Zoran Cvetkovic

Oversampled filter banks

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIR and give a parameterization of a class of filter banks satisfying this property. Then, we focus on non-subsampled filter banks. Non-subsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.

Nonuniform oversampled filter banks for audio signal processing

In emerging audio technology applications, there is a need for decompositions of audio signals into oversampled subband components with time-frequency resolution which mimics that of the cochlear filter bank and with high aliasing attenuation in each of the subbands independently, rather than aliasing cancellation properties. We present a design of nearly perfect reconstruction nonuniform oversampled filter banks which implement signal decompositions of this kind.

Resolution enhancement of images using wavelet transform extrema extrapolation

One problem of image interpolation refers to magnifying a small image without loss in image clarity. We propose a wavelet based method which estimates the higher resolution information needed to sharpen the image. This method extrapolates the wavelet transform of the higher resolution based on the evolution of the wavelet transform extrema across the scales. By identifying three constraints that the higher resolution information needs to obey, we enhance the reconstructed image through alternating projections onto the sets defined by these constraints.

Tight Weyl-Heisenberg frames in l/sup 2/(Z)

Tight Weyl-Heisenberg frames in l/sup 2/(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl-Heisenberg frames in l/sup 2/(Z) with arbitrary rational oversampling ratios. This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.

Discrete-time wavelet extrema representation: design and consistent reconstruction

The paper studies wavelet transform extrema and zero-crossings representations within the framework of convex representations in /spl Lscr/(Z). Wavelet zero-crossings representation of two-dimensional signals is introduced as a convex multiscale edge representation as well. One appealing property of convex representations is that the reconstruction problem can be solved, at least theoretically, using the method of alternating projections onto convex sets. It turns out that in the case of the wavelet extrema and wavelet zero-crossings representations this method yields simple and practical reconstruction algorithms. Nonsubsampled filter banks that implement the wavelet transform for the two representations are also studied in the paper. Relevant classes of nonsubsampled perfect reconstruction FIR filter banks are characterized. This characterization gives a broad class of wavelets for the representations which are derived from those of the filter banks which satisfy a regularity condition. >

New fast recursive algorithms for the computation of discrete cosine and sine transforms

Fast recursive algorithms for the computation of the discrete cosine and sine transforms are developed. An N-point discrete cosine transform (DCT) or discrete sine transform (DST) can be computed from two N/2-point DCTs or DSTs. Compared to the existing algorithms the algorithms have less multiplications by two, and add operations are better positioned, giving rise to faster computation and easier VLSI implementation. >

Locally adaptive wavelet-based image interpolation

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local smoothness/singularity characteristics. The proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper. Better performance comes at the expense of higher complexity.

Rectification of the EMG is an unnecessary and inappropriate step in the calculation of Corticomuscular coherence

Corticomuscular coherence (CMC) estimation is a frequency domain method used to detect a linear coupling between rhythmic activity recorded from sensorimotor cortex (EEG or MEG) and the electromyogram (EMG) of active muscles. In motor neuroscience, rectification of the surface EMG is a common pre-processing step prior to calculating CMC, intended to maximize information about action potential timing, whilst suppressing information relating to motor unit action potential (MUAP) shape. Rectification is believed to produce a general shift in the EMG spectrum towards lower frequencies, including those around the mean motor unit discharge rate. However, there are no published data to support the claim that EMG rectification enhances the detection of CMC. Furthermore, performing coherence analysis after the non-linear procedure of rectification, which results in a significant distortion of the EMG spectrum, is considered fundamentally flawed in engineering and digital signal processing. We calculated CMC between sensorimotor cortex EEG and EMG of two hand muscles during a key grip task in 14 healthy subjects. CMC calculated using unrectified and rectified EMG was compared. The use of rectified EMG did not enhance the detection of CMC, nor was there any evidence that MUAP shape information had an adverse effect on the CMC estimation. EMG rectification had inconsistent effects on the power and coherence spectra and obscured the detection of CMC in some cases. We also provide a comprehensive theoretical analysis, which, along with our empirical data, demonstrates that rectification is neither necessary nor appropriate in the calculation of CMC.

Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate

A scheme for simple oversampled analog-to-digital (A/D) conversion using single-bit quantization is presented. The scheme is based on recording positions of zero-crossings of the input signal added to a deterministic dither function. This information can be represented in a manner such that the bit rate increases only logarithmically with the oversampling factor r. The input band-limited signal can be reconstructed from this information locally with O(1/r) pointwise error, resulting in an exponentially decaying distortion-rate characteristic. In the course of studying the accuracy of the proposed A/D conversion scheme, some new results are established about reconstruction of band-limited signals from irregular samples using linear combination of functions with fast decay. Schemes for local interpolation of band-limited signals from quantized irregular samples are also proposed.

Resilience properties of redundant expansions under additive noise and quantization

Representing signals using coarsely quantized coefficients of redundant expansions is an interesting source coding paradigm, the most important practical case of which is oversampled analog-to-digital (A/D) conversion. Signal reconstruction from quantized redundant expansions and the accuracy of such representations are problems which are not well understood and we study them in this paper for uniform scalar quantization in finite-dimensional spaces. To give a more global perspective, we first present an analysis of the resilience of redundant expansions to degradation by additive noise in general, and then focus on the effects of uniform scalar quantization. The accuracy of signal representations obtained by applying uniform scalar quantization to coefficients of redundant expansions, measured as the mean-squared Euclidean norm of the reconstruction error, has been previously shown to be lower-bounded by an 1/r/sup 2/ expression. We establish some general conditions under which the 1/r/sup 2/ accuracy can actually be attained, and under those conditions prove a 1/r/sup 2/ upper error bound. For a particular kind of structured expansions, which includes many popular frame classes, we propose reconstruction algorithms which attain the 1/r/sup 2/ accuracy at low numerical complexity. These structured expansions, moreover, facilitate efficient encoding of quantized coefficients in a manner which requires only a logarithmic bit-rate increase in redundancy, resulting in an exponential error decay in the bit rate. Results presented in this paper are immediately applicable to oversampled A/D conversion of periodic bandlimited signals.