The relation between computing part of the FFT spectrum and the so-called generalized FFT (GFFT) is clarified, leading to a new algorithm for performing partial FFTs. The method can be applied when only part of the output is required or when the input data sequence contains many zeros. Such cases arize for example in decimation and interpolation and also in computing linear convolutions. The technique consists of decomposing the DFT into several generalized DFTs. Efficient algorithms for these generalized DFTs exist. The computational complexity of the new approach is roughly equal to the complexity of previous techniques, but the structure is superior, because only one type of butterfly is used and a few lines of code are sufficient. The theoretical properties of the GDFT are given. The case of multidimensional signals, defined on arbitrary sampling lattices is also considered.

This paper proposes adaptive line enhancers with new coefficient update algorithms on the basis of least-square-error criteria. Adaptive algorithms by least-squares are known to converge faster than stochastic-gradient ones. However they have high computational complexity due to matrix inversion. To avoid matrix inversion the proposed algorithms adapt only one coefficient to detect one sinusoid. Both FIR and IIR types of adaptive algorithm are presented, and the techniques to reduce the influence of additive noise is described in this paper. The proposed adaptive line enhancers have simple structures and show excellent convergence characteristics. While the convergence of gradient-based algorithms largely depend on their stepsize parameters, the proposed ones are free from them.

A systematic synthesis is presented to realize any digital filter into a power-wave digital filter. After three canonical matrix representations are introduced, a set of key concepts which comprises cascade interconnection of digital two-ports, pole localization, and computability is presented for the canonical cascade synthesis of lossless digital two-ports. The synthesis procedure consists of global decomposision and local decomposition. The procedure is so general as to give a unified solution to arbitrary frequency responses realization, and is so useful as to find new circuit structures. The synthesized circuits are of robustness and modularity. An illustrative example is included.

This paper presents a novel stereophonic acoustic echo canceling scheme without preprocessing. To accurately estimate echo path keeping the high level of performance in echo erasing, this scheme uses two filters, of which one filter is utilized as a guideline which does not erases echo but helps updating of the other filter, which actually erases echo. In addition, we propose a new filter dividing technique to apply to the filter divide scheme, and utilize this as the guideline. Numerical examples demonstrate that the proposed scheme improves the convergence behavior compared to conventional methods both in system mismatch (i.e., normalized coefficients error) and Echo Return Loss Enhancement (ERLE).

This paper proposes an algorithm for the design of FIR digital filters whose coefficients have CSD representations. The total number of nonzero digits is specified. A set of filters whose frequency responses have less than or equal to a given Chebyshev error have their coefficients in a convex polyhedron in the Euclid space. The proposed algorithm searches points where a coefficient is maximum or minimum in the convex polyhedron by using linear programing. These points are connected whih the origin to make a convex cone. Then the algorithm evaluates CSD points near these edges of the cone. Moving along these edges means the scaling of frequency responses. The point where the frequency response is the best among all the candidates under the condition of specified total number of nonzero digits is selected as the solution. Several techniques are used to reduce the calculation time. Design examples show that the proposed method can design better frequency responses than the conventional methods.

A memory address allocation method for digital signal processors of indirect addressing with indexed auto-modification is proposed. At first, address auto-modification amounts for a given program are analyzed. And then, address allocation of program variables are moved and shifted so that both indexed and simple auto-modifications are effectively exploited. For further reduction in overhead codes, a memory address allocation method coupled with computational reordering is proposed. The proposed methods are applied to the existing compiler, and generated codes prove their effectiveness.

