[Removal of Power Line Interference and other Single Frequency Tones from Signals]

Transcription

1 Department of Computer Science and Electronics 08 [Removal of Power Line Interference and other Single Frequency Tones from Signals] MSc Thesis REPORT LEVEL: 20 P, D-LEVEL D A report submitted to the Department of Computer Science and Electronics, Mälardalen University, in part fulfilment filment of the Degree of Master of Science in Electronics with Biomedical Engineering By Sheeraz Gul Tareen Stn05002@student.mdh.se Tutor: Mikael Ekström Supervisor: Prof. Rashid Baig 1

2 Table of Contents DEDICATION 7 ACKNOWLEDGEMENTS 8 ABSTRACT 9 1 CHAPTER Problem Description The Purpose of Thesis Report Layout Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter References 12 2 CHAPTER General Overview Heart Mechanism and Purpose of ECG Diagnosis Background and Motivations Thesis Specifications Thesis Aims and Objectives The Choice for MATLAB Software 17 3 CHAPTER Digital Signal Processing (DSP) What are Filters What are Digital Filters? Advantages of Digital Filters Types of Digital Filters Computational Properties and structure of Digital Filters Algorithm 21 2

3 3.7 DIGITAL FILTER ORDER, STEP-SIZE AND COEFFICIENTS Order of a Digital Filter Step-Size of a Digital Filter Coefficient of the Digital Filter CHAPTER Introduction Explanation of Adaptive Filter Adaptive Filters and Digital Signal Processing Adaptive Filtering The General Structure of Adaptive Filters Performance, Stability and Robustness of the Adaptive Algorithm Convergence Criteria for Adaptive Algorithm System Identification Configuration Using an Adaptive Filter 29 5 CHAPTER Introduction Advantages of Filters and Adaptive Algorithm Finite Impulse Response (FIR) FIR Filters Advantages and Disadvantages Advantages: Disadvantages: Comparison between FIR and IIR Filters Adaptive FIR Signal Processor 34 6 CHAPTER Adaptive Filter Algorithms Introduction to LMS Algorithm Overview of the Structure and Operation of the LMS Algorithm Design of an Adaptive Filter Algorithm Noise Cancellation Adaptive Noise Cancellation Interference Cancellation by Adaptive Filtering 42 7 CHAPTER Main Objective Design by DSP Technique 45 3

4 7.3 MATLAB Software Implementation Verification for Refinement of Signal by LMS Removal of Power Line Interference (50 Hz) from ECG Signal by LMS Algorithm Removing of Harmonics and High Frequency Noise from Original ECG Signal Algorithm Implementation and Verification 53 8 CHAPTER CONCLUSION AND FUTURE RESEARCH Conclusion Suggestion for Future Work/Future Enhancement 56 9 APPENDIX A MATLAB CODE FOR ECG SIGNAL APPENDIX C MATLAB CODE FOR HARMONICS AND HIGH FREQUENCY NOISES FROM ECG SIGNAL BY GENERAL NOTCH REJECTION FILTER REFERENCES 65 4

5 List of Figures FIGURE 21 ECG signal with QRS complex 14 FIGURE 4.1 Principle of an Adaptive Filter 26 FIGURE 4.2 The general structure of an adaptive filter 27 FIGURE 4.3 System Identification Configuration for Adaptive Filter 29 FIGURE 5.1 FINITE IMPULSE RESPONSE (FIR) FILTER STRUCTURE 34 FIGURE 5.2 The Adaptive Signal Processor 38 FIGURE 6.1 LMS ADAPTIVE ALGORITHM 37 FIGURE 6.2 OUTLINE OF ADAPTIVE TRANSVERSAL FILTER 39 FIGURE 6.3 NOISE CANCELLATION EXAMPLE 40 FIGURE 6.4 BLOCK DIAGRAM OF ADAPTIVE NOISE CANCELLER 41 FIGURE 6.5 INTERFERENCE CANCELLATION BY ADAPTIVE FILTERING 42 5

6 Mind is not a vessel to be filled, but a fire to be kindled. 6

7 DEDICATION I owe immense sense of gratitude to my beloved Parents and family members who supported me financially as well as morally, throughout my career. I also dedicate the thesis to my university teachers who remained the source of encouragement throughout. Finally, I would like to thanks my sister Nasreen Akhtar who is educationist, friend Noor who is doctor and all other friends for their support and encouragement during the critical time to finish this greatest task of my life. 7

8 ACKNOWLEDGEMENTS I start with the name of Almighty Allah for providing me with the unique opportunity to finalise this thesis. It would not have been possible for me to complete this thesis Removal of Power Line Interference and other Single Frequency Tones from Signals, except for the able guidance and constructive suggestions of my thesis supervisor (Prof. Rashid Baig), thesis tutors (Mikael Ekström). Their supervision and encouragement has made it possible for me to complete this task, which is very important for practical work. 8

