Adaptive Filter Design using LMS Algorithm and Sigma Delta Modulation

Authors: Hiba Khan, Mr. Rakesh Mandliya

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Abstract

This paper presents the implementation and design of adaptive noise cancelling filters using the hybrid LMS and Sigma Delta Modulation approach. It has been clearly shown how the process of Sigma Delta Conversion used in ADCs can achieve higher speeds even after employing Oversampling above Nyquist rate with the LMS algorithm. The various parameters affecting the design and performance of the Delta Sigma employed filter design have been analyzed. Stability considerations of higher order sigma delta modulators have also been analyzed to attain an optimized approach to decide upon the design of the SDM. Variation in the SNR has been shown with changes in Over Sampling Rate.

Introduction

Adaptive filter design finds its applications in several fields of signal processing such as speech processing, analog to digital conversion, image processing etc. The very essence of adaptive filtering rests on the principle that the noise conditions faced by signals can vary. Adaptive filter adjust their coefficients to minimize an error signal and can be realized as finite impulse response (FIR), infinite impulse response (IIR), lattice and transform domain filter. Although real world signals are analog, it is often desirable to convert them into the digital domain using an analog to digital converter (ADC). Signal processing in the digital domain is useful in digital storage, biomedical applications, and industrial applications - from instrumentation to communication. Sigma Delta Modulators achieve a high degree of insensitivity to analog circuit imperfections, thus making them a good choice to realize embedded analog-to-digital interfaces. Application based and sophisticated design techniques demand Radio Frequency Identification Techniques which find its application in object tracking, etc. Sigma Delta ADC is high resolution ADC and acts as a major building block in RFID applications.

Conclusion

In this work, analysis of lower order and higher order Sigma Delta Modulator in conjugation with the LMS algorithm has been done on the basis of Signal to Noise Ratio and Effective Number of Bits. The noise shaping property of Sigma Delta Modulator has made it popular in the application where high Signal to Noise Ratio is desired. The significant property of noise shaping, pushes the noise in the range out of band of interest which reduces the requirement of sharp cut off anti aliasing filter. As, the oversampling ratio increases the Signal to Noise Ratio also increases. Higher SNR values can be achieved at lower OSR also, if higher orders of modulators are used. But as the number of integrators in the modulator increases this affects in the position of poles of the Noise Transfer Function which can make the loop filter unstable. It can be concluded from the results and conclusions that the sigma delta scheme is a highly efficient technique that can be utilized for the design of Adaptive Filters which yield low Quantization Noise due to the noise shaping principle employed inherently in the proposed technique.