Coprime (pair of) DFT filter banks (coprime DFTFB), which process signals like a spectral analyzer in time domain, divides the power spectrum equally into MN bands by employing two DFT filter banks (DFTFBs) of size only M and N respectively, where M and N are coprime integers. With coprime DFTFB, frequencies in wide sense stationary (WSS) signals can be effectively estimated with a much lower sampling rates than the Nyquist rates. However, the imperfection of practical FIR filter and the correlation based detection mode give rise to two kinds of spurious peaks in power spectrum estimation, that greatly limit the application of coprime DFTFB. Through detailed analysis of the spurious peaks, this paper proposes a modified spectral analyzer based on dual coprime DFTFBs and sub-decimation, which not only depresses the spurious peaks, but also improves the frequency estimation accuracy. The mathematical principle proof of the proposed spectral analyzer is also provided. In discussion of simultaneous signals detection, an O-extended MN-band coprime DFTFB (OExt M-N coprime DFTFB) structure is naturally deduced, where M, N, and O are coprime with each other. The original MN-band coprime DFTFB (M-N coprime DFTFB) can be seen a special case of the OExt M-N coprime DFTFB with extending factor O equals ‘1’. In the numerical simulation section, BPSK signals with random carrier frequencies are employed to test the proposed spectral analyzer. The results of detection probability versus SNR curves through 1000 Monte Carlo experiments verify the effectiveness of the proposed spectrum analyzer.

In this paper, we propose a new class of two dimensional (2D) M-channel (M-ch) non-separable filter banks (FBs) based on cosine modulated filter banks (CMFBs) via a new diagonally modulation scheme. Until now, many researchers have proposed 2D non-separable CMFBs. Nevertheless, efficient direction-selective CMFBs have not been yet. Thanks to our new modulations with diagonal shifts, proposed CMFBs have several frequency supports including direction-selective ones which cannot be realized by conventional ones. In a simulation, we show design examples of proposed CMFBs and their various directional frequency supports.

The wideband noise controlling performance of the delayless subband adaptive filtering technique is affected by the group delay and in-band aliasing distortion of analysis filter banks. A method of recursive second-order cone programming is proposed to design the uniform DFT modulated analysis filter banks, with a small in-band aliasing error and low group delay. Simulation results show that the noise controlling performance is improved with small residual noise power spectra, a high noise attenuation level and fast convergence rate.

In this paper, we propose a novel lattice structure of two dimensional (2D) nonseparable linear-phase paraunitary filter banks (LPPUFBs) called 2D GenLOT. Muramatsu et al. have previously proposed a lattice structure of 2D nonseparable LPPUFBs which have efficient frequency response. However, the proposed structure requires less number of design parameters and computational costs than the conventional one. Through some design examples and simulation results, we show that both filter banks have comparable frequency response and coding gain.

This paper proposes a synthesis method of 2-channel IIR paraunitary filter banks by successive extraction of 2-port lattice sections. When a power symmetry transfer function is given, a filter bank is realized as cascade of paraunitary 2-port lattice sections. The method can synthesize both odd- and even-order filters with Butterworth or elliptic characteristics. The number of multiplications per second can also be reduced.

This letter proposes a novel design approach for optimal contourlet filter banks based on the parametric 9/7 filter family. The Laplacian pyramid decomposition is replaced by optimal 9/7 filter banks with rational coefficients, and directional filter banks are activated using a pkva 12 filter in the contourlets. Moreover, based on this optimal 9/7 filter, we present an image denoising approach using a contourlet domain hidden Markov tree model. Finally, experimental results show that our approach in denoising images with texture detail is only 0.20 dB less compared to the method of Po and Do, and the visual quality is as good as for their method. Compared with the method of Po and Do, our approach has lower computational complexity and is more suitable for VLSI hardware implementation.

In this paper, a design method of two-dimensional (2-D) orthogonal symmetric wavelets is proposed by using a lattice structure for multi-dimensional (M-D) linear-phase paraunitary filter banks (LPPUFB), which the authors have proposed as a previous work and then modified by Lu Gan et al. The derivation process for the constraints on the second-order vanishing moments is shown and some design examples obtained through optimization with the constraints are exemplified. In order to verify the significance of the constraints, some experimental results are shown for Lena and Barbara image.