9 ABSTRACT Removal of Power Line Interference and other Single Frequency Tones from Signals With the latest advancements in electronics, several techniques are used for removal of unwanted entities from signals especially that are implied in the most sophisticated applications. The removal of power line interference from most sensitive medical monitoring equipments can also be removed by implementing various useful techniques. The power line interference (50/60 Hz) is the main source of noise in most of bio-electric signals. The thesis report presents the removal of power line interference and other single frequency tones from ECG signal using the advanced adaptive filtering technique with LMS (least mean square) algorithm. The thesis is based on digital signal processing (DSP) techniques with MATLAB package, with the emphases on design of adaptive LMS algorithm. The adaptive interference removal technique can be used for removal of power line interference in various potential applications such as recording Electrocardiograms (ECG), Electroencephalogram (EEG) and Electromyogram (EMG). MATLAB package will be used in the thesis work which is a powerful tool for the interactive design in most of the scientific applications and complex engineering calculations. As an additional in order to achieve the goal of thesis it will also be investigated and implemented for the removal of harmonics (hum) and high frequency noise from ECG signal by using general notch rejection filters, which are partial milestone for the thesis. 9

10 1 CHAPTER-1 THESIS INTRODUCTION 1.1 Problem Description The medical monitoring devices are more sensitive for the biomedical signal recording and need more accurate results for every diagnosis. It is complicated to get accurate result for every biomedical signal s recording while patient is diagnosis by medical monitoring equipments such as ECG, EEG and EMG. The low frequency signal is destroyed by power line interference of 50/60 Hz noise, this noise is also source of interference for biomedical signal recording. The signal can also be corrupted by electromagnetic field (EMF) by the machinery which is placed nearby. [1] The frequency of power line interference 50/60 Hz is nearly equal to the frequency of ECG, so this 50/60 Hz noise can destroyed the output of ECG signal while the patient is diagnosis at hospital or some where else. The recording of ECG signal can not give accurate result due to the power supply or by environment. [1] There are many reasons for the corruption of ECG signal while recording in hospital or some other place due to the external interference which comes from power transformer or high voltage electric power lines and internal interference comes from the internal power supplies. Other problem occurs by harmonics and high frequency noises. In a noise signal, the signal component holds harmonics with different amplitude and frequency. The harmonics frequency is integral multiple of fundamental frequency such as 50Hz. Due to these interferences the quality of ECG signal can not be ideal so it is needed to improve the quality of required output of ECG signal. 1.2 The Purpose of Thesis The fundamental purpose of this thesis is to remove 50/60 Hz noise and other single frequency tones from ECG signal by the designing and implementation of least mean square (LMS) algorithm based upon the FIR filters using MATLAB environment. The additional milestone of the thesis is to investigation and implementation of the removal of harmonics and high frequency noise by using general notch rejection filters from ECG signal in MATLAB environment. 10

11 1.3 Report Layout This section provides a summary of the all the chapters covered in this report Chapter-1 This chapter gives the introduction to the thesis, the problem description, purpose and also detail of report layout of the thesis report Chapter-2 This chapter provides the details of problem of power line interference in ECG. And also present the general overview, heart mechanism & purpose of ECG diagnosis, description of the thesis, details of the background and motivation, thesis specifications, aim & objectives of the thesis and this chapter also contain why using MATLAB package Chapter-3 This chapter details the basic theory of digital filters, digital signal processing, what are filters & digital filters, advantages of digital filters, categories of digital filters, computational property & structure of digital filters algorithm and also contains an overview on the digital filter s order, step-size & coefficient Chapter-4 This chapter provides the introduction of adaptive filters and its explanation. It also provides the detail of adaptive filters with respect to digital signal processing, adaptive filtering concept, general structure for adaptive filtering and performance, stability and robustness of adaptive algorithm. This chapter also gives the details of convergence criteria and system identification configuration using an adaptive filter Chapter-5 This chapter provides the introduction to adaptive algorithm, advantages of adaptive filters and adaptive algorithm, FIR filters details, its advantages and disadvantages. It also gives a brief comparison of the two filters and why the FIR filters and LMS algorithm is best suited for this thesis. It also gives the brief description of the filtering solution for removal of power line AC interference and adaptive FIR filter processor. 11

12 1.3.6 Chapter-6 This chapter presents the brief description of adaptive filter algorithm and the least mean square (LMS) algorithm which is to be employed in this thesis to perform the noise cancellation. It also gives the overview of the structure & operation of the LMS algorithm, the design of adaptive filter algorithm, noise cancellation adaptive noise cancelation and interference cancellation Chapter-7 In this chapter the design, analysis and simulation results are described. It also give the details of main objective & how design by DSP technique and the technique of software implementation & verification for refinement for signal by LMS, which includes removal of power line interference from ECG signal & removal of power line interference from voice signal and also described its simulation results. It also gives the detail and graphs of removing of humming and high frequency noise from ECG signal. Finally the algorithm implementation and verification has been presented Chapter-8 This chapter provided the conclusion and future research. It also gives the detail of the thesis goal, its achievement and what has been concluded after completion this thesis References The list of information gathered from books, university library database, journals and internet sites. 12

