Theory Of Multirate Filter Banks Research Articles

Analysis of Signals via Non-Maximally Decimated Non-Uniform Filter Banks

This paper addresses the important problem of reconstructing a signal from multiple multirate observations. The observations are modeled as the output of an analysis bank, and time-domain analysis is carried out to design an optimal FIR synthesis bank. We pose this as a minimizing the mean-square problem and prove that at least one optimal solution is always possible. A parametric form for all optimal solutions is obtained for a non-maximally decimated filter bank. The necessary and sufficient conditions for an optimal solution, that results in perfect reconstruction (PR), are derived as time-domain pseudocirculant conditions. This represents a novel theoretical contribution in multirate filter bank theory. We explore PR in a more general setting. This results in the ability to design a synthesis bank with a particular delay in the reconstruction. Using this delay, one can achieve PR in cases where it might not have been possible otherwise. Further, we extend the design and analysis to non-uniform filter banks and carry out simulations to verify the derived results.

Optoelectronic image scanning with high spatial resolution and reconstruction fidelity

In imaging systems the detector arrays deliver at the output time-discrete signals, where the spatial frequencies of the object scene are mapped into the electrical signal frequencies. Since the spatial frequency spectrum cannot be bandlimited by the front optics, the usual detector arrays perform a spatial undersampling and as a consequence aliasing occurs. A means to partially suppress the backfolded alias band is bandwidth limitation in the reconstruction low-pass, at the price of resolution loss. By utilizing a bilinear detector array in a pushbroom-type scanner, undersampling and aliasing can be overcome. For modeling the perception, the theory of discrete systems and multirate digital filter banks is applied, where aliasing cancellation and perfect reconstruction play an important role. The discrete transfer function of a bilinear array can be imbedded into the scheme of a second-order filter bank. The detector arrays already build the analysis bank and the overall filter bank is completed with the synthesis bank, for which stabilized inverse filters are proposed, to compensate for the low-pass characteristics and to approximate perfect reconstruction. The synthesis filter branch can be realized in a so-called ‘‘direct form,’’ or the ‘‘polyphase form,’’ where the latter is an expenditure-optimal solution, which gives advantages when implemented in a signal processor. This paper attempts to introduce well-established concepts of the theory of multirate filter banks into the analysis of scanning imagers, which is applicable in a much broader sense than for the problems addressed here. To the author’s knowledge this is also a novelty.

New precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal FIR equalizers

In this paper, we propose a new precoding method for intersymbol interference (ISI) cancellation by using non-maximally decimated multirate filterbanks. Unlike the existing preceding methods, such as the TH and trellis precodings, the new preceding (i) may be independent of the ISI channel; (ii) is linear and does not have to implement any modulo operation; (iii) gives the ideal FIR equalization at the receiver for any FIR ISI channel including spectral-null channels; (iv) expands the transmission bandwidth in a minimum amount. The precoding is built on non-maximally decimated multirate filterbanks. Based on multirate filterbank theory, we present a necessary and sufficient condition on an FIR ISI transfer function in terms of its zero set such that there is a linear FIR N/spl times/M precoder so that an ideal FIR equalizer exists, where the integers K and N are arbitrarily fixed. The condition is easy to check. As a consequence of the condition, for any given FIR ISI transfer function (not identically 0), there always exist such linear FIR precoders. Moreover, for almost all given FIR ISI transfer functions, there exist linear FIR precoders with size N/spl times/(N-1), i,e., the bandwidth is expanded by 1/N. In addition to the conditions on the ISI transfer functions, a method for the design of the linear FIR precoders and the ideal FIR equalizers is also given. Numerical examples are presented to illustrate the theory.

Hierarchical transform and subband coding of video signals

The new coding scheme introduced here allows the coding of different resolution video signals. The coding is performed in a way that makes it possible to decode either the whole or only some parts of the transmitted format. Transform and subband coding methods are considered. Transform coding is described in the light of the multirate filter bank theory. Coding systems of increasing efficiency are studied. The case of pure intra coding is quite easy to handle. More efficient systems include a temporal predictor. Some emphasis will be put on those systems and especially on motion compensated schemes. The method proposed in this paper is the coding of the subbands using for prediction only the information of the same subbands or of the bands of lower order in the previous decoded picture.

A theory of multirate filter banks

Multirate filter banks produce multiple output signals by filtering and subsampling a single input signal, or conversely, generate a single output by upsampling and interpolating multiple inputs. Two of their main applications are subband coders for speech processing and transmultiplexers for telecommunications. Below, we derive a theoretical framework for the analysis, synthesis, and computational complexity of multirate filter banks. The use of matrix notation leads to basic results derived from properties of linear algebra. Using rank and determinant of filter matrices, it is shown how to obtain aliasing/ crosstalk-free reconstruction, and when perfect reconstruction is possible. The synthesis of filters for filter banks is also explored, three design methods are presented, and finally, the computational complexity is considered.