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<p>Adaptive filters provide a dynamic and efficient way to process signals in real-time, making them indispensable in numerous applications where adaptation to changing conditions is critical. The Normalized Least Mean Square (NLMS) is one among the most commonly used filters due to its adaptive step size with high convergence speed. In this paper, Delayed NLMS (DNLMS) and Delayed ErrorNLMS (DENLMS) adaptive filter structure variants are tested using Xilinx Spartan 6 series deviceandits performance are analysed.To deplete the clock period and path delay in a combinational circuit, cut-set Retiming technique is proposed in the adaptive filters to achieve higher throughput and lower critical path delay.The performance analysis of conventional NLMS with Retimed DNLMS (RDNLMS) and Retimed DENLMS (RDENLMS)along with the direct form (DF), transposed form (TF) and hybrid forms (TDF) are obtained and tabulated. Further the Signal to Noise Ratio (SNR) and Mean Square Error (MSE) of the different adaptive filters are analysed. The results show that, the proposed TF-RDENLMS adaptive filter implementation has achieved clock period of 13.39ns whereas the conventional un-retimed NLMS adaptive filter structure has 29.96ns, thereby resulting in minimization of 55.3%critical path delay.Xilinx Spartan 6 FPGA series implementation of retimed adaptive filter achieves maximum operating frequency of 74.67&#xa0;MHz as compared to conventional un-retimed structure with 33.37&#xa0;MHz. Hence the speedup factor is approximately 2.24, which means that the proposed retimed adaptive filter operates at about 2.24 times the speed of the conventional un-retimed structure. For the first time in audio processing, cut-set retiming is used in this work’s innovative FPGA implementation of the Delayed Error Normalized Least Mean Square (DENLMS) adaptive filter. The Transposed Form Retimed DENLMS (TF-RDENLMS), which runs on a Xilinx Spartan-6, works at a speed of 74.67&#xa0;MHz, is 2.24 times faster, and has a delay of 13.39 ns. With an SNR of 89.79 dB, it also provides excellent noise reduction. This method balances performance with low power and area overhead, providing a high-speed, effective solution for real-time voice and communication systems. In addition, theproposed filter RDENLMS produces minimum noise with an SNR value of 89.79dB and very low MSE, which indicates that the filter can adapt to fluctuations and instabilities in signal environment.</p>

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Enhanced adaptive filtering in audio systems: normalized least mean square with Cut-Set retiming

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Jagadeeswari M,
  • Rishabavarthani P,
  • Kumarganesh S,
  • Kannadhasan S

摘要

Adaptive filters provide a dynamic and efficient way to process signals in real-time, making them indispensable in numerous applications where adaptation to changing conditions is critical. The Normalized Least Mean Square (NLMS) is one among the most commonly used filters due to its adaptive step size with high convergence speed. In this paper, Delayed NLMS (DNLMS) and Delayed ErrorNLMS (DENLMS) adaptive filter structure variants are tested using Xilinx Spartan 6 series deviceandits performance are analysed.To deplete the clock period and path delay in a combinational circuit, cut-set Retiming technique is proposed in the adaptive filters to achieve higher throughput and lower critical path delay.The performance analysis of conventional NLMS with Retimed DNLMS (RDNLMS) and Retimed DENLMS (RDENLMS)along with the direct form (DF), transposed form (TF) and hybrid forms (TDF) are obtained and tabulated. Further the Signal to Noise Ratio (SNR) and Mean Square Error (MSE) of the different adaptive filters are analysed. The results show that, the proposed TF-RDENLMS adaptive filter implementation has achieved clock period of 13.39ns whereas the conventional un-retimed NLMS adaptive filter structure has 29.96ns, thereby resulting in minimization of 55.3%critical path delay.Xilinx Spartan 6 FPGA series implementation of retimed adaptive filter achieves maximum operating frequency of 74.67 MHz as compared to conventional un-retimed structure with 33.37 MHz. Hence the speedup factor is approximately 2.24, which means that the proposed retimed adaptive filter operates at about 2.24 times the speed of the conventional un-retimed structure. For the first time in audio processing, cut-set retiming is used in this work’s innovative FPGA implementation of the Delayed Error Normalized Least Mean Square (DENLMS) adaptive filter. The Transposed Form Retimed DENLMS (TF-RDENLMS), which runs on a Xilinx Spartan-6, works at a speed of 74.67 MHz, is 2.24 times faster, and has a delay of 13.39 ns. With an SNR of 89.79 dB, it also provides excellent noise reduction. This method balances performance with low power and area overhead, providing a high-speed, effective solution for real-time voice and communication systems. In addition, theproposed filter RDENLMS produces minimum noise with an SNR value of 89.79dB and very low MSE, which indicates that the filter can adapt to fluctuations and instabilities in signal environment.