13 2 CHAPTER-2 INTRODUCTION TO ECG SIGNAL WITH POWER LINE INTERFERENCE 2.1 General Overview The electric power lines are main source of electricity transportation from grid station to the consumers. Power transformers are used for the transform of voltage which is generated from the grid station. The purpose of electricity generation is for the powering electronic & electrical technologies acquired from various sources of energy. The source of energy for first power plant was wood, while today it relies mainly on coal, nuclear energy, natural gas, hydroelectric and petroleum geothermal sources. [2] Due to the large amount of power involved, transmission normally takes place at high voltages (110 kv or above). Electricity is usually transmitted over long distance through overhead power transmission lines. Most transmission lines operate with three-phase alternating current (AC). The standard frequency in North America is 60 Hz; while 50 Hz in rest of world. The power line interference 50/60 Hz is the source of interference in bio potential measurement and it corrupt the biomedical signal s recordings such as Electrocardiogram (ECG), the Electroencephalogram (EEG) and the Electromyography (EMG) which are extremely important for the diagnosis of patients. It is hard to find out the problem because the frequency range of ECG signal is nearly same as the frequency of power line interference. The figure 2.1 shows the one period of uncorrupted ECG signal with QRS complex. The ECG signal contains the information within the frequency range of around 50 Hz that is why it is called QRS complex. The QRS complex is a waveform which is most important in all ECG s waveforms and it comes into view in usual and unusual signals in an ECG. [3] 13

14 Figure 2.1- ECG signal with QRS complex [3] Adaptive filters are used to eliminate the power line interference (60 Hz) and they are proposed to obtain the impulse response of the normal QRS complex. [4] In the figure above, an uncorrupted ECG signal shows an original signal graph for ECG signal which demonstrate the diagnosis of heart activities for heart patient. Consequently, it is analysis that how to remove the power line interference of 50/60 Hz which is a problem for biomedical signal measurement. Electromagnetic interface (EMI) from 50/60 Hz power line noise is present in cable holding ECG signal. [5] Several solutions for the removal of power line interference have been expressed. The main source of interference is AC power line interference. The interference is caused by magnetic fields as well as by the electric fields. When special signal recording techniques are applied, which minimize the interference therefore some AC noise remains as a consequence of unbalanced input impedances. Further removal of AC noise must be accomplished either by analog or digital filters Heart Mechanism and Purpose of ECG Diagnosis The heart is a muscular organ, it pump the blood throughout the body and collecting blood circulating back from the body. [6] Electrical impulses are the main source of generation of regular normal heartbeat. The heart muscle must be activated electrically before the beginning of its mechanical function. When the electrical abnormalities of the heart occur then the heart cannot pump blood properly and supply enough to the 14

15 body and brain. This can cause unconsciousness within second and death within minutes. [7] An ECG recording is important for clinical diagnosis and treatment; it is a graphical recording of electrical impulses generated by heart. The ECG is needed to be done when chest pain occurred such as heart attack, shortness of breath, faster heartbeats, irregular heartbeats, high blood pressure, high cholesterol, check the heart s electrical activity. [6] 2.2 Background and Motivations. The Electrocardiograph (ECG) signal is an electrical signal generated by the heart s beats and can be used to examine some of the functions of the heart. The ECG signal can be distorted with noise of 50/60 Hz and by some other sources. The noise from electric power system is a major source of noise during the recording or monitoring of ECG. [8] Different noises have different frequencies; the noise with low frequency is being problem with ECG signal and some time high frequency noises also interfere ECG i.e. mobile phone. If the physical or mathematical variable changes rapidly then it can be high frequency and if it changes slowly then it would be low frequency. If the variable does not change at all then it is said that it has zero frequency. The frequency is measured in cycle/second or in "Hertz". For example the electric power used in daily life in United State is 60 Hz and 50 Hz in the rest of world. Most of the electronic devices such as ECG, transmitter, receiver, computer etc get power from power line. The 50 Hz alternative current (AC) is reduced in voltage, rectified and than filter to obtain low voltage direct current (DC). This is used to give power to those electronic devices. [9] Numbers of adaptive filter solution had been proposed for noise cancellation in ECG. The adaptive filter remove or reduces the mean squared error between primary input (ECG signal) and the reference input (noise with ECG signal) [4] While recording ECG signal, the critical problem is unwanted noise from power line interference. There are different noises which affect ECG signal but 50/60 Hz interference from power line distribution is most critical and also 1 Hz power line interference due to patient s movement. Various methods were developed for the removal of power line interference from last two decade. The suitable and prime methods were based on ECG filtering. [10] There have been different filtering solutions, which were introduced for the removal of power line AC interference. The crucial problem of power line interference was found in ECG signal. In this project the power line interference of 50/60 Hz is major purpose to remove it from ECG signal. Different filtering solution has been studied to find out the 15

