Multirate Signal Processing

Architecture and circuit design are the two most e ective means of reducing power in CMOS VLSI. This paper presents an application of formal mathematics to create a power e cient architecture of an FFT implemented in asynchronous circuit technology that achieves signi cant power reduction over other FFT architectures. Multirate signal processing concepts are applied to the FFT to localize communication and remove the need for globally shared results in the FFT computation. A novel architecture is produced from the polyphase components that is mapped to an asynchronous architecture. The asynchronous design continues the localization of communication and can be mapped to standard cell libraries such as radiation-hardened libraries for space electronics. We present a methodology based on multirate signal processing techniques and asynchronous design style that supports signi cant reduction in power over conventional design practices.

In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discretetime signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q = 1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained.

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition-and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the lowresolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.

General single-channel, multirate optimal filtering problem. Note that the estimate and observation signals may be at different rates.. .. .. 4.4 An illustration of ordinary causal FIR Wiener filtering and the relationship between samples of sequencesd[n] and x[n], P = 3.. .. .. . 4.5 An illustration of single-channel, multirate causal FIR Wiener filtering and the relationship between samples of sequencesd[n] and x[m], P = 2.

In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discretetime signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q = 1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained.

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition-and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the lowresolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.

In this letter, a new set of speech feature parameters based on multirate signal processing and the Teager energy operator is introduced. The speech signal is first divided into nonuniform subbands in mel-scale using a multirate filterbank, then the Teager energies of the subsignals are estimated. Finally, the feature vector is constructed by log-compression and inverse discrete cosine transform (DCT) computation. The new feature parameters have robust speech recognition performance in the presence of car engine noise.

Signal decimation aimed at optimal spectral packing has a variety of applications in areas ranging from array processing to image processing. In this article we propose and discuss a new method for determining decimation grid and prefilter that best fit the spectral extension of any 2D signal defined on an arbitrary sampling lattice. The method has been implemented and tested on digital images in order to evaluate quality degradation due to optimal spectral truncation.

It is well known that the frequency sampling approach to the design of Finite Impulse Response digital filters allows recursive implementations which are computationally efficient when most of the frequency samples are integers, powers of 2 or nulls. The design and implementation of decimation (or interpolation) filters using this approach is studied herein. Firstly, a procedure is described which optimizes the tradeoff between the stopband energy and the deviation of the passband from the ideal filter. The search space is limited to a small number of samples (in the transition band), imposing the condition that the resulting filter have a large number of zeroes in the stopband. Secondly, three different structures to implement the decimation (or interpolation) filter are proposed. The implementation complexity, i.e. the number of multiplications and additions per input sample, are derived for each structure. The results shown that, without taking into account finite word-length effects, the most efficient implementation depends on the filter length to decimation (or interpolation) ratio.

It is well known that the frequency sampling approach to the design of Finite Impulse Response digital filters allows recursive implementations which are computationally efficient when most of the frequency samples are integers, powers of 2 or nulls. The design and implementation of decimation (or interpolation) filters using this approach is studied herein. Firstly, a procedure is described which optimizes the tradeoff between the stopband energy and the deviation of the passband from the ideal filter. The search space is limited to a small number of samples (in the transition band), imposing the condition that the resulting filter have a large number of zeroes in the stopband. Secondly, three different structures to implement the decimation (or interpolation) filter are proposed. The implementation complexity, i.e. the number of multiplications and additions per input sample, are derived for each structure. The results shown that, without taking into account finite word-length effects, the most efficient implementation depends on the filter length to decimation (or interpolation) ratio.

In many imaging applications, including sensor arrays, MRI and CT,data is often sampled on non-rectangular point sets with non-uniform density. Moreover, in image and video processing, a mix of non-rectangular sampling structures naturally arise. Multirate processing typically utilizes a normalized integer indexing scheme, which masks the true physical dimensions of the points. However, the spatial correlation of such signals often contains important information.This paper presents a theory of signals defined on regular discrete sets called lattices, and presents an associated form of a finite Fourier transform denoted here as multiresolution lattice discrete Fourier transform (MRL-DFT). Multirate processing techniques such as decimation, interpolation and polyphase representations are presented in a context which preserves the true spatial dimensions of the sampling structure.Moreover, the polyphase formulation enables systematic representation and processing for sampling patterns with variable spatial density, and provides a framework for developing generalized FFT and regridding algorithms.

ABSTRACT Signal decimation aimed at optimal spectral packing has a variety of applications in areas ranging from array processing to image processing. In this article we propose and discuss a new method for determining decimation grid and prefilter that best fit the spectral extension of any 2D signal defined on an arbitrary sampling lattice. The method has been implemented and tested on digital images in order to evaluate quality degradation due to optimal spectral truncation.