• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.9
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• pp.33-42
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• 1997

Fixed-point optimization utility software that can aid scaling and wordlength determination of digital signal processign algorithms written in C or C$\^$++/ language is developed. This utility consists of two programs: the range estimator and the fixed-point simulator. The former estimates the ranges of floating-point variables for automatic scaling purpose, and the latter translates floating-point programs into fixed-point equivalents for evaluating te fixed-point performance by simulation. By exploiting the operator overloading characteristics of C$\^$++/ language, the range estimation and the fixed-point simulation can be conducted just by modifying the variable declaration of the original program. This utility is easily applicable to nearly all types of digital signal processing programs including non-linear, time-varying, multi-rate, and multi-dimensional signal processing algorithms. In addition, this software can be used for comparing the fixed-point characteristics of different implementation architectures.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.3
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• pp.454-468
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• 1997

This paper presents a bitwidth optimization algorithm for efficient hardware sharing in digital signal processing system. The proposed algorithm determines the fixed-point representation for each signal through bitwidth optimization to generate the hardware requiring less area. To reduce the operator area, the algorithm partitions the abstract operations in the design description into several groups, such that the operations in the same group can share an operator. The partitioning result are fed to a high-level synthesis system to generate the pipelined fixed-point datapaths. The proposed algorithm has been implemented in SODAS-DSP an automatic synthesis system for fixed-point DSP hardware. Accepting the models of DSP algorithms in schematics, the system automatically generates the fixed-point datapath and controller satisfying the design constraints in area, speed, and SNR(Signal-to-Noise Ratio). Experimental results show that the efficiency of the proposed algorithm by generates the area-efficient DSP hardwares satisfying performance constraints.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.647-649
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• 2004

When a controller is implemented by a one-chip processor with fixed-point operations, the finite alphabet problem usually occurs since parameters and signals should be taken in a finite set of values. This paper formulates PID finite alphabet PID control problem which combines the PID controller with the finite alphabet problem. We will propose a PID parameter tuning method based on an optimization algorithm under the finite alphabet condition. The PID parameters can be represented by a fixed-point representation, and then the problem is formulated as an optimization with constraints that parameters are taken in the finite set. Some simulation are to be performed to exemplify the performance of the PID parameter tuning method proposed in this paper.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.11C
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• pp.1491-1497
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• 2004

The psychoacoustic model in MPEG audio layer-III (MP3) encoder is optimized for the fixed-point processing. The optimization process consists of determining the data word length of arithmetic unit and the algorithm for transcendental functions that are often used in the psychoacoustic model. In order to determine the data word length, we defined a statistical model expressing the relation between the fixed-point operation errors of the psychoacoustic model and the probability of alteration of the allocated bits doe to these errors. Based on the simulations using this model, we chose a 24-bit data path and constructed a 24-bit fixed-point MP3 encoder. Sound quality tests using the constructed fixed-point encoder showed a mean degradation of -0.2 on ITU-R 5-point audio impairment scale.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.11 s.353
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• pp.95-117
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• 2006

In this paper, we describe the optimization of the link-level performance and the complexity of floating-point and fixed-point methods in IEEE 802.16e OFDMA/TDD mobile modem. In floating-point design, we propose the channel estimation methods for downlink traffic channel and select the optimized method using computer simulation. So we also propose efficent algorithms for time and frequency synchronization, Digital Front End and CINR estimation scheme to optimize the system performance. Furthermore, we describe fixed-point method of uplink traffic and control channels. The superiority of the proposed algorithm is validated using the performances of Detection, False Alarm, Missing Probability and Mean Acquisition Time, PER Curve, etc. For fixed-point design, we propose an efficient methodology for optimized fixed-point design from floating-point At last, we design fixed-point of traffic channel, time and frequency synchronization, DFE block in uplink and downlink. The tradeoff between performance and complexity are optimized through computer simulations.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.1-9
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• 2023

Our aim in this paper is to give some new proofs to fixed point theorems due to Abdou [1] for mappings satisfying Reich type contractions in modular metric spaces. We removed the restriction that ω satisfies the ∆₂-type condition imposed on the results of [1]. Furthermore, Lemma 2.6 of [1] which was crucial in the proofs of the results of [1] is not needed in the proofs of our results. Our method of proof is simpler and interesting.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.957-988
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• 2023

We define new classes of expansive-type mappings in the setting of modular 𝜔^G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔^G-complete modular 𝜔^G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.361-391
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• 2024

In this paper, a pair of ω-compatible self mappings in the setting of modular G-metric space is defined. We prove the existence and uniqueness of common fixed point of pairs of ω-compatible self mappings in a G-complete modular G-metric space. Furthermore, we give an example to justify our claims. The results established in this paper extend, improve, generalize and complement some existing results in literature.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.101-116
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• 2005

Using the iterative method, we derive an controller realization of the bilinear system, which is resulted from the system reformulation. We utilize Banach Fixed Point Theorem to support proposed controller, and the simulation results are also illustrated to verify usefulness of this technique.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).