In this paper, essential features of the recently introduced modified discrete Fourier transform DFT (MDFT) filter bank are presented. First, it is shown that all analysis and synthesis filters-obtained by appropriate complex modulation of a low-pass prototype filter-are linear phase. This is important for subband image coding applications. Another important property is the structure-inherent alias cancellation: all odd alias spectra are automatically compensated in the synthesis filter bank. Further, the MDFT filter bank provides perfect reconstruction for the same prototypes as for cosine-modulated filter banks. Thus, the same design methods can be used. Finally, different mappings of the input signal into the subbands are discussed and a comparison to the well-known cosine-modulated filter banks is given.

Modified DFT filter banks with perfect reconstruction

This paper investigates the theory and structure of a large subclass of M-channel linear-phase perfect-reconstruction FIR filter banks-systems with analysis and synthesis filters of length L/sub i/=K/sub i/M+/spl beta/, where /spl beta/ is an arbitrary integer, 0/spl les//spl beta/<M, and K/sub i/ is any positive integer. For this subclass of systems, we first investigate the necessary conditions for the existence of linear-phase perfect-reconstruction filter banks (LPPRFBs). Next, we develop a complete and minimal factorization for all even-channel linear-phase paraunitary systems (the most general lapped orthogonal transforms to date). Finally, several design examples as well as comparisons with previous generalized lapped orthogonal transforms (GenLOTs) in image compression are presented to confirm the validity of the theory.

http://thanglong.ece.jhu.edu/Tran/Pub/lpprfb.pdf

On M-channel linear phase FIR filter banks and application in image compression

An image encoder for encoding the image data so as to make the image quality of a selected area better than that of the other areas without increasing the amount of data is disclosed. The encoder comprises an area selecting section for selecting a specific area in an image, an area position and shape encoding section for encoding the position and shape of the selected area, a coding parameter adjusting section for adjusting various parameters used to control the image quality and the amount of data in encoding a dynamic image and performing control so that the image quality of the area is encoded more preferably than the image quality of the other areas, a parameter encoding section for encoding the above parameters, a dynamic image encoding section for encoding input dynamic-image data by using the above various parameters, and an encoded data integrating section for combining encoded data by the area position and shape encoding section, the parameter encoding section and the dynamic image encoding section and transmit or store the data. An image decoder applied to the image encoder is also disclosed.

Image encoder and image decoder

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We investigated the theory of wavelet transforms and their relation to Laboratory applications. The investigators have had considerable success in the past applying wavelet techniques to the numerical solution of optimal control problems for distributed-parameter systems, nonlinear signal estimation, and compression of digital imagery and multidimensional data. Wavelet theory involves ideas from the fields of harmonic analysis, numerical linear algebra, digital signal processing, approximation theory, and numerical analysis, and the new computational tools arising from wavelet theory are proving to be ideal for many Laboratory applications. 1. Background And Research Objectives The theory of wavelet transforms is a recent development drawing contributions from a number of different fields, including harmonic analysis, digital signal processing, approximation theory, and numerical analysis. A wavelet transform provides a linear representation of functions in terms of dilates and translates of a suitable basis function-the mother wavelet. The basis vectors are localized spatially by the translation parameter and lie on exponentially scaled intervals in the frequency domain, so wavelet expansions enjoy simultaneous time/frequency localization that is lacking in Fourier expansions, plus an octavescaled frequency resolution that makes them particularly economical for analyzing processes whose spectrum is biased towards lower frequencies, including much high-resolution sensor data. Wavelet expansions also exist for digital signals and are known as discrete wavelet transforms (DWTs). Such transforms are instances of multirate digital filter banks having the special property that, in the infinite sampling rate limit, they converge to a decomposition of the corresponding continuous-time signal in terms of a basis of continuous wavelets. This means that there is a duality for wavelet transforms analogous to the relationship between the Principal investigator, e-mail: vxf@lanl.gov *

웨이블릿 이론과 응용 = Wavelet theory and Its applications

A multirate (MR) filter bank is called size-limited if the total number of output samples equals the number of input samples. A method called symmetric extension improved performance in subband image compression systems compared to the earlier method of circular convolution. However, the symmetric extension method was developed only for two-band uniform filter banks, and required even-length linear phase analysis filters. The authors generalize the symmetric extension method to the M-band, possibly nonuniform filter banks, where M/spl ges/2. The length restriction on the analysis filters is relaxed. >

Generalized symmetric extension for size-limited multirate filter banks

Several methods for applying perfect reconstruction quadrature mirror filter (PR QMF) banks to finite-length signals are described and compared. Although simple periodization produces a transform that does not increase the size of the transformed signal, it has the disadvantage of introducing a jump discontinuity at the signal's boundary. Various methods of transforming smoother extensions are considered and analyzed in terms of their ability to conserve data storage costs and reproduce the signal in a numerically efficient manner. A complete classification of two-channel schemes based on periodizing symmetric (reflected) signal extensions and using linear phase filters is described, for both even- and odd-length signals. More general techniques based on transforming linear signal extrapolations and truncating the resulting subbands to conserve data size are also presented. An example using reflected boundary extension is discussed. >

Reflected boundary conditions for multirate filter banks

A simplified lattice architecture is given for 2-channel perfect reconstruction multirate filter banks when the filters are even-order linear phase FIR filters. This approach provides a factorization procedure for the type-1 polyphase component matrix, E(z), for the analysis filter bank. The architecture used ensures that the perfect reconstruction property is structurally imposed by the mathematical form of the factorization. An application is given to the factorization of the filter bank employed in the FBI's standard for digital coding of fingerprint images, and comparisons are made with previous lattice architectures for even-order linear phase filters. >

A simple lattice architecture for even-order linear phase perfect reconstruction filter banks

We present a simple extension for rational transfer matrices of known results characterizing the invariant factors of causal FIR matrices with FIR inverses. This includes and generalizes previous characterizations of causal FIR multirate filter banks with anticausal FIR inverses, the so-called cafacafi systems. In particular, we extend (to the rational case) the result that G(z) is a square cafacafi system if and only if its determinantal degree is equal to its McMillan degree.

C.M. Brislawn

Papers

Reflected boundary conditions for multirate filter banks

A simple lattice architecture for even-order linear phase perfect reconstruction filter banks

Rational transfer matrices with FIR inverses