NOISE CANCELLATION USING LMS ALGORITHM
OBJECTIVE
• INTRODUCTION
• ADAPTIVE FILTER
• BLOCK DIAGRAM
• LEAST MEAN SQUARE - LMS
• ADVANTAGES AND DISADVANTAGES
• MATLAB CODE
• CONCLUSION
ADAPTIVE NOISE CANCELLATION
➢ Adaptive noise cancellation is the approach used for estimating a desired
signal d(n) from a noise-corrupted observation.
x(n) = d(n) + v1(n)
➢ Usually the method uses a primary input containing the corrupted signal
and a reference input containing noise correlated in some unknown way
with the primary noise.
➢ The reference input v1(n) can be filtered and subtracted from the primary
input to obtain the signal estimate 𝑑 ̂(n).
➢ As the measurement system is a black box, no reference signal that is
correlated with the noise is available.
An adaptive filter is composed of two parts, the digital filter and the
adaptive algorithm.
• A digital filter with adjustable coefficients wn(z) and an adaptive algorithm
which is used to adjust or modify the coefficients of the filter.
• The adaptive filter can be a Finite Impulse Response FIR filter or an
Infinite Impulse Response IIR filter.
ALGORITHMS FOR ADAPTIVE EQUALIZATION
• There are three different types of adaptive filtering algorithms.
➢ Zero forcing (ZF)
➢ least mean square (LMS)
➢ Recursive least square filter (RLS)
• Recursive least square is an adaptive filter algorithm that recursively finds the coefficients
that minimize a weighted linear least squares cost function relating to the input signals.
• This approach is different from the least mean-square algorithm that aim to reduce the
mean-square error.
Least Mean Square - LMS
• The LMS algorithm in general, consists of two basics procedure:
1. Filtering process, which involve, computing the output (d(n - d)) of a linear filter in
response to the input signal and generating an estimation error by comparing this
output with a desired response as follows:
y(n) is filter output and is the desired response at time n
2. Adaptive process, which involves the automatics adjustment of the parameter of the
filter in accordance with the estimation error.
➢ where wn is the estimate of the weight value vector at time n, x(n) is the input
signal vector.
➢ e(n) is the filter error vector and μ is the step-size, which determines the filter
convergence rate and overall behavior.
➢ One of the difficulties in the design and implementation of the LMS adaptive
filter is the selection of the step-size μ. This parameter must lie in a specific
range, so that the LMS algorithm converges.
➢ LMS algorithm, aims to reduce the mean-square error.
The convergence characteristics of the LMS adaptive algorithm depends on two
factors: the step-size μ and the eigenvalue spread of the autocorrelation matrix .
The step-size μ must lie in a specific range
where 𝜆𝑚𝑎𝑥 is the largest eigenvalue of the autocorrelation matrix Rx.
• A large value of the step-size μ will lead to a faster convergence but may be less
stable around the minimum value. T
Performance Analysis and Simulation of Decimator for Multirate ApplicationsIJEEE
In this paper, a decimator design has been presented for multirate digital signal processing. The decimator design has been analysed and simulated for performance comparison in terms of filter order and ripple factor. Direct form-I with decimation factor 2 have been used for performance and ripple analysis. The decimators have been designed & simulated using MATLAB. It can be observed from the simulated results that as we increase the filter order, ripple factor decreases, for the same filter structure. On the other hand, increasing filter order will increase its area and implementation cost.
Performance Analysis of Acoustic Echo Cancellation TechniquesIJERA Editor
Mainly, the adaptive filters are implemented in time domain which works efficiently in most of the applications. But in many applications the impulse response becomes too large, which increases the complexity of the adaptive filter beyond a level where it can no longer be implemented efficiently in time domain. An example of where this can happen would be acoustic echo cancellation (AEC) applications. So, there exists an alternative solution i.e. to implement the filters in frequency domain. AEC has so many applications in wide variety of problems in industrial operations, manufacturing and consumer products. Here in this paper, a comparative analysis of different acoustic echo cancellation techniques i.e. Frequency domain adaptive filter (FDAF), Least mean square (LMS), Normalized least mean square (NLMS) &Sign error (SE) is presented. The results are compared with different values of step sizes and the performance of these techniques is measured in terms of Error rate loss enhancement (ERLE), Mean square error (MSE)& Peak signal to noise ratio (PSNR).
Comparison of different Sub-Band Adaptive Noise Canceller with LMS and RLSijsrd.com
Sub-band adaptive noise is employed in various fields like noise cancellation, echo cancellation and system identification etc. It reduces computational complexity and improve convergence rate. In this paper we perform different Sub-band noise cancellation method for simulation. The Comparison with different algorithm has been done to find out which one is best.