Two discrete-time Wirtinger-type inequalities relating the power of a finite-length signal to that of its circularly-convolved version are developed. The usual boundary conditions that accompany the existing Wirtinger-type inequalities are relaxed in the proposed inequalities and the equalizing sinusoidal signal is free to have an arbitrary phase angle. A measure of this sinusoidal signal's power, when corrupted with additive noise, is proposed. The application of the proposed measure, calculated as a ratio, in the evaluation of the power of a sinusoid of arbitrary phase with the angular frequency π/N, where N is the signal length, is thoroughly studied and analyzed under additive noise of arbitrary statistical characteristic. The ratio can be used to gauge the power of sinusoids of frequency π/N with a small amount of computation by referring to a ratio-versus-SNR curve and using it to make an estimation of the noise-corrupted sinusoid's SNR. The case of additive white noise is also analyzed. A sample permutation scheme followed by sign modulation is proposed for enlarging the class of target sinusoids to those with frequencies M π/N, where M and N are mutually prime positive integers. Tandem application of the proposed scheme and ratio offers a simple method to gauge the power of sinusoids buried in noise. The generalization of the inequalities to convolution kernels of higher orders as well as the simplification of the proposed inequalities have also been studied.

A fast and accurate method for Generalized Harmonic Analysis is proposed. The proposed method estimates the parameters of a sinusoid and subtracts it from a target signal one by one. The frequency of the sinusoid is estimated around a peak of Fourier spectrum using binary search. The binary search can control the trade-off between the frequency accuracy and the computation time. The amplitude and the phase are estimated to minimize the squared sum of the residue after extraction of estimated sinusoids from the target signal. Sinusoid parameters are recalculated to reduce errors introduced by the peak detection using windowed Discrete-Time Fourier Transform. Audio signals are analyzed by the proposed method, which confirms the accuracy compared to existing methods. The proposed algorithm has high degree of concurrency and is suitable to be implemented on Graphical Processing Unit (GPU). The computational throughput can be made higher than the input audio signal rate.

Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.

A user-friendly simulator PANDA (Program for the Analysis of Networks with Digital Arithmetic) is introduced, which can analyze the frequency responses, coefficient sensitivities and roundoff noise of given linear shift-invariant digital networks from their structural descriptions.

An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two. The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions. The properties of their autocorrelation functions are studied. The non-periodic complementary sequences are the intersection between anti-symmetric and symmetric periodic sequences. These non-periodic and periodic complementary sequences are identified to be special cases of non-periodic and periodic (or cyclic) orthogonal wavelet transforms. This relationship leads to the novel approach.

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 new procedure to derive low-sensitivity second-order digital filters is presented. This procedure is simple compared to other existing methods. First, a denominator polynomial of a filter transfer function is characterized in terms of ω0 and ωb, which are defined as a center angular frequency and a 3 dB bandwidth of a bandpass filter, respectively. On the other hand, the denominator polynomial is also expressed as a general form including multiplier coefficients and some integer parameters corresponding to existent degrees of freedom. Then the sensitivities of cos ω0 and tan with respect to a multiplier coefficient, which are referred to as frequency sensitivities, are calculated. The integer parameters are determined so that the frequency sensitivities are reduced for small ω0 and ωb. This procedure yields several forms of transfer functions including those of well-known low-sensitivity circuits. One of them is new and the corresponding circuit structures are also given. In addition to its low sensitivity, the new filter has a useful feature; ω0 and ωb are determined independently by each of two multiplier coefficients.

In the design of digital filters, it is desirable to achieve lower sensitivity. Wave digital filters (WDF's) are considered one solution to this problem, and two design approaches have been proposed. However, WDF's have complicated structures compared with conventional ones. This will make it difficult to implement WDF's. The aim of this paper is to reduce the difficulty owing to the complexity of the network structures. Two kinds of simplification techniques are presented. One is to reduce the number of adders. For this purpose, new series and parallel sections and a new port matching scheme are proposed. The other is to construct WDF's using identical 3-port adaptors except the one to match the port resistance. Examples of WDF's with proposed structures are provided and the effectiveness of the proposed techniques is also shown.