16 best solution for the removal of power line interference from ECG signal. Digital filter has been selected to overcome this problem; there are few filtering solutions which were examined before to manipulate the power line interference from signal which can be divided into following categories. [10]. Low Pass Filters General Notch-Rejection Filters Adaptive Filters Global filters In the thesis two filtering solutions has been chosen for the removal of power line interference, its respective harmonics and high frequency noise from Original ECG signal. The removal of power line interference (50Hz) from ECG signal can be removed by adaptive filtering while the harmonics and high frequency noise can be removed by implementing general notch rejection filters. 2.3 Thesis Specifications. The fundamental aim of thesis is to analyze the power line interference by starting a simple approach from fundamentals of digital signal processing (DSP), digital filters and then adaptive filters with LMS implementations. The power line interference, some other signal frequency tones signals and harmonics impacts on the ECG signal which can be described by MATLAB software simulation. The main objective is to remove 50 Hz power line interference from ECG signal by using LMS adaptive algorithm based upon FIR filter. The additional milestone of the project is to remove harmonics and high frequency noises by using general notch rejection filters and windowed sinc low pass filters. This method can be employed in a number of useful applications in which the prime concern is to get the original ECG signal and the contaminated entities are critically removed. 2.4 Thesis Aims and Objectives. To describe the power line interference, main cause of power line interference in ECG Signal and to carry out a literature survey on removal of power line interference from ECG signal. To give solution for the removal of power line interference in ECG signal and to investigation of different methods and to point out the best possible methodology for the removal of power line interference. To search for the adaptive filtering technique for removal of 50/60 Hz power line frequency interference and to have extensive knowledge in, DSP i.e. adaptive filtering, FIR, IIR, LMS algorithm etc 16

17 To illustrate the suitable method or process to remove the noise, other unwanted components, undesired tones and interferences from information signal. To search for the best possible method available to be used for the removal of power line interference through the internet, journals & books and analysis of different kind of signals using MATLAB software. In additional to investigate and analyze the harmonics and high frequency interference in original ECG signal and to remove these noises by using general notch rejection filters and windowed sinc low pass filter. In the project, the deductive experimental research strategy is preferable, in this view the investigation, observation and testing to get the desired objectives can be accomplished on the basis of experimental works and to continue the future research and development regarding this view. 2.5 The Choice for MATLAB Software MATLAB is commercial software product, which is available from the Mathworks. It consist of main engine having strong mathematical function built-in which perform the computational and other extended-function libraries for special purpose applications. [11] The MATLAB software provides a variety of functions that make it easy and flexible while simulation for interactive designing, advance analyzing, exploration and visualizing signals, filters and windows. It provides the tools for finite impulse response (FIR) and infinite impulse response (IIR), digital filter design, implementation and analysis. It also provides the toolbox for application such as speech & audio processing, medical imaging & instruction, wired & wireless communication and financial modeling & analysis. [12]- [14] MATLAB has set of construct for plotting scientific graphs from raw or computed data. [11] It is a high performance language, most productive development and interactive environment for engineering and technology implementations software package. MATLAB enables to perform different functions which included, electronic programming, technical computing applications, scientific & engineering graphical illustration, accurate numerical calculation, algorithms development, application development including graphical user interface building, graph and report or software simulation etc. [12]- [14] 17

18 3 CHAPTER-3 BASIC THEORY OF DIGITAL FILTERS 3.1 Digital Signal Processing (DSP) Digital signal processing (DSP) is well-known as compared to analog signal processing in different applications. [13] The signals are time varying quantities which carry information i.e. audio signal, video signals, biological signals (electrical pulses from the heart) and communications signals. [11] A digital signal is define as the signal that has discrete amplitude and time. These signals are represented by sequences of numbers with finite precision and can be used when processing information by computer. [15] The processing of the signals which deals with sound and images are known as Digital Signal Processing. In DSP the digital signal processor can be a small microprocessor or a large programmable digital computer, which perform the desired operations on the input signal. [16] The application of Signal Processing has grown very fast and implemented the advanced techniques in speech recognition, image recognition, image enhancement, audio enhancement, noise reduction, speech & audio encoding and storage, digital music, communication and data transmission, biometrics, biomedical applications, radar, sonar and military applications. [13] [11] Digital signal processing systems are introduced in many different applications such as multimedia, video recording, CD player, mobile phones, computers and modem, DSP systems acquired famous due to their reliability, accuracy, small physical sizes and flexibility. 3.2 What are Filters A filter is a device when a signal is given; it changes to some desired form by changing its shape, amplitude, frequency or phase frequency. They are usually employed to remove the noise, extract information signals and separate two or more combined signals. [17] There are two main classes of filter, analog and digital filters. These filters are used for different applications; the selection for the filter depends upon the required output of the application. 18