NOISE CANCELLATION USING LMS ALGORITHM
OBJECTIVE
• INTRODUCTION
• ADAPTIVE FILTER
• BLOCK DIAGRAM
• LEAST MEAN SQUARE - LMS
• ADVANTAGES AND DISADVANTAGES
• MATLAB CODE
• CONCLUSION
ADAPTIVE NOISE CANCELLATION
➢ Adaptive noise cancellation is the approach used for estimating a desired
signal d(n) from a noise-corrupted observation.
x(n) = d(n) + v1(n)
➢ Usually the method uses a primary input containing the corrupted signal
and a reference input containing noise correlated in some unknown way
with the primary noise.
➢ The reference input v1(n) can be filtered and subtracted from the primary
input to obtain the signal estimate 𝑑 ̂(n).
➢ As the measurement system is a black box, no reference signal that is
correlated with the noise is available.
An adaptive filter is composed of two parts, the digital filter and the
adaptive algorithm.
• A digital filter with adjustable coefficients wn(z) and an adaptive algorithm
which is used to adjust or modify the coefficients of the filter.
• The adaptive filter can be a Finite Impulse Response FIR filter or an
Infinite Impulse Response IIR filter.
ALGORITHMS FOR ADAPTIVE EQUALIZATION
• There are three different types of adaptive filtering algorithms.
➢ Zero forcing (ZF)
➢ least mean square (LMS)
➢ Recursive least square filter (RLS)
• Recursive least square is an adaptive filter algorithm that recursively finds the coefficients
that minimize a weighted linear least squares cost function relating to the input signals.
• This approach is different from the least mean-square algorithm that aim to reduce the
mean-square error.
Least Mean Square - LMS
• The LMS algorithm in general, consists of two basics procedure:
1. Filtering process, which involve, computing the output (d(n - d)) of a linear filter in
response to the input signal and generating an estimation error by comparing this
output with a desired response as follows:
y(n) is filter output and is the desired response at time n
2. Adaptive process, which involves the automatics adjustment of the parameter of the
filter in accordance with the estimation error.
➢ where wn is the estimate of the weight value vector at time n, x(n) is the input
signal vector.
➢ e(n) is the filter error vector and μ is the step-size, which determines the filter
convergence rate and overall behavior.
➢ One of the difficulties in the design and implementation of the LMS adaptive
filter is the selection of the step-size μ. This parameter must lie in a specific
range, so that the LMS algorithm converges.
➢ LMS algorithm, aims to reduce the mean-square error.
The convergence characteristics of the LMS adaptive algorithm depends on two
factors: the step-size μ and the eigenvalue spread of the autocorrelation matrix .
The step-size μ must lie in a specific range
where 𝜆𝑚𝑎𝑥 is the largest eigenvalue of the autocorrelation matrix Rx.
• A large value of the step-size μ will lead to a faster convergence but may be less
stable around the minimum value. T
Performance Analysis and Simulation of Decimator for Multirate ApplicationsIJEEE
In this paper, a decimator design has been presented for multirate digital signal processing. The decimator design has been analysed and simulated for performance comparison in terms of filter order and ripple factor. Direct form-I with decimation factor 2 have been used for performance and ripple analysis. The decimators have been designed & simulated using MATLAB. It can be observed from the simulated results that as we increase the filter order, ripple factor decreases, for the same filter structure. On the other hand, increasing filter order will increase its area and implementation cost.
Performance Analysis of Acoustic Echo Cancellation TechniquesIJERA Editor
Mainly, the adaptive filters are implemented in time domain which works efficiently in most of the applications. But in many applications the impulse response becomes too large, which increases the complexity of the adaptive filter beyond a level where it can no longer be implemented efficiently in time domain. An example of where this can happen would be acoustic echo cancellation (AEC) applications. So, there exists an alternative solution i.e. to implement the filters in frequency domain. AEC has so many applications in wide variety of problems in industrial operations, manufacturing and consumer products. Here in this paper, a comparative analysis of different acoustic echo cancellation techniques i.e. Frequency domain adaptive filter (FDAF), Least mean square (LMS), Normalized least mean square (NLMS) &Sign error (SE) is presented. The results are compared with different values of step sizes and the performance of these techniques is measured in terms of Error rate loss enhancement (ERLE), Mean square error (MSE)& Peak signal to noise ratio (PSNR).
Comparison of different Sub-Band Adaptive Noise Canceller with LMS and RLSijsrd.com
Sub-band adaptive noise is employed in various fields like noise cancellation, echo cancellation and system identification etc. It reduces computational complexity and improve convergence rate. In this paper we perform different Sub-band noise cancellation method for simulation. The Comparison with different algorithm has been done to find out which one is best.
Digital Implementation of Costas Loop with Carrier RecoveryIJERD Editor
Demodulator circuit is a basic building block of wireless communication. Digital implementation of
demodulator is attracting more attention for the significant advantages of digital systems than analog systems.