For low-complexity linear-phase FIR digital filters which have coefficients expressed as canonic signed digit (CSD) code, a design method to impose power-of-two DC gain is proposed. Output signal level can easily be compensated to that of input so that cascading many stages do not cause any gain errors, which are harmful in, for example, high precision measurement systems. The design is formulated as an optimization problem with magnitude response constraints. The integer linear programming modified for CSD codes is solved by the branch and bound method. The design example shows the effectiveness of the obtained filter in comparison with existing CSD filters. Also, an evaluation method for the area to implement the filter into field programmable gate array (FPGA) is proposed. The implementation example shows that the minimum critical path is obtained with only a little increase in the die area.

In practical applications of digital filters it is more realistic to treat multiplier coefficients as finite intervals than restricting them to infinite or very long word-length representations. However, this can not be done it the frequency response performance under interval assumption is difficult to analyze. In this paper, it is proved that stable lattice allpass filters possess bounded continuous phase response when lattice parameters vary in bounded intervals. It is shown that sharp bounds on the interval phase response can be computed easily at an arbitrary frequency using a simple recursive procedure. Application of this property to the problem of finite word-length lattice allpass filter design is also discussed. By formulating this problem as an interval design it is possible to solve it efficiently independent of the number system used to represent multiplier coefficients.

A description language for matrix and vector expressions and its compiler for DSPs are shown. They provide both a user-friendly programming environment and efficient codes. In order to increase throughput and to reduce amount of methods based on mathematical laws are introduced. A method to decide the matrix and vector storage location suitable for processing on DSP is also proposed.

In multidimensional signal sampling, the orthogonal sampling scheme is the simplest one and is employed in various applications, while a non-orthogonal sampling scheme is its alternative candidate. The latter sampling scheme is used mainly in application where the reduction of the sampling rate is important. In three-dimensional (3-D) signal processing, there are two typical sampling schemes which belong to the non-orthogonal samplings; one is face-centered cubic sampling (FCCS) and the other is body-centered cubic sampling (BCCS). This paper proposes a new design method for 3-D band-limiting FIR filters required for such non-orthogonal sampling schemes. The proposed method employs the McClellan transformation technique. Unlike the usual 3-D McClellan transformation, however, the proposed design method uses 2-D prototype filters and 2-D transformation filters to obtain 3-D FIR filters. First, 3-D general sampling theory is discussed and the two types of typical non-orthogonal sampling schemes, FCCS and BCCS, are explained. Then, the proposed design method of 3-D bandlimiting filters for these sampling schemes is explained and an effective implementation of the designed filters is discussed briefly. Finally, design examples are given and the proposed method is compared with other method to show the effectiveness of our methos.

This paper proposes a design technique for 3-D non-separable QMF banks with Face-Centered Cubic Sampling (FCCS) and Body-Centered Cubic Sampling (BCCS). In the proposed technique, 2-D McClellan transformation is applied to a suitably designed 2-D prototype QMF to obtain 3-D QMFs. The design examples given in this paper demonstrate advantages of the proposed method.

Change detection methods are used to detect changes between two frames in an image sequence. Fundamental techniques for detecting changes use a difference image between the two frames. The change of each pixel is detected if difference values exceed a pre-set threshold, which is determined on the basis of the estimated value of the variance of noises on the frames. Not only the noises on the frames but also illumination changes between the frames are critical problems for change detection. A recently proposed approach gives a threshold derived from the average of the difference image over areas which are estimated as non-change parts. However, such a threshold may not be appropriate since the approach uses no physical parameters such as light sources, the reflection of objects. This paper proposes a new change detection method based on a physical model, which describes physical parameters such as light sources and the reflection of objects, known as an illumination model. First, we show the derivation of a new threshold based on the illumination model. The threshold is derived from the angle of the light of sources, the gray level of background objects, and the normal-vector of the background objects. A new change detection algorithm using such a threshold is shown. Next, we show experimental results and comparison, in which the proposed method improves the accuracy of detection results, compared to change detection by using the conventional threshold. We also give discussion on the features of the proposed method.