In this paper a new general method for approximation of arbitrary multiband filter loss specifications, including all classical, maximally flat and equiripple approximations as special cases, is proposed. It is possible to specify different magnitude behavior (flat or equiripple of given degree) and different maximal losses in the different passbands and to optimize all transmission and attenuation zeroes positions or to have some of them fixed. The optimization procedures for adjustment of the filter response are based on modified Remez algorithm and are performed in s-domain what is regarded since recently as an advantage in the case of design of parallel allpass structures based IIR digital filters. A powerful algorithm and appropriate software are developed following the method and their efficiency is verified through design examples.

FIR digital filters composed of parallel multiple subfilters are proposed. A binary expression of an input signal is decomposed into multiple shorter words, which drive the subfilters having different length. The output error is evaluated by mean squared and maximum spectra. A fast algorithm is also proposed to determine optimal filter lengths and coefficients of subfilters. Many examples confirm that the proposed filters generate smaller output errors than conventional filters under the condition of specified number of multiplications and additions in filter operations. Further, multiplier and adder structures (MAS) to perform the operations of the proposed filters are also presented. The number of gates used in the proposed MAS and its critical path are estimated. The effectiveness of the proposed MAS is confirmed.

We present a finite-difference time-domain (FD-TD) method with the perfectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-time modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and its MD-WDFs' representation by using the current-controlled voltage sources. In order to estimate the lower bound of numerical errors which come from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD method based on the MD-WDFs over the Yee algorithm. Simultaneously, we estimate numerical errors in practical problems as a function of grid cell size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we analyze several typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method based on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.

This letter proposes a Perfect-Reconstruction (PR) encryption scheme based on a PR QMF bank. Using the proposed scheme, signals can be encrypted and reconstructed perfectly by using two Periodically Time-Varying (PTV) digital filters respectively. Also we find that the proposed scheme has a "good" encryption effect and compares favorably with frequency scramble in the aspects of computation complexity, PR property, and degree of security.

This paper presents a method to analyze and minimize output errors of 2-D non-separable FIR filters with finite wordlength. Finiteness in the wordlength causes output errors, which can be analyzed in the frequency domain when the statistics of input signals are known. The output errors can be minimized by optimizing responses corresponding to all levels of input impulses. A new ROM-based filter structure is proposed in which the optimized impulse responses are stored in the ROM. The output signals are generated by superposing the impulse responses corresponding to the input levels. Many simulation results confirm that the output signals of the proposed filters have far less errors compared to conventional filters. The hardware size of the ROM-based filters is estimated and compared with that of conventional structures. The proposed structures are more effective than the conventional ones especially when the signal wordlength is short.

This paper discusses a design method for two-dimensional (2-D) periodically time-variant digital filters (PTVDFs) whose filter coefficients vary periodically. First, 2-D periodicities for a variation of filter cefficients are considered, from which two and four-phase variations of coefficients are shown to be suitable for practical applications. Then, the input-output relation (transfer function) for 2-D separable-denominator (SD) PTV DFs is derived, which results in a linear combination of the baseband input signal and its modulated versions. Finally, in order ro approximate given filter specifications, the structure for 2-D SD PTV DFs is given and a design method is proposed. It is shown that, compared with the 2-D SD time-invariant DFs, approximation error can be reduced with the proposed SD PTV DFs.

It is shown that two-dimensional linear phase FIR digital filters with various shapes of frequency response can be designed and realized as modular array structures free of multiplier coefficients. The design can be performed by judicious selection of two low order linear phase transfer functions to be used at each module as kernel filters. Regular interconnection of the modules in L rows and K columns conditioned with boundary coefficients 1, 0 and 1/2 results in higher order digital filters. The kernels should be chosen appropriately to, first, generate the desired shape of frequency response characteristic and, second, lend themselves to multiplierless realization. When these two requirements are satisfied, the frequency response can be refined to possess narrower transition bands by adding additional rows and columns. General properties of the frequency response of the array are investigated resulting in Theorems that serve as valuable tools towards appropriate selection of the kernels. Several design examples are given. The array structures enjoy several favorable features. Specifically, regularity and lack of multiplier coefficients makes it suitable for high-speed systolic VLSI implementation. Computational complexity of the structure is also studied.

In this paper, new wavelet bases are presented. We address problems associated with the proposed matched filter in multirate systems, using an optimum receiver that maximises the SNR at the sampling instant. To satisfy the Nyquist (ISI-free transmission) and matched filter (maximum SNR at the sampling instant) criteria, the overall system filtering strategy requires to split the narrowest filter equally between transmitter and receiver. In data transmission systems a raised-cosine filter is therefore often used to bandlimit signals from which wavelet bases are derived. Sampling in multiresolution subspaces is also discussed.

A classs of type 1 linear phase FIR digital filters is proposed. The filter can be realized using a parallel, modular and regular array structure. It is shown that, under some simple constraints, the consisting modules of the array can be realized free of multiplier coefficients. Such two dimensional mesh arrays are specially suitable for realization with special-purpose systolic hardware for high-speed digital signal processing tasks. Compared to the array structure, proposed by the authors, for multiplierless realization of maximally flat FIR digital filters, this class needs less adders to fulfill the same magnitude response requirements. Another attractive property of the proposed array is that a number of highpass or lowpass filters with different passband widths can be realized simultaneously in a very economical way.