In the main part of this paper, we present a systematic discussion for the optimum interpolation approximation in a shift-invariant wavelet and/or scaling subspace. In this paper, we suppose that signals are expressed as linear combinations of a large number of base functions having unknown coefficients. Under this assumption, we consider a problem of approximating these linear combinations of higher degree by using a smaller number of sample values. Hence, error of approximation happens in most cases. The presented approximation minimizes various worst-case measures of approximation error at the same time among all the linear and the nonlinear approximations under the same conditions. The presented approximation is quite flexible in choosing the sampling interval. The presented approximation uses a finite number of sample values and satisfies two conditions for the optimum approximation presented in this paper. The optimum approximation presented in this paper uses sample values of signal directly. Hence, the presented result is independent from the so-called initial problem in wavelet theory.

This paper discusses a new structure of M-channel IIR perfect reconstruction filter banks. A novel building block defined as a cascade connection of some IIR building blocks and FIR building blocks is presented. An IIR building block is written by state space representation, where we easily obtain a stable filter bank by setting eigenvalues of the state transition matrix into the unit circle. Due to cascade connection of building blocks, we are able to design a system with a larger number of free parameters while keeping the stability. We introduce the condition which obtains the new building block without increasing of the filter order in spite of cascade connection. Additionally, by showing the simulation results, we show that this implementation has a better stopband attenuation than conventional methods.

In this paper, theoretical properties of deinterlacer banks are analyzed. Deinterlacer banks are novel filter banks in the sense that a progressive video sequence is separated into two progressive video sequences of a half frame rate and, furthermore, interlaced sequences are produced as intermediate data. Unlike the conventional filter banks, our deinterlacer banks are constructed in a way unique to multidimensional systems by using invertible deinterlacers, which the authors have proposed before. The system is a kind of shift-varying filter banks and it was impossible to derive the optimal bit-allocation control without any equivalent parallel filter banks. This paper derives an equivalent polyphase matrix representation of the whole system and its equivalent parallel structure, and then shows the optimal rate allocation for the deinterlacer banks. Some experimental results justify the effectiveness of the optimal rate allocation through our theoretical analysis.

In this letter, we present a new numerical design method for 2-D FIR quincunx filter banks (QFB) with low-delay, equiripple magnitude response, and perfect reconstruction (PR). The necessary conditions for the system delay of QFB are derived. The dual affine scaling variant of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters, and a linearization scheme is introduced to satisfy the PR constraint for QFB. We have included several simulation examples to show the efficacy of this proposed design technique.

In this paper, we present a design and implementation of the M-channel linear-phase filter banks with unequal-length and same center of symmetry. The filter banks are separated into paraunitary and biorthogonal case. We discuss both cases. A novel filter bank can be regarded as a special class of generalized lapped transform with arbitrary number of channels M. In image coding applications, long basis functions should be used to avoid the blocking artifacts in low-frequency bands, while short basis functions should be used to reduce the ringing artifacts in high-frequency bands. Having the same center of symmetry is suitable for progressive image coder [SPIHT]. Filter banks with such characteristics can be achieved structurally by taking acount of the lattice structure. Finally, several design and image coding examples are shown.

In this letter, our proposed approach exploits the use of original and simplest Cellular Neural Network (CNN) for 2D Doubly Complementary (DC) Infinite Impulse Response (IIR) filter banks design. The properties of feedback and feedforward templates are studied for this purpose. Through some examples it is shown how generalizations of these templates can be used for DC IIR filter banks design. We modify Lagrangian function which is used for optimizing a low-pass filter design considering the constraint for stability of CNN. The brief conclusions with design examples that illustrate the proposed method and an image enhancement and restoration applications of designed filter banks are presented.

In this letter, a numerical design approach for FIR diamond-shaped filter banks (DFB) with perfect reconstruction (PR) and low delay for tree-structured HDTV coding is presented. The system delay of the designed DFB can be controlled below the category of the linear-phase. Moreover, the necessary conditions for the system delay of the designed DFB are derived. The considered problem is formulated as the minimization of the real and imaginary parts of weighted peak ripple errors of the designed analysis filters subject to PR constraints. Simulation example is provided to show the efficacy of this proposed design technique.

