• Journal of the Korean School Mathematics Society
• /
• v.13 no.3
• /
• pp.345-356
• /
• 2010

Variables and expressions are essential for doing mathematics. Especially abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ are current rules that we usually follow. In this paper, we devised a Card-Game for exercising abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ in calculating expressions, designed a teaching unit for the calculation of expressions using the Card-Game in the variables and expressions strand, and discussed the implications of using the Card-Game for motivating students, cooperative learning, diagnosis and correction of errors, and so on.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.27 no.3C
• /
• pp.256-262
• /
• 2002

This paper presents a novel radix-4 modular multiplication algorithm based on the sign estimation technique (3). The sign estimation technique detects the sign of a number represented in the form of a carry-sum pair. It can be implemented with 5-bit carry look-ahead adder. The hardware speed of the cryptosystem is dependent on the performance modular multiplication of large numbers. Our algorithm requires only (n/2+3) clock cycle for n bit modulus in performing modular multiplication. Our algorithm out-performs existing algorithm in terms of required clock cycles by a half, It is efficient for modular exponentiation with large modulus used in RSA cryptosystem. Also, we use high-speed adder (7) instead of CPA (Carry Propagation Adder) for modular multiplication hardware performance in fecal stage of CSA (Carry Save Adder) output. We apply RL (Right-and-Left) binary method for modular exponentiation because the number of clock cycles required to complete the modular exponentiation takes n cycles. Thus, One 1024-bit RSA operation can be done after n(n/2+3) clock cycles.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.18 no.6
• /
• pp.815-823
• /
• 1993

In this paper, the structure of modified multiplication-free adaptive filter(M-MADF) and convergence analysis are presented. To evaluate the performance of proposed M-MADF algorithm, fractionally spaced equalizer (FSE) is used. The input signals are quantized using DPCM and the reference signals is processed using a first-order linear prediction filter, and the outputs are processed by a conventional adaptive filter. The filter coefficients are updated using the Sign algorithm. Under the assumption that the primary and reference signals are zero mean, wide-sense stationary and Gaussian, theoretical results for the coefficient misalignment vector and its autocorrelation matrix of the filter are driven. The convergence properties of Sign. MADF and M-MADF algorithm for updating of the coefficients of a digital filter of the fractionally spaced equalizer (FSE) are investigated and compared with one another. The convergence properties are characterized by the steady state error and the convergence speed. It is shown that the convergence speed of M-MADF is almost same as Sign algorithm and is faster that MADF in the condition of same steady error. Especially it is very useful for high correlated signals.

• The Journal of the Acoustical Society of Korea
• /
• v.6 no.2
• /
• pp.15-18
• /
• 1987

Multiplication free adaptive digital filtering algorithms are discussed. The proposed. The proposed algorithm uses delta modulation digital filter and the relevant filter weights are updated using the SIGN algorithms to realize an adaptive digital filter without multiplication operations. It is shown that the resulting algorithm can be implemented using simple up/down counting operations. The convergence characteristics of the proposed adaptive digital filtering algorithm and .others are investigated for a system identification problem.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.30B no.6
• /
• pp.28-34
• /
• 1993

An algorithm for MMADF(modified multiplication-free adaptive filter) which need not to multiplication arithmatic operation is proposed to improve the performance of FSE (fractionally spaced equalizer) which reduce the ISI(intersymbol interference) in signal transfer channel. The input signals are quantized using DPCM and the reference signals is processed using a first-order linear prediction filter. The convergence properties of Sign. MADF and M-MADF algorithm for updating of the coefficients of a FIR digital filter of the fractionally spaced equalizer (FSE) are investigated and compared with one another. The convergence properties are characterized by the steady state error and the convergence speed. It is shown that the convergence speed of M-MADF is almost same as Sign algorithm and is faster than MADF in the condition of same steady state error. Especially it is very useful for high correlated signals.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.39 no.2
• /
• pp.137-146
• /
• 2002

In order to remove the intersymbol interference(ISI) phenomenon in data transmission channel, the structure and convergence analysis of the improved multiplication free adaptive digital filter(IMADF) is presented. Under conditions of zero-mean, wide-sense stationary and white Gaussian noise, it is shown that this paper analyze the convergence characteristics of the IMADF with a fractionally-spaced equalizer(FSE). In the experimental results, the convergence characteristics of the IMADF algorithm is almost same as the sign algorithm, but is better than the MADF algorithm. Here, this algorithm has useful characteristics when the correlation of the input signal is highly.

• Journal of the Korean School Mathematics Society
• /
• v.15 no.4
• /
• pp.627-641
• /
• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.26 no.9B
• /
• pp.1226-1235
• /
• 2001

The convergence analysis of the improved multiplication free adaptive digital filter (IMADF) with a fractionally-spaced equalizer (FSE) to remove the intersymbol interference (ISI) in fast data transmission is presented. The IMADF structure use the one-step predicted filter in the multiplication-free adaptive digital filter (MADF) structure using the DPCM and Sign algorithm. In the experimental results, the IMADF algorithm has reduced the computational complexity by use of only the addition operation without a multiplier. Also, under the condition of identical stationary-state error, it could obtain the stabled convergence characteristic that the IMADF algorithm is almost same as the sign algorithm, but is better than the MADF algorithm. Here, this algorithm has effective characteristics when the correlation of the input signal is highly.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.46 no.1
• /
• pp.59-67
• /
• 2009

In this paper, we have proposed the structure of the IMADF(improved modified multiplication-free adaptive filter) to cancel the adaptive noise in biomedical signals. The IMADF structure use the one-step predicted filter in the multiplication-free adaptive digital filter(MADF) structure using the DPCM and Sign algorithm. And then we use the heart phantom model based on the magnetocardiographic (MCG) to test the biomedical signals and analyze the signal of it. Their functions of the heart phantom occur from the multidipole current source. This can play role the same in the real function of the human heart to study it. In the experimental results, the IMADF algorithm has reduced the computational complexity by use of only the addition operation without a multiplier. Also, under the condition of identical stationary-state error, it could obtain the stabled convergence characteristics that the IMADF algorithm is almost same as the sign algorithm, but is better than the MADF algorithm. Here, this algorithm has effective characteristics when the correlation of the input signal is highly.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.47 no.9
• /
• pp.37-43
• /
• 2010

An Interference Cancellation Wireless Repeater transmitts directly amplified the RF signal input to extend the coverage of the base station. Such a repeater inevitably suffers from the feedback interferences due to the environment and the adaptive Interference Cancelling System(ICS) is necessary. In this paper, the Variable Stepsize Complex Sign -Sign(VSCSS) LMS algorithm for ICS is presented. The algorithm can be implemented without multiplication/division arithmetic operation so that the required logic resources can be dramatically reduced in FPGA implementation. The performance of the proposed algorithm was analyzed in comparison with CSS-LMS algorithm and the learning curves obtained from simulation showed an excellent agreement with the theorical prediction. The simulation result with ICS in fading feedback channel environment showed the performance of the proposed algorithm is competible with NLMS algorithm.