The carrier signal extraction is the main problem in synchronous demodulation in design of demodulator based
on Software Defined Radio. When transmitter or receiver in motion, it is difficult for demodulator to generate
carrier signal same in frequency and phase as transmitter carrier signal due to Doppler shift and Doppler rate.
Here the digital implementation of Costas loop for QPSK demodulation in continuous mode is discussed with
carrier recovery using phase locked loop.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Adaptive Digital Filter Design for Linear Noise Cancellation Using Neural Net...iosrjce
Noise is the most serious issue in the filters and adaptive filters are subjected to this unwanted
component. This paper deals with the problem of the adaptive noise and various adaptive algorithms functions
which when implemented practically shows that the noise is cancelled or removed by the neural network
approach using the exact random basis function. The adaptive filters are used to control the noise and it has a
linear input and output characteristics. This approach is done so as to get the minimum possible error so that to
obtain the error free desired signal. The designed filter will reduce this noise from measured signal by a
reference signal which is highly correlated with the noise signal. This approach gives excellent result for this
signal processing technique that removes or eliminates the linear noise from the different functions. The
simulation results are also mentioned so as to gives a vivid idea of reduced noise using neural networks
algorithm.
FPGA IMPLEMENTATION OF NOISE CANCELLATION USING ADAPTIVE ALGORITHMSEditor IJMTER
This paper describes the concept of adaptive noise cancelling. The noise cancellation
using the Recursive Least Squares (RLS) to remove the noise from an input signal. The RLS adaptive
filter uses the reference signal on the Input port and the desired signal on the desired port to
automatically match the filter response in the Noise Filter block. The filtered noise should be completely
subtracted from the "noisy signal” of the input Sine wave & noise input signal, and the "Error Signal"
should contain only the original signal. Finally, the functions of field programmable gate array based
system structure for adaptive noise canceller based on RLS algorithm are synthesized, simulated, and
implemented on Xilinx XC3s200 field programmable gate array using Xilinx ISE tool.
Echo Cancellation Algorithms using Adaptive Filters: A Comparative Studyidescitation
An adaptive filter is a filter that self-adjusts its transfer function according to an
optimization algorithm driven by an error signal. Adaptive filter finds its essence in
applications such as echo cancellation, noise cancellation, system identification and many
others. This paper briefly discusses LMS, NLMS and RLS adaptive filter algorithms for
echo cancellation. For the analysis, an acoustic echo canceller is built using LMS, NLMS
and RLS algorithms and the echo cancelled samples are studied using Spectrogram. The
analysis is further extended with its cross-correlation and ERLE (Echo Return Loss
Enhancement) results. Finally, this paper concludes with a better adaptive filter algorithm
for Echo cancellation. The implementation and analysis is done using MATLAB®,
SIMULINK® and SPECTROGRAM V5.0®.
In this work, we develop a new approach to active noise cancellation. Theoretically, we use a 180 degree phase
shift of the noise, i.e. generate an anti-noise, to cancel the original signal. Here, we have designed FIR filter
which is driven by the input signal and has the noise signal as the feedback, and output of which is the required
result. The active noise control system contains an electro-acoustic device that cancels the unwanted audio
signal by generating an anti-noise of equal amplitude and opposite phase. The original, unwanted sound and the
anti-noise combine acoustically, resulting in the cancellation of both sounds. The effectiveness of cancellation
of the unwanted signal depends on the accuracy of the amplitude and phase of the generated anti-noise.
Digital Implementation of Costas Loop with Carrier RecoveryIJERD Editor
Demodulator circuit is a basic building block of wireless communication. Digital implementation of
demodulator is attracting more attention for the significant advantages of digital systems than analog systems.
The carrier signal extraction is the main problem in synchronous demodulation in design of demodulator based
on Software Defined Radio. When transmitter or receiver in motion, it is difficult for demodulator to generate
carrier signal same in frequency and phase as transmitter carrier signal due to Doppler shift and Doppler rate.
Here the digital implementation of Costas loop for QPSK demodulation in continuous mode is discussed with
carrier recovery using phase locked loop.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Adaptive Digital Filter Design for Linear Noise Cancellation Using Neural Net...iosrjce
Noise is the most serious issue in the filters and adaptive filters are subjected to this unwanted
component. This paper deals with the problem of the adaptive noise and various adaptive algorithms functions
which when implemented practically shows that the noise is cancelled or removed by the neural network
approach using the exact random basis function. The adaptive filters are used to control the noise and it has a
linear input and output characteristics. This approach is done so as to get the minimum possible error so that to
obtain the error free desired signal. The designed filter will reduce this noise from measured signal by a
reference signal which is highly correlated with the noise signal. This approach gives excellent result for this
signal processing technique that removes or eliminates the linear noise from the different functions. The
simulation results are also mentioned so as to gives a vivid idea of reduced noise using neural networks
algorithm.
