It is known that cardiac and respiratory rhythms in electrocardiograms (ECGs) are highly nonlinear and non-stationary. As a result, most traditional time-domain algorithms are inadequate for characterizing the complex dynamics of the ECG. This paper proposes a new ECG sensor card and a statistical-based ECG algorithm, with the aid of a reduced binary pattern (RBP), with the aim of achieving faster ECG human identity recognition with high accuracy. The proposed algorithm has one advantage that previous ECG algorithms lack—the waveform complex information and de-noising preprocessing can be bypassed; therefore, it is more suitable for non-stationary ECG signals. Experimental results tested on two public ECG databases (MIT-BIH) from MIT University confirm that the proposed scheme is feasible with excellent accuracy, low complexity, and speedy processing. To be more specific, the advanced RBP algorithm achieves high accuracy in human identity recognition and is executed at least nine times faster than previous algorithms. Moreover, based on the test results from a long-term ECG database, the evolving RBP algorithm also demonstrates superior capability in handling long-term and non-stationary ECG signals.

Electrocardiograph (ECG) technology is vital for biometric security, and blood oxygen is essential for human survival. In this study, ECG signals and blood oxygen levels are combined to increase the accuracy and efficiency of human identification and verification. The proposed scheme maps the combined biometric information to a matrix and quantifies it as a sparse matrix for reorganizational purposes. Experimental results confirm a much better identification rate than in other ECG-related identification studies. The literature shows no research in human identification using the quantization sparse matrix method with ECG and blood oxygen data combined. We propose a multi-dimensional approach that can improve the accuracy and reduce the complexity of the recognition algorithm.

In this note, we give an alternative approach to introduce the mean value theorem. By first establishing Cauchy-type Mean Value Theorem, we can easily derive other Mean Value Theorem, and their consequences. We believe this approach is more effective in presenting this topic in a typical calculus class.

In recent years, discrete wavelet transform (DWT) provides an useful platform for digital information hiding and copyright protection. Many DWT-based algorithms for this aim are proposed. The performance of these algorithms is in term of signal-to-noise ratio (SNR) and bit-error-rate (BER) which are used to measure the quality and the robustness of an embedded audio. However, there is a tradeoff relationship between the embedded-audio quality and robustness. The tradeoff relationship is a signal processing problem in the wavelet domain. To solve this problem, this study presents an optimization-based scaling scheme using optimal multi-coefficients quantization in the wavelet domain. Firstly, the multi-coefficients quantization technique is rewritten as an equation with arbitrary scaling on DWT coefficients and set SNR to be a performance index. Then, a functional connecting the equation and the performance index is derived. Secondly, Lagrange Principle is used to obtain the optimal solution. Thirdly, the scaling factors of the DWT coefficients are also optimized. Moreover, the invariant feature of these optimized scaling factors is used to resist the amplitude scaling. Experimental results show that the embedded audio has high SNR and strong robustness against many attacks