19 3.3 What are Digital Filters? Digital filters and signal processing systems or algorithms which are classified as discrete-time systems and are normally implemented on a digital signal processing (DSP) chip or special purpose hardware and software in a general purpose computer. These software approaches are in a mean of computational structures. Analog filters are replacing by the digital filters because of digital filter s well known advantages and good performance in the advanced era of communication system. [18] Digital filters are in smaller size, much lower component tolerances, greater accuracy, greater reliability, ability to share multiple filtering tasks than analog filters. [19] There are two types of filters that can be design as analogue or digital filters. Digital filters are progressively replacing analogue filter day by day. [20] The designing of the digital filter needed to remove the unwanted noise from the original signal i.e. if the a signal x(k) is processed in a discrete system the output signal will be y(k), if this output signal y(k) is different from the original signal x(k) then it must be needed to modify the system to get the required output. Then digital filter will be the solution to manipulate this problem. [19] Digital filters are extremely used in noise cancellation, echo cancellation and also in the field of biomedical engineering to remove unwanted noise from ECG, EMG and EEG. As with the advancement in the technology many signal manipulations like multiplication, subtraction, differentiation, PID and filtering which were previously carried out through dedicated hardware are now implemented equally well or even better by the use of Processors (microprocessors, DSP chips, microcontrollers, CPLDs etc).once a signal is captured and converted through ADC, it becomes a numerical value with certain characteristics, any kind of mathematical algorithm then can be written to manipulate this value. After the required manipulation the desired output can be produced using the DAC converter. Digital Filters are same as the analogue filters as far as their functions is concerned, which is to separate a desired portion of signal frequencies from the undesired ones but their physical realization is quite different as in essence digital filters are different mathematical relations written in a specific algorithm meant to be executed by computers. 3.4 Advantages of Digital Filters The digital filters can provide many advantages; a brief summery is given below. 1 The charm of the digital filters lies in the fact that digital filters are realized in the form of piece of software so can be adapted for any required amendment with out any increase in cost or effort on the electronic circuit. 19

20 2 As digital filter is a programmable filter are often implemented in a computer using a high level programming language so it can be reused if required to produce cost effective solution. In digital filters for digital design the characteristics of digital component do not change over time [21] 3 Plenty of support is available for design and testing of digital filters in the form of CAD and other pre-built package on a general-purpose computer or workstation. 4 By using programmable processes it can be easily modified to change its frequency response or other characteristic. [17] 5 Realization of the digital filters can be made using the generic hardware (PC, DAC, ADC, CPLDs) without indulging in the design of specific hardware, which also helps in reducing the cost and time required in this process. 6 Digital filters can be used in biomedical instruments where frequency is very low and analog filters are unpractical. [17] 7 Digital filters are most common use in any modern communication system and digital systems are unaffected by temperature variation. [21] 8 With the advancement in technology the digital filters can be managed at low frequency signals precisely. The technology of the DSP is increasing very fast, so the digital filter are applied for the high frequency signal as well i.e. RF (radio frequency) domain, which in the past was the limited to analog technology. [22] 9 Digital filters can be seen as the direct result of the advancement made in the computers and computing technology so it will continue to benefit from the increase in speed and power of computing chips in the future. 10 Digital filters are small in size, consume less power and can be implemented with less cost and it also store data for future use. [17] 11 Digital filters can made accurate processing, permits the implementation of many different operations and become more economical. [19] 3.5 Types of Digital Filters The most imperative tools of DSP are a digital filtering. The separations of signals are principally utilized by electronic filters, which are combined and the refurbishment of distorted signals that can be distorted due to the certain reasons. Digital filters are implemented in real time, the desired output is removal of noise and they are implemented in dedicated hardware or computer using a high level language. [17] By 20

21 the software control, digital filter can be easily changed and are well-suited to do this task as compared to analogue filters because of their outstanding results. The digital filters are divided into two basic types, Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. [23]- [13] - [24] which are known as non recursive and recursive filters. [25] These types of digital filters can perform paramount required tasks yet they are categorized either as non recursive filter known as Finite Impulse Response (FIR) filters or a recursive filter known as Infinite Impulse Response (IIR) filters.[26]- [25] The term non recursive filter & finite impulse response (FIR) filter and recursive filter & infinite impulse response (IIR) filter are almost synonymous. [19]. Non recursive that as implied by the name has a finite length impulse response and recursive that has an impulse response of infinite length. Both types of filters can be used in the realization of the noise cancellation but an FIR filter was chosen since it is simple and stable. [26] The variety of design methods has been involved for the designing of digital filters to meet different specifications. The lowest order filter is chosen to avoid the overdesign. The choice between the filter type (recursive and non recursive) is done due to the computational property and the storage required for the implementation. 3.6 Computational Properties and structure of Digital Filters Algorithm The computational property of digital filters algorithm is most important for its structure. For any digital filter structure it must be needed to work out its computational property because the computational property of the digital filter algorithm affect on the performance of digital filter. For the description of computational properties of digital filter algorithm latency and throughput are used. Latency is the time for the data flow which applied to a general digital algorithm to reach the output. Throughput is the measurement of frequency input data applied to a system. [21] The structure of digital filter can be described by signal flow graph, they are used to convert a given transfer function into computational procedure. The structure used is depending on type of the filter. In IIR filter s commonly used forms are direct form, cascade form and parallel form and in FIR filters the direct form or transversal structure is most widely used because of its ease of implementation. Two other structures are frequency sampling and fast convolution techniques [17] 21

