In this paper we present the Multiple Sub-Filters (MSF) parallel structure, LMS adaptive algorithm, for acoustic echo cancellation. The performance of the MSF based echo canceller has been compared with conventional echo canceller which is a Single Long Filter (SLF) used to model the impulse response of the acoustic echo channel. The convergence performance of the MSF parallel structure is studied for common error and different error adaptive algorithms. Simulation results show that MSF with both adaptation algorithms provide better convergence over the SLF. However, the steady state error performance of the different error adaptation algorithm is poor as compared to that of common error as well as that of SLF adaptation algorithm. The sacrifice in steady state error performance can be compensated to achieve fast convergence by introducing independent adaptation step size as there is decoupled weight updation equation of each sub-filter. The combination of both the adaptation algorithm in MSF can achieve a trade-off between steady state and convergence rate.

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This paper contributes a novel design of sensor with a heart-shaped dual-core photonic crystal fiber (PCF) to detect cancerous cells in human cervical, blood, adrenal glands, and breast. Cancer-infected cells and their normal cells are considered in liquid form having their own refractive indices. In the designed PCF, the two heart-shaped cores separated by a large circular air hole serve as two independent waveguides. The large circular air hole is infiltrated by sample cells from different body parts. Detection of cancer-contaminated cells by the proposed PCF is based on the mode-coupling theory. According to the mode-coupling theory, the guided optical light transmits periodically from one core to another, throughout the PCF length. During this transmission, the optical light interacts with the cancerous cell, which is filled in the center air hole of the PCF. Due to this interaction, the dip wavelength of the transmission spectrum is sensitive to the corresponding cancerous cell filled in the center air hole of the PCF. The variation in the PCF transmission spectrum for cancerous cells and their normal cells is observed by using the finite element method. The dip wavelength shift of the cancer cell in reference to its normal cell has been measured from the transmission spectrum to determine the sensing performance of the proposed sensor. The sensitivity achieved of the proposed sensor for cervical cancer cell, blood cancer cell, adrenal gland cancer cell, and breast cancer cells are 7916.67 nm/RIU, 8571.43 nm/RIU, 9285.71 nm/RIU, and 10,000 nm/RIU, respectively, with a maximum detection limit of 0.024. Therefore, the proposed PCF sensor suggests high sensitivity with a rapid cancer detection mechanism.

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Adaptive filters are very useful in the present world. It is a well known fact that the performance of adaptive filters is highly dependent upon the type of input sequence. Further the uncorrelated input shows a better convergence speed than the correlated input. But most of the real world signals are correlated. Various methods have been proposed to preprocess these inputs by transforming these inputs to different domain and then filtering. These include DFT-LMS, DCT-LMS, DST-LMS and DWT-LMS among some of the popular algorithms.In this paper we analyzed and compared convergence properties of these different transform domain algorithms via computer simulations. The results showed that DWT-LMS perform better than others under certain criterion. Index Terms-Adaptive filters, Convergence, Least Mean Square (LMS), Discrete Cosine Transform LMS (DCT-LMS), Discrete Sine Transform LMS (DST-LMS), Discrete Wavelet Transform (DWT-LMS).