In the literature [9], the optimum discrete interpolation of one-dimensional signals is presented which minimizes various measures of approximation error simultaneously. In the discussion, the ratio λ of the weighted norm of the approximation error and that of the corresponding input signal plays an essential role to determine the structure of the set of signals. However, only the upper bound of λ is provided in [9]. In this paper, we will present more exact and systematic discussion of the optimum discrete interpolation of one-dimensional signals which minimizes various measures of approximation error at the same time. In this discussion, we will prove that the exact value of λ is identical with the upper limit, for ω (|ω| π), of the largest eigen value of a matrix including the weighting function W(ω) and the Fourier transforms of the optimum interpolation functions. Further, we will give a sufficient condition for W(ω) under which the ratio λ is equal to one, where the approximation error, if it is interpolated by sinc, is included in the set of band-limited signals defined by W(ω). Finally, as application of the presented approximation, we will propose a direction to interactive signal processing on Internet and a transmultiplexer system included in it. The transmultiplexer system included in this discussion can realize flexible arrangement of sub-bands which is inevitable in realizing the above proposal on interactive signal processing.

In this paper, we present a numerical design method for two-dimensional (2-D) FIR linear-phase (LP) quincunx filter banks (QFB) with equiripple magnitude response and perfect reconstruction (PR). The necessary conditions for the filter length of analysis filters are derived. A dual affine scaling variant (DASV) of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters and an approximation scheme is introduced to satisfy the PR constraint for the 2-D filter banks (FB). The simulation examples are included to show the effectiveness of this proposed design technique.

Since IIR filters have lower computational complexity than FIR filters, some design methods for IIR filter banks have been presented in the recent literatures. Smith et al. have proposed a class of linear phase IIR filter banks. However this method restricts the order of the numerator to be odd and has some drawbacks. In this paper, we present two design methods for linear phase IIR filter banks. One is based on Lagrange-Multiplier method, and optimal IIR filter banks in least squares sense are obtained. In an other approach, IIR filter banks with the maximum number of zeros are derived analytically.

A constant modulus adaptive array algorithm is derived using analysis and synthesis filter banks to permit adaptive digital beamforming for wideband signals. The properties of the CMA adaptive array using the filter banks are investigated. This array would be used to realize adaptive digital beamforming when this is difficult by means of ordinary (that is, non-subband) processing due to the limited speed of signal processor operations. As an actual application, we present a beamspace adaptive array structure that combines the analysis and synthesis filter banks with RF-domain multibeam array antennas, such as those utilizing optical signal processing.

In this letter, a design method of linear-phase paraunitary filter banks is proposed for an odd number of channels. In the proposed method, a non-linear unconstrained optimization process is assumed to be applied to a lattice structure which makes the starting guess of design parameters simple. In order to avoid insignificant local minimum solutions, a recursive initialization procedure is proposed. The significance of our proposed method is verified by some design examples.

In the literatures [5] and [10], a systematic discussion is presented with respect to the optimum interpolation of multi-dimensional signals. However, the measures of error in these literatures are defined only in each limited block separately. Further, in these literatures, most of the discussion is limited to theoretical treatment and, for example, realization of higher order linear phase FIR filter bank is not considered. In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. Firstly, we outline necessary formulation for the time-limited interpolation functions ψm(t) (m=0,1,. . . ,M-1) realizing the optimum approximation in each limited block separately, where m are the index numbers for analysis filters. Secondly, under some assumptions, we will present analytic or piece-wise analytic interpolation functions φm(t) minimizing various measures of approximation error defined at discrete time samples n=0, 1, 2,. . . . In this discussion, φm(n) are equal to ψm(n) n=0, 1, 2,. . . . Since ψm(t) are time-limited, φm(n) vanish outside of finite set of n. Hence, in designing discrete filter bank, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are φm(n). Finally, we will present one-dimensional linear phase M channel FIR filter bank with high attenuation characteristic in each stop band. In this design, we adopt the cosine-sine modulation initially, and then, use the iterative approximation based on the reciprocal property.