A novel condition for complex FIR digital filters to have linear phase is presented. It naturally includes the linear phase conditions for real FIR filters as special cases.

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.

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.

Digital signal processors (DSPs) usually employ indirect addressing using an address register (AR) to indicate their memory addresses, which often introduces overhead codes in AR updates for next memory accesses. In this paper, AR update scheme is extended such that address can be efficiently modified by 2 in addition to conventional 1 updates. An automatic address allocation method of program variables for this new addressing model is presented. The method formulates program variables and AR modifications by a graph, and extracts a maximum chained triangle graph, which is accessed only by AR 1 and 2 operations, so that the estimated number of overhead codes is minimized. The proposed methods are applied to a DSP compiler, and memory allocations derived for several examples are compared with memory allocations by other methods.

This paper proposes a new design method of variable FIR digital filters. The method uses a multi-dimensional linearphase FIR filter as a prototype. The principle of the proposed method is based on the fact that the crosssectional characteristics of a 2-D filter along with a line vary if the intersection of this line is changed. The filter characteristics can be varied by recalculating all the filter coefficients from proposed equations, which leads to an advantage that the variable range is very wide. Another advantage is that the passband and stopband deviations are completely predetermined in the design procedures and that the passband edge can be accurately settled to a desired frequency while keeping the transition band width unchanged. First the proposed design method is explained and the effect of the transition band of 2-D filters is discussed. Then the calculation cost required in updating the filter coefficients are considered. Finally two design examples are presented and the proposed method is compared with the existing one, which shows the usefulness of our method.

A blur restoration scheme for images with linear motion blurred objects in still background is proposed. The proposed scheme starts from a rough detection of locations of blurred objects. This rough segmentation of the blurred regions is based on an analysis of local orientation map. Then, parameters of blur are identified based on a linear constant-velocity motion blur model for every detected blurred region. After the blur parameters are estimated, the locations of blurred objects can be refined before going to a restoration process by using information from the identified blur parameters. Blur locations are refined by observing local power of the blurred image which is filtered by a high-pass filter. The high-pass filter has approximately a frequency characteristic that is complementary to the identified blur point spread function. As a final step, the image is restored by using the estimated blur parameters and locations based on an iterative deconvolution scheme applied with a regularization concept. Experimental examples of simulated and real world blurred images are demonstrated to confirm the performance of the proposed scheme.

It is sometimes required to change the frequency characteristics of a digital filter during its operation. In this paper a new synthesis of variable even-order IIR digital filters is proposed. The cut-off frequency of the filter can be changed by a single parameter. The fundamental filter structure is a cascade of second-order sections. The multiplier coefficients of each section are determined by using the Taylor series expansion of the lowpass to lowpass frequency transformation. For this method any second-order section can be used as a prototype, but here in this paper only the direct form and the lattice form are described. Unlike the conventional method, any transfer functions can be used for the proposed method. Finally a designed example shows that the proposed filter has wider tuning range than the conventional filter, and the advantage of the proposed filters is confirmed.

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.

A least squares approximation method of recursive digital filters for finite interval response with zero value outside the interval is presented. According to the characteristic of the method, the modified Gauss Method is utilized in iteratively determining design parameters. Convergence, together with the stability of the resulting filter, are guaranteed.