This letter presents an efficient design method of multiplierless 2-D state-space digital filters (SSDFs) based on a genetic algorithm. The resultant multiplierless 2-D SSDFs, whose coefficients are represented as the sum of two powers-of-two terms, are attractive for high-speed operation and simple implementation. The design problem of multiplierless 2-D SSDFs described by Roesser's local state-space model is formulated subject to the constraint that the resultant filters are stable. To ensure the stability for the resultant 2-D SSDFs, a stability test routine is embedded in th design procedure.

We present a method of extracting the digital inphase (I) and quadrature (Q) components from oversampled bandpass signals using narrow-band bandpass Hilbert transformers. Down-conversion of the digitized IF signals to baseband and reduction of the quantization noise are accomplished by the multistage decimator with the complex coefficient bandpass digital filters (BPFs), which construct the bandpass Hilbert transformers. Most of the complex coefficient BPFs in the multistage decimator can be replaced with the lowpass filters (LPFs) under some conditions, which reduces computational burden. We evaluate the signal to quantization noise ratio of the I and Q components for the sinusoidal input by computer simulation. Simulation results show that the equivalent amplitude resolution of the I and Q components can be increased by 3 bits in comparison with non-oversampling case.

This paper discusses a new design method for 2-D variable FIR digital filters, which is an extension of our previous work for 1-D case. The method uses a 3-D prototype FIR filter whose cross-sections correspond to the desired characteristics of 2-D variable FIR filters. A 2-D variable-angle FIR fan filter is given as a design example.

A bounded complex (BC) digital transfer function realized with a II-cascade structure of Lossless Bounded Complex (LBC) two-pairs is known to have low magnitude sensitivity. In this letter, it is shown that the two-pairs parameters depend directly on some invariants of the transfer function corresponding to the transmission zeros of the structure. An analysis of the existence and the numbering of these invariants leads to a simplified automated LBC filter structure design avoiding the need for polynomial manipulations. These results are also easily applied for the real filtering case.

The factored state space approach (FSS) can be a powerful mathematical tool for the synthesis and analysis of non state space digital filters. In the following letter, this technique is used for the rederivation of some classes of low sensitivity filters described by a II-cascade two-pair structure. This method leads to a simplified synthesis algorithm (with applications to automated synthesis procedures for many classes of non state space digital filters) as well as a straightforward analysis of roundoff noise and norm scaling problems.

In this paper we propose a method for increasing the reliability in multiprocessor realization of lowpass and highpass FIR digital filters possessing a maximally flat magnitude response. This method is based on the use of array realization of the filter which has been proposed earlier by the authors. It is shown that if a processing module of the array functions erroneously, it is possible to exclude the module and still obtain a lowpass FIR filter. However, as a price we should tolerate a slight degradation in the magnitude response of the filter that is equivalent to a wider transition band. We also analyze the behavior of the filter when our proposed schemes are implemented on more than one module. The justification of our approach is based on that a slight degradation of the spectral characteristics of a filter may be well tolerated in most filtering applications and thus a graceful degradation in the frequency domain can sufficiently reduce the vulnerability to errors.

The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.

The requirement of structural boundedness or passivity leads to important classes of digital filters among which are the wave digital (WD) filters and the LBR cascade structures having low coefficient sensitivity. Contrary to the WD filters, the LBR filters are directly synthesized in z-domain and several authors presented different approaches for a better understanding of the synthesis procedure especially for complex transfer functions. Some tentatives were also made to give parallels between passive analog and digital filters (i.e. WD or LBR filters). A general approach to LBR synthesis with transmission zeros not necessarily on the unit circle is presented along with some explicit expressions for the LBR (and the generalized complex counterpart LBC) filter parameters for the realization of an input transfer function. The results can be of interest in automated procedures for low sensitivity digital filter design.

It is often desired to change the cutoff frequencies of digital filters in some applications like digital electronic instruments. This paper proposes a design of variable lowpass digital filters with wider ranges of cutoff frequencies than conventional designs. Wave digital filters are used for the prototypes of variable filters. The proposed design is based on the frequency scaling in the s-domain, while the conventional ones are based on the z-domain lowpass-to-lowpass transformations. The first-order approximation by the Taylor series expansion is used to make multiplier coefficients in a wave digital filters obtained from a frequency-scaled LC filter become linear functions of the scaling parameter, which is similar to the conventional design. Furthermore this paper discusses the reduction of the approximation error. The curvature is introduced as the figure of the quality of the first-order approximation. The use of the second-order approximation to large-curvature multiplier coefficients instead of the first-order one is proposed.

This paper studies multidimensional linear periodically shift-variant digital filters (LPSV filters). The notion of a generalized multidimensional transfer function is presented for LPSV filters. The frequency characteristic of the filters is discussed in terms of this transfer function. Since LPSV filters can decompose the spectrum of an input signal into some spectral partitions and rearrange the spectrum, LPSV filters can serve as a frequency scrambler. To show the effect of multidimensional frequency scramble, 2-D LPSV filters are designed based on the 1-D Parks-McClellan algorithm. The resultant LPSV filters divide the input spectrum into some components that are permuted and possibly inverted with keeping the symmetric of the spectrum. Experimental results are presented to illustrate the effectiveness of frequency scramble for real images.

The design of N-dimensional (N-D) FIR filters requires in general an enormous computational effort. One of the most successful methods for design and implementation is the McClellan transformation. In this paper a numerically simple technique for determining the coefficients of the transformation is suggested. This appears to be the simplest available method for the design of N-D hyperspherically symmetric FIR filters with excellent symmetry.