22 3.7 DIGITAL FILTER ORDER, STEP-SIZE AND COEFFICIENTS The design of digital filter involves determining the order of filter and the values of coefficients in the representation of different equation. [19] The order, step-size and coefficient are essential to define performance of a digital filter, which are described below: Order of a Digital Filter The filter order describes the maximum exponents in the numerator or denominator of z-transform equation of digital filter [28] and also expressed as the number of previous inputs which are used to calculate the current output. [27] The order of the digital filter is important for its performance. If the filter order is larger, then better frequency magnitude response performance of the filter can be achieved. In FIR filters there is no denominator in its transfer function so it is often equal to the taps. In IIR filters it is equal to number of delay elements in filter structure. [28] Different filter s orders are describes as: Zero-Order Filter The zero-order filter is described as the current output y n depends only on its current input x n and not on any previous input. [27] yn = xn First-Order Filter The first-order filter only use the previous input and the current input is not used, so the previous input (xn-1) is required to calculate yn. [27] yn = xn Second-Order Filter The second-order filter compute the current output yn, two previous inputs (xn-1 and xn-2) are needed; this is therefore called a second-order filter. [27] yn = (xn + xn-1 + xn-2) / 3 22

23 3.7.2 Step-Size of a Digital Filter Step-Size is necessary for the use of LMS algorithm, which can be determine by the cross-correlation between the reference and primary signals. The step-size depend of the eigen value, if the eigen value is maximum then the stepsize for convergence will also be maximum. The rate of convergence is proportional to the step-size and the minimum eigen value, which is shown in the following equation: [26] 1/τ 2µλ min In the equation above, µ is the step-size, λ min is the minimum eigen value, and τ is the overall time-constant Coefficient of the Digital Filter. Coefficient of the digital filter is known as tap weight, which is used to multiply against delayed signal sample values within a digital filter structure. For an FIR filter, the filter coefficients are the impulse response of the filter. [28] The coefficient of the digital filter can be expressed clearly from the equations which are described in the previous section in order of digital filter and are shown in following table. [29] Zero order: y n = a 0 x n First order: y n = a 0 x n + a 1 x n-1 Second order: y n = a 0 x n + a 1 x n-1 + a 2 x n-2 In the table above the zero-order, first-order and second-order of digital filter is presented, which shows the coefficient of the digital filter as well. The constants e.g. a 0, a 1, a 2... showing in the above equations are called the filter coefficients. 23

24 4 CHAPTER-4 ADAPTIVE FILTERS 4.1 Introduction The adaptive filter can be defined as, a filter which self adjust its transfer function according to an optimizing algorithm and object can be achieve by the modification of its characteristics. [2] Adaptive signal processing has been introduced and its growth to the advanced related fields of digital computing, DSP and high speed integrated circuit technology has been made rapidly. The least mean square (LMS) adaptive filtering algorithm s first paper was published in 1959 by Widrow and Hoff. [30] Adaptive filters are extensively used in the variety of application and they had been firstly proposed by Kelly of Bell Telephone Laboratories around 1965, [20] most of the applications are in telecommunication for the cancellation of noise and echoes in the transmission channel and also used in digital controller for active noise control. [31] An adaptive filter is a digital filter whose characteristics change in an unknown environment input signal. In the advanced era of cellular phone, digital television, wireless communication and digital multimedia commercial services, advanced adaptive signal processing may give the better solution for the technical problem. [30] The adaptive filter is also used in the field of biomedical, sonar, radar and image signal processing, telecommunication for noise cancellation etc. 4.2 Explanation of Adaptive Filter Adaptive signal processing is more famous due to the property of its digital techniques which is characterized by flexibility and accuracy in the field of communication and control. [32] In the advancement of digital signal processing s application, adaptive filter become more popular in different devices such as medical monitoring equipments, mobiles phones and other communication devices. Most of the adaptive filters are digital due to the complexity of optimizing algorithm, which perform digital signal processing and adapt their performance based on the input signal. [2] When the fixed specification of any application is unknown or can not be satisfied by time invariant filters then an adaptive filter is required to manipulate this problem. 24

