Yuichi Kida

Bio: Yuichi Kida is an academic researcher from Ohu University. The author has contributed to research in topics: Approximation error & Interpolation. The author has an hindex of 6, co-authored 36 publications receiving 99 citations.

Theory of the optimum discrete running approximation of multi-dimensional approximately band-limited signals

Abstract: In this paper, we present an n-dimensional running discrete approximation that minimizes various worst-case measures of error, simultaneously. We derive continuous space-limited n-dimensional interpolation-functions satisfying condition that is called discrete orthogonality. Then, we present a set of signals that satisfies two conditions of the optimum approximation.

The optimum approximation of a multidimensional filter bank having analysis filters with small nonlinear characteristics

Abstract: Firstly, we present the optimum interpolation approximation for multi-dimensional vector signals. The presented approximation shows high performance such that it minimizes various worst-case measures of error of approximation simultaneously. Secondly, we consider a set of restricted multi-dimensional vector signals that all elements of the corresponding generalized spectrum vector are separable-variable functions. For this set of restricted multi-dimensional vector signals, we present the optimum interpolation approximation. Moreover, based on this property, putting the variables to be identical with each other in the approximation, we present a certain optimum interpolation approximation for generalized filter bank with generalized non-linear analysis filters. This approximation also shows the high performance similar to the above-mentioned approximations. Finally, as a practical application of the optimum interpolation approximation for multi-dimensional vector signals, we present a discrete numerical solution of linear partial differential equations with many independent variables.

The optimum approximate reconstruction of a signal from the discrete sample values of the prescribed multiple waves

Abstract: For a set of signals that each signal is defined by means of a certain spectrum-vector composed of a finite number of extended Fourier transforms of component waves, one of the authors presents an extended optimum approximation but a running approximation is not treated [4]. In this paper, we show the outline of the result given in [4] as a premise of the arguments, firstly. Then, under the conditions that the required time-interval in the approximation is wide but limited and the measures of error are continuous, we present the optimum running approximation for this set of signals by using a certain one-to-one correspondence between the error in the wide time-interval and the error in its small segment. It is shown that the presented running approximation minimizes various worst-case measures of approximation error simultaneously and the corresponding interpolation functions are obtained by solving sets of linear equations having constant coefficient-matrices. Finally, we present an example for a multi-input one-output system having separate pass band to eliminate the prescribed noise band.

Design of distributed sub-band networks having the minimum total weighted energy based on the concept of generating function of networks

Abstract: We present two topics in this paper. First topic is the optimum running approximation of signals by a FIR filter bank minimizing various worst-case continuous measures of error, simultaneously. As a direct application, we obtain a favorable sub-band multi-input multi-output transmission system that is useful to multi-path sensor network with transmission paths having the minimum transmission power and error of approximation at the same time at each channel independently. We assume that a Fourier transform F(ω) of a signal f(t) is band-limited approximately under a Nyquist frequency but its side-lobes over the Nyquist frequency are small. We introduce a positive low-pass weight function and we define a set of signals Ξ such that a weighted-square-integral of F(ω) by this weight function is bounded by a given positive constant A. Firstly, we consider a finite number of signals densely scattered in the initial set of signals and present one-to-one correspondences between a signal and its running approximation or the error of approximation in a certain small segment in the time domain. Based on this one-to-one correspondence, we show that any continuous worstcase measures of error in any time-limited interval can be expressed by the corresponding measures of error in the small segment in the time axis. Combining this one-to-one correspondence with the optimum approximation proved by Kida, we present a running approximation minimizing various continuous worst-case measures of error and continuous upper-limit of many measures of the approximation formula, at the same time.

Digital Signal Processing A Computer Based Approach

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TDM-FDM Transmultiplexer: Digital Polyphase and FFT

Abstract: The cascading of a discrete Fourier transform processor and a digital polyphase network is shown to reduce the computation rate in frequency multiplexing-demultiplexing systems to a value close to minimum. Implementation advantages of that technique are pointed out. The highest efficiency is achieved when the number of channels is close to a power of 2, which is demonstrated by the '60-channel frequency-division-multiplexing (FDM)-2 X 30-channel time- division-multiplexing (TDM) transmultiplexer; a rough estimate of the computation rate is carried out in a practical case and appears to be quite within reach of the present technological capabilities. Significant cost advantage over equivalent analog equipment is expected. A digital version of the 12-channel FDM system using the same technique is also considered.

Synthesis of randomness in the radiated fields of antenna array

Abstract: An alternative approach is based on statistically computed signal analysis technique for the design of antenna array exhibiting lower side lobes in their radiation pattern. New and generalized expressions for the array factor of all physically realizable linear antenna arrays are introduced. An algorithm based on the statistically computed signal analysis is designed. By considering the random elements, distance between the sensors, their mean, variance, average amplitude pattern and correlation of the amplitude between the two angles, some mathematical formulations have been done and shown with the help of MATLAB. Based on these generalized expressions, a new way of synthesizing arrays with reduced side lobes is available. It applies to end fire antenna array, which may have either even or odd numbers of sensors with restricted elements spacing. Final expressions shown are a clear relationship between elements excitation and null location in the radiation patterns.

The optimum approximation of a multidimensional filter bank having analysis filters with small nonlinear characteristics

Abstract: Firstly, we present the optimum interpolation approximation for multi-dimensional vector signals. The presented approximation shows high performance such that it minimizes various worst-case measures of error of approximation simultaneously. Secondly, we consider a set of restricted multi-dimensional vector signals that all elements of the corresponding generalized spectrum vector are separable-variable functions. For this set of restricted multi-dimensional vector signals, we present the optimum interpolation approximation. Moreover, based on this property, putting the variables to be identical with each other in the approximation, we present a certain optimum interpolation approximation for generalized filter bank with generalized non-linear analysis filters. This approximation also shows the high performance similar to the above-mentioned approximations. Finally, as a practical application of the optimum interpolation approximation for multi-dimensional vector signals, we present a discrete numerical solution of linear partial differential equations with many independent variables.