FPGA IMPLEMENTATION OF NOISE CANCELLATION USING ADAPTIVE ALGORITHMSEditor IJMTER
This paper describes the concept of adaptive noise cancelling. The noise cancellation
using the Recursive Least Squares (RLS) to remove the noise from an input signal. The RLS adaptive
filter uses the reference signal on the Input port and the desired signal on the desired port to
automatically match the filter response in the Noise Filter block. The filtered noise should be completely
subtracted from the "noisy signal” of the input Sine wave & noise input signal, and the "Error Signal"
should contain only the original signal. Finally, the functions of field programmable gate array based
system structure for adaptive noise canceller based on RLS algorithm are synthesized, simulated, and
implemented on Xilinx XC3s200 field programmable gate array using Xilinx ISE tool.
Echo Cancellation Algorithms using Adaptive Filters: A Comparative Studyidescitation
An adaptive filter is a filter that self-adjusts its transfer function according to an
optimization algorithm driven by an error signal. Adaptive filter finds its essence in
applications such as echo cancellation, noise cancellation, system identification and many
others. This paper briefly discusses LMS, NLMS and RLS adaptive filter algorithms for
echo cancellation. For the analysis, an acoustic echo canceller is built using LMS, NLMS
and RLS algorithms and the echo cancelled samples are studied using Spectrogram. The
analysis is further extended with its cross-correlation and ERLE (Echo Return Loss
Enhancement) results. Finally, this paper concludes with a better adaptive filter algorithm
for Echo cancellation. The implementation and analysis is done using MATLAB®,
SIMULINK® and SPECTROGRAM V5.0®.
In this work, we develop a new approach to active noise cancellation. Theoretically, we use a 180 degree phase
shift of the noise, i.e. generate an anti-noise, to cancel the original signal. Here, we have designed FIR filter
which is driven by the input signal and has the noise signal as the feedback, and output of which is the required
result. The active noise control system contains an electro-acoustic device that cancels the unwanted audio
signal by generating an anti-noise of equal amplitude and opposite phase. The original, unwanted sound and the
anti-noise combine acoustically, resulting in the cancellation of both sounds. The effectiveness of cancellation
of the unwanted signal depends on the accuracy of the amplitude and phase of the generated anti-noise.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
CW RADAR, FMCW RADAR, FMCW ALTIMETER, AND THEIR PARAMETERSveerababupersonal22
It consists of cw radar and fmcw radar ,range measurement,if amplifier and fmcw altimeterThe CW radar operates using continuous wave transmission, while the FMCW radar employs frequency-modulated continuous wave technology. Range measurement is a crucial aspect of radar systems, providing information about the distance to a target. The IF amplifier plays a key role in signal processing, amplifying intermediate frequency signals for further analysis. The FMCW altimeter utilizes frequency-modulated continuous wave technology to accurately measure altitude above a reference point.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Adaptive Filters dsp.ppt
1. Content Beyond Syllabi
EE8591 Digital signal processing
Adaptive Filters & Filter design using MATLAB
Dr. N.G.P. INSTITUTE OF TECHNOLOGY
Au Autonomous Institution
Approved by AICTE, New Delhi, Affiliated to Anna University, Chennai,
Recognized by UGC & Accredited by NAAC and NBA (BME, CSE, ECE, EEE &Mechanical)
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
2. 2
introduction
Linear filters :
the filter output is a linear function of the filter input
Design methods:
• 1 The classical approach
frequency-selective filters such as
lowpass / bandpass / notch filters etc
• 2 Optimal filter design
Mostly based on minimizing the mean-square value
of the error signal [1]
3. 3
Wiener filter
• work of Wiener in 1942 and Kolmogorov in 1939
• it is based on a priori
statistical information
• when such a priori
information is not available,
which is usually the case,
it is not possible to design
a Wiener filter in the first
place
[1]
4. 4
Adaptive filter
• the signal and/or noise characteristics are often
nonstationary and the statistical parameters vary
with time
• An adaptive filter has an adaptation algorithm, that is
meant to monitor the environment and vary the filter
transfer function accordingly
• based in the actual signals received, attempts to find
the optimum filter design [1]
5. 5
Adaptive filter
• In a stationary environment, the filter is expected to
converge, to the Wiener filter
• In a nonstationary environment,
the filter is expected to
track time variations and
vary its filter coefficients
accordingly
[1]
6. 6
Adaptive filter
• The basic operation now involves two
processes :
1. a filtering process, which produces an output signal
in response to a given input signal.
2. an adaptation process, which aims to adjust the
filter parameters (filter transfer function) to the
(possibly time-varying) environment
Often, the (avarage) square value of the error signal
is used as the optimization