**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**10

# Search results for: Cross Correlation in the Frequency Domain

##### 10 Integrating Fast Karnough Map and Modular Neural Networks for Simplification and Realization of Complex Boolean Functions

**Authors:**
Hazem M. El-Bakry

**Abstract:**

**Keywords:**
Boolean Functions,
Simplification,
KarnoughMap,
Implementation of Logic Functions,
Modular NeuralNetworks.

##### 9 Integrating Fast Karnough Map and Modular Neural Networks for Simplification and Realization of Complex Boolean Functions

**Authors:**
Hazem M. El-Bakry

**Abstract:**

In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

**Keywords:**
Boolean functions,
simplification,
Karnough map,
implementation of logic functions,
modular neural networks.

##### 8 Improving Quality of Business Networks for Information Systems

**Authors:**
Hazem M. El-Bakry,
Ahmed Atwan

**Abstract:**

**Keywords:**
Usability Criteria,
Computer Networks,
Fast
Information Processing,
Cross Correlation,
Frequency Domain.

##### 7 A Fast Neural Algorithm for Serial Code Detection in a Stream of Sequential Data

**Authors:**
Hazem M. El-Bakry,
Qiangfu Zhao

**Abstract:**

In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.

**Keywords:**
Fast Code/Data Detection,
Neural Networks,
Cross Correlation,
real/complex values.

##### 6 Fast Complex Valued Time Delay Neural Networks

**Authors:**
Hazem M. El-Bakry,
Qiangfu Zhao

**Abstract:**

**Keywords:**
Fast Complex Valued Time Delay Neural
Networks,
Cross Correlation,
Frequency Domain

##### 5 A New Implementation of PCA for Fast Face Detection

**Authors:**
Hazem M. El-Bakry

**Abstract:**

**Keywords:**
Fast Face Detection,
PCA,
Cross Correlation,
Frequency Domain

##### 4 Fast Painting with Different Colors Using Cross Correlation in the Frequency Domain

**Authors:**
Hazem M. El-Bakry

**Abstract:**

**Keywords:**
Fast Painting,
Cross Correlation,
Frequency Domain,
Parallel Processing

##### 3 Fast Object/Face Detection Using Neural Networks and Fast Fourier Transform

**Authors:**
Hazem M. El-Bakry,
Qiangfu Zhao

**Abstract:**

**Keywords:**
Conventional Neural Networks,
Fast Neural
Networks,
Cross Correlation in the Frequency Domain.

##### 2 A Modified Cross Correlation in the Frequency Domain for Fast Pattern Detection Using Neural Networks

**Authors:**
Hazem M. El-Bakry,
Qiangfu Zhao

**Abstract:**

**Keywords:**
Fast Pattern Detection,
Neural Networks,
Modified Cross Correlation

##### 1 A Novel Hopfield Neural Network for Perfect Calculation of Magnetic Resonance Spectroscopy

**Authors:**
Hazem M. El-Bakry

**Abstract:**

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)" that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.

**Keywords:**
Hopfield Neural Networks,
Cross Correlation,
Nuclear Magnetic Resonance,
Magnetic Resonance Spectroscopy,
Fast Fourier Transform.