A new cost function based on multi-band decomposition of the estimation error and application of a different step-size for each band is used in connection with the least-mean-square criterion to improve the fidelity of estimates as compared to those obtained with conventional least-mean-square adaptive algorithms. The basic new idea is to trade off time and frequency resolutions of the adaptive algorithm along the frequency domain by using different step-sizes in the analysis of distinct frequencies in accordance with the frequency-localized statistical behavior of the imput signal. The mathematical background for a stochatic approach to the multi-band decomposition-based scheme is presented and algorithms with fixed and variable step-sizes are derived. Computer experiments compare the performance of multiband and conventional least-mean-square methods when applied to system identification.

In this paper, we present a novel way to design biorthogonal and paraunitary linear phase filter banks. The square error of the perfect reconstruction of the filter bank is expressed in quadratic form of filter coefficients and the cost function is minimized by solving linear equation iteratively without nonlinear optimization. With some modifications, this method is extended to the design of paraunitary filter banks. Furthermore, the lattice structure of odd-channel paraunitary filter banks is also derived. Design examples are given to validate the proposed method.

A new structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is introduced and the mathematical background for the soulution of the related adaptive filtering problem is derived. The presented structure gives rise to AR spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Adaptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS alogorithms. Also, computer experiments comparing the performance of conventional and the proposed multi-band methods are depicted and discussed.

In this work, a new structure of M-channel linear-phase paraunitary filter banks is proposed, where M is even. Our proposed structure can be regarded as a modification of the conventional generalized linear-phase lapped orthogonal transforms (GenLOT) based on the discrete cosine transform (DCT). The main purpose of this work is to overcome the limitation of the conventional DCT-based GenLOT, and improve the performance of the fast implementation. It is shown that our proposed fast GenLOT is superior to that of the conventional technique in terms of the coding gain. This work also provides a recursive initialization design procedure so as to avoid insignificant local-minimum solutions in the non-linear optimization processes. In order to verify the significance of our proposed method, several design examples are given. Furthermore, it is shown that the fast implementation can be used to construct M-band linear-phase orthonormal wavelets with regularity.

The purpose of this paper is to provide a practical tool for performing a shift operation in orthonormal compactly supported wavelet bases. This translation τ of a discrete sequence, where τ is a real number, is suitable for filter bank implementations. The shift operation in this realization is neither related to the analysis filters nor to the synthesis filters of the filter bank. Simulations were done on the Daubechis wavelets with 12 coefficients and on complex valued wavelets. For the latter ones a real input sequence was used and split up into two subsequences in order to gain computational efficiency.

A systematic theory of the optimum multi-path interpolation using parallel filter banks is presented with respect to a family of n-dimensional signals which are not necessarily band-limited. In the first phase, we present the optimum spacelimited interpolation functions minimizing simultaneously the wide variety of measures of error defined independently in each separate range in the space variable domain, such as 8 8 pixels, for example. Although the quantization of the decimated sample values in each path is contained in this discussion, the resultant interpolation functions possess the optimum property stated above. In the second phase, we will consider the optimum approximation such that no restriction is imposed on the supports of interpolation functions. The Fourier transforms of the interpolation functions can be obtained as the solutions of the finite number of linear equations. For a family of signals not being band-limited, in general, this approximation satisfies beautiful orthogonal relation and minimizes various measures of error simultaneously including many types of measures of error defined in the frequency domain. These results can be extended to the discrete signal processing. In this case, when the rate of the decimation is in the state of critical-sampling or over-sampling and the analysis filters satisfy the condition of paraunitary, the results in the first phase are classified as follows: (1) If the supports of the interpolation functions are narrow and the approximation error necessarily exists, the presented interpolation functions realize the optimum approximation in the first phase. (2) If these supports become wide, in due course, the presented approximation satisfies perfect reconstruction at the given discrete points and realizes the optimum approximation given in the first phase at the intermediate points of the initial discrete points. (3) If the supports become wider, the statements in (2) are still valid but the measure of the approximation error in the first phase at the intermediate points becomes smaller. (4) Finally, those interpolation functions approach to the results in the second phase without destroying the property of perfect reconstruction at the initial discrete points.

It is known that the resolution conversion based on orthogonal transform has a problem that is difference of luminance between the converted image and the original. In this paper, the scale factor of the system employing various orthogonal transforms is generally formulated by considering the DC gain, and the condition of alias free for DC component is indicated. If the condition is satisfied, then the scale factor is determined by only the basis functions.

A new type of analog-to-digital (A/D) converter is introduced. The structure is based on a magnitude-preserving quadrature mirror filter (QMF) bank where the analysis bank is composed on IIR switched-capacitor (SC) filters. The analog output samples of the analysis filters are converted into digital form using individual A/D converters and combined by an IIR digital filter synthesis filter bank. This A/D converter is useful in applications where only the magnitude of the spectrum of the analog signal needs to be preserved. The structure incorporates the advantages of sub-band coding and reduces considerably the effect of mismatches among the sub-band A/D converters. In addition, the proposed scheme leads to an increase in the conversion speed by a factor of M when an M-channel QMF bank is used. An illustrative example verifying the good performance of the proposed approach is included.

One of the problems with subband image coding is the increase in image sizes caused by filtering. To solve this, it has been proposed to process the filtering by transforming input sequence into a periodic one. Then filtering is implemented by circular convolution. Although this technique solves the problem, there are very strong restrictions, i.e., limitation on the filter type and on the filter bank structure. In this paper, development of this technique is presented. Consequently, any type of linear phase FIR filter and any structure of filter bank can be used.