25 4.3 Adaptive Filters and Digital Signal Processing The designing of digital filter requires the approved specification with fixed coefficients. If this specification is time varying or not accessible then this problem can be manipulate by digital filter with adaptive coefficients, which is know as adaptive filter. [33] The adaptive fitters are utilized and successfully increased its application under several regions of telecommunications and biomedical engineering i.e. interference reduction, noise, speech and image encoding, echo cancellation, equalization of dispersive channels, and system identification. [34]-[33] Digital signal processing has well-known repute in the modern times, which is used for the number of different application in different fields of technologies; biomedical engineering is one of them where the unwanted noise from ECG can be removed by digital filters. [34] In the modern era of communication system, adaptive signal processing is one of the most important technologies used for numbers of different algorithms. Generally the main problem in the biomedical systems is noise cancellation, which is considered as adaptive noise cancellation in hi-tech and mature technology found in the in biomedical systems, telecommunications systems, industrial control, aerospace, and music etc. [35] Adaptive filtering is the technique which is used to set the parameters. [33] It is one of several tools which are made available by the digital signal processing (DSP). Usually filters are essential part of any system which performs any kind of manipulation or signal processing to eliminate any unwanted portion or noise induced in the signal. So the digital filters have an appearance in the form of adaptive filtering, which provides better performance by adjusting to changes in the noise factors. 4.4 Adaptive Filtering Adaptive filtering is properly used due to its esteemed knowledge of signal makeup, that s why signal analysis is related to the adaptive processing. [32] Literally, the word adaptive means to adjust with other environment (system) by having the same response as the system itself to some phenomenon which is taking place in it surroundings. Or technically the system which tries to adjust its parameter, depending upon the other system s behavior and it s surrounding. The systems which carries out its functionality after undergoes the process of adaptation is called filter. The term filter means to take the unnecessary particles (frequency component) from its input signal and process them to generate required output under certain specific rules. [36] There are various principal option for the implementation of adaptive signal processing, e.g. the LMS algorithm. [31] 25

26 The adaptive filters are much famous due to their economical quality, fast processing, their short period of time adaptation and residual error is small after adaptation. [25] Adaptive filtering is the most important technique which is used is numbers of biomedical applications. [4] The principal of adaptive filter is required to understand the adaptive filtering clearly which is showed in the figure 4.1. The error signal e(n) can be generated by the output of the programmable, variable-coefficient digital filter subtracted from a reference signal y(n). [32] y(n) X(n) PROGRAMMABLR DIGITAL FILTER y(n) + Input Signal Reference e(n) ADAPTIVE ALGORITHM FOR COEFFICIENT UPDATING Fig. 4.1-Principle of an Adaptive Filter [32] The adaptive filter can be classified in the following areas: [32] The optimization criterion The algorithm for coefficient updating The programmable filter structure The type of signal processed 4.5 The General Structure of Adaptive Filters There are numbers of different structures for the implementation of adaptive filter; the type for the structure chosen is based on the requirement of the application and computational complexity of the process. [33] The basic structure of the adaptive filter is shown in figure 4.1, here the input signal is filtered for the required output and then 26

27 passed through further processing. The filter s output is observed by determines its quality for particular application. After measuring the quality it also examined by a circuit whether it is need to improve the quality of the output signal. This processing loop continues until the filter s parameters are adjusted properly, so the filter s output quality should be as good as possible. [37] Filter Input Adaptive Filter Filter Outpu t 2 Filter Adaptatio n Rules Quality Assessmen t Figure 4.2- The general structure of an adaptive filter. [37] The choice of filter structure and adaptation algorithm is important for the design adaptive filter; the structure can be non recursive or recursive. [25] 4.6 Performance, Stability and Robustness of the Adaptive Algorithm The performance of the adaptive algorithm is important for all systems; it is also essential how adaptive system is functioning. For any application the adaptive algorithm provide competent performance evaluations for the structures of various filter and adaptive algorithm. The LMS algorithm is the most popular adaptive algorithm and its performance is dependent on the filter order, signal condition and convergence parameter (μ). [38] The adaptive system is used for the solution for any practical problem; the question appears about the stability of adaptive algorithm whether or not the algorithm is stable. In general the adaptive filters based on FIR structure are naturally stable. [30] 27

28 To satisfy the robustness of the adaptive algorithm the value of step size μ needs to be small. [39] Robustness is an important criterion which is difficult to measure in a quantitative approach. The satisfaction for the robustness of the adaptive algorithm can be gained by the removal of external noise disturbances and arithmetic quantization noise. [30] 4.7 Convergence Criteria for Adaptive Algorithm The convergence criterion is the important performance in the adaptive algorithm which must be according to the required or particular application. [30] For the convergence of LMS algorithm there are different procedures. The LMS algorithm must has the convergence condition, which is necessary for the convergence of the mean is E [є (n)] 0 as n [1] The convergence ability of the LMS algorithm can be examined by the range of convergence factors which provide the stability. [33] Faster convergence is better solution for the allocation of additional resources in high frequency operation such as mobile radio, cellular telephone, digital television (HDTV). In low frequency application such as adaptive echo cancellation and audio band noise cancellation, the convergence criterion is slow and this simple and adequate solution is provided by LMS algorithm. [30] The convergence performance of the LMS algorithm for FIR filter structure is controlled by the autocorrelation matrix Rx. T Rx = E[ x * ( n) x ( n)] [30] The condition of the satisfaction can be checked and LMS algorithm s condition must be satisfied if the step size parameter satisfies the condition. [1] The autocorrelation matrix Rx is necessary for the convergence. The condition which is important for the convergence criterion and the convergence factor of LMS algorithm must be chosen in the range is 0< μ < 1 / λ max [33]-[30] Were λ max is the largest eigen value of the correlation matrix Rx. The speed of the LMS algorithm s convergence is dependent on eign value. [33] The choice of μ in the locality of 1/ λ max is the best convergence for the adaptive algorithm. [1]-[30] 28

