR filterbanks with very high stopband attenuation. One of the problems with this choice is that a bump of about 4 dB always exists near the transition band of the analysis and synthesis filters. The stopband attenuation of the high-pass analysis filter is also 10 dB lower than that of the low-pass filter. By choosing β(z) and α(z) as an all-pass function and a type-II linear-phase finite impulse response (FIR) function, respectively, the bumping can be significantly suppressed. In addition, the stopband attenuation of the high-pass filter can be controlled easily. The design problem is formulated as a polynomial approximation problem and is solved efficiently by the Remez exchange algorithm. The extension of this method to the design of a class of IIR wavelet bases is also considered.published_or_final_versio

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

Multiplier-less low-delay FIR and IIR wavelet filter banks with SOPOT coefficients

In this paper, a new family of multiplier-less two-channel low-delay wavelet filter banks using the PR structure in [3] and the SOPOT(sum-of-powers-of-two) representation is proposed. In particular, the functions α(z) and β(z) in the structure are chosen as nonlinear-phase FIR and IIR filters, and the design of such multiplier-less filter banks is performed using the genetic algorithm. The proposed design method is very simple to use, and is sufficiently general to construct low-delay wavelet bases with flexible length, delay, and number of zero at π (or 0) in their analysis filters. Several design examples are given to demonstrate the usefulness of the proposed method

Design and Implementation of Complexity Reduced Digital Signal Processors for Low Power Biomedical Applications

Wearable health monitoring systems can provide remote care with supervised, inde-pendent living which are capable of signal sensing, acquisition, local processing and transmission. A generic biopotential signal (such as Electrocardiogram (ECG), and Electroencephalogram (EEG)) processing platform consists of four main functional components. The signals acquired by the electrodes are amplified and preconditioned by the (1) Analog-Front-End (AFE) which are then digitized via the (2) Analog-to-Digital Converter (ADC) for further processing. The local digital signal processing is usually handled by a custom designed (3) Digital Signal Processor (DSP) which is responsible for either anyone or combination of signal processing algorithms such as noise detection, noise/artefact removal, feature extraction, classification and compres-sion. The digitally processed data is then transmitted via the (4) transmitter which is renown as the most power hungry block in the complete platform. All the afore-mentioned components of the wearable systems are required to be designed and fitted into an integrated system where the area and the power requirements are stringent. Therefore, hardware complexity and power dissipation of each functional component are crucial aspects while designing and implementing a wearable monitoring platform. The work undertaken focuses on reducing the hardware complexity of a biosignal DSP and presents low hardware complexity solutions that can be employed in the aforemen-tioned wearable platforms. A typical state-of-the-art system utilizes Sigma Delta (Σ∆) ADCs incorporating a Σ∆ modulator and a decimation filter whereas the state-of-the-art decimation filters employ linear phase Finite-Impulse-Response (FIR) filters with high orders that in-crease the hardware complexity [1–5]. In this thesis, the novel use of minimum phase Infinite-Impulse-Response (IIR) decimators is proposed where the hardware complexity is massively reduced compared to the conventional FIR decimators. In addition, the non-linear phase effects of these filters are also investigated since phase non-linearity may distort the time domain representation of the signal being filtered which is un-desirable effect for biopotential signals especially when the fiducial characteristics carry diagnostic importance. In the case of ECG monitoring systems the effect of the IIR filter phase non-linearity is minimal which does not affect the diagnostic accuracy of the signals. The work undertaken also proposes two methods for reducing the hardware complexity of the popular biosignal processing tool, Discrete Wavelet Transform (DWT). General purpose multipliers are known to be hardware and power hungry in terms of the number of addition operations or their underlying building blocks like full adders or half adders required. Higher number of adders leads to an increase in the power consumption which is directly proportional to the clock frequency, supply voltage, switching activity and the resources utilized. A typical Field-Programmable-Gate-Array’s (FPGA) resources are Look-up Tables (LUTs) whereas a custom Digital Signal Processor’s (DSP) are gate-level cells of standard cell libraries that are used to build adders [6]. One of the proposed methods is the replacement of the hardware and power hungry general pur-pose multipliers and the coefficient memories with reconfigurable multiplier blocks that are composed of simple shift-add networks and multiplexers. This method substantially reduces the resource utilization as well as the power consumption of the system. The second proposed method is the design and implementation of the DWT filter banks using IIR filters which employ less number of arithmetic operations compared to the state-of-the-art FIR wavelets. This reduces the hardware complexity of the analysis filter bank of the DWT and can be employed in applications where the reconstruction is not required. However, the synthesis filter bank for the IIR wavelet transform has a higher computational complexity compared to the conventional FIR wavelet synthesis filter banks since re-indexing of the filtered data sequence is required that can only be achieved via the use of extra registers. Therefore, this led to the proposal of a novel design which replaces the complex IIR based synthesis filter banks with FIR fil-ters which are the approximations of the associated IIR filters. Finally, a comparative study is presented where the hybrid IIR/FIR and FIR/FIR wavelet filter banks are de-ployed in a typical noise reduction scenario using the wavelet thresholding techniques. It is concluded that the proposed hybrid IIR/FIR wavelet filter banks provide better denoising performance, reduced computational complexity and power consumption in comparison to their IIR/IIR and FIR/FIR counterparts