29 If the matrix Rx has large eigenvalue then the vaule of μ must be much smaller than the upper band. As a result the convergence speed of the coefficient will be primarily dependent on the value of the smallest eigenvalue. [33] 4.8 System Identification Configuration Using an Adaptive Filter When both the unknown system and adaptive filter are prepared by the same input signal x(n) then adaptive filter is used in system identification configuration.[30] To reduce the problems of system identification, adaptive filter have excellent ability to match its output to unknown system and due to adaptive filter s best capability for adaptation, it is also used for the removal of interference and disturbance in the signal. [34] In system identification configuration, the desire signal is the output of unknown system [33] and the input signal x(n) is set for under analysis, the reference signal a(n) is produced with input signal and the error signal e(n) is generated by the system output. [30]-[32] e(n) = d(n) - y(n) noise, w(n) Unknown System H(z) + y(n) + input, x(n) a(n) Adaptive Filter ^ H(z) ^ y(n) + -, output output d(n) error, e(n) Figure 4.3- System Identification Configuration for Adaptive Filter [34] -[30]-[32] The parameters of the adaptive filters are then activated to minimize the particular function error signal e(n). In system identification configuration when the adaptive filter accumulated the stable values then error signal e(n) will be reduced.[30] It can be possible for adaptive filter to converge it to a good model to match after convergence of 29

30 the unknown system by giving sufficient degree of freedom to the adaptive filter. [34]- [33] The system identification configuration is the essential adaptive filtering concept. [30] This is used to remove the error signal while processing of any input signal with noise. It is necessary for good performance of adaptive filter to remove the noise which is mixed with input of the system; otherwise this noise appears at the output and can decrease the quality of the output. 30

31 5 CHAPTER-5 ADAPTIVE ALGORITHM FOR FIR FILTERS 5.1 Introduction The adaptive algorithm for FIR filters are is widely used in different applications such as biomedical, communication and control due to its easily implementation, stability and best performance. Its simplicity makes it attractive for many applications where it is need to minimize computational requirements. 5.2 Advantages of Filters and Adaptive Algorithm Today s medical monitoring equipments and other devices facing variety of interfering signals which are usually corrupted by noise and other interferences. The power line interference (50/60 Hz) in ECG signal is the major problem in the field of biomedical (medical monitoring equipments) and field of communication (cell phone and communication devices). So filters play an important role for removal of unwanted signal or noise from original input signal by removing the selected frequencies from incoming signal. They became much popular due to the increase of the digital signal processing. The designing of the adaptive filter, it s rational to choose the adaptive algorithm and LMS algorithm can be selected for this designing purpose, which is core contributing factor for the success of algorithm functioning. [30] Filters are used in biomedical instruments, as the frequency of biomedical instruments are very low so digital filters are much popular for low frequency applications. [17] For any application of the adaptive filters, the input signal and the reference input required being process; the least mean square is used to adjust the weight of the adaptive filter in order to minimize the error. The best solution to remove the unwanted signal or noise from the input signal, the reference noise must be filter out by using adaptive filtering method due to its good performance and reliability. 31

32 5.3 Finite Impulse Response (FIR) A finite Impulse Response (FIR) filter are type of digital filters [40] and consists of weighting sequence (impulse response) among non-recursive digital filters which is finite in length. [41] FIR filters are non recursive digital filters [40] has been selected for this thesis due to their good characteristics and can be used to implement in any sort of frequency response digitally. The series of multipliers, delays and adders are used for FIR filters implementation for filter s output. The output of the non recursive digital filter is formed from the weighted linear combination of current input and previous value of the input. [19] ^ y(n) a 0 X X X a n X a 1 a Figure 5.1- Finite impulse response (FIR) filter structure [42] The filter structure of FIR is presented in the figure 5.2, which described the relationship between input and output sequences which also described the basic structure and diagram of FIR filter having a length of N (where N is filter order) and the input samples are operated by the delays of results. All the delayed samples are multiplied by suitable coefficient as the h k is the coefficient value for multiplication for output at time n. [42] The selection of FIR filter is due to coefficient sensitivity, round off noise, stability and suitable for high speed applications. [13] FIR and IIR filters are two different classes of digital filters, these digitals filters can be implemented for different application. The selection of any type of digital filter is based on the practical implementation of required application. The FIR filter is mostly applied for adaptive filtering and the main choice of FIR filter was its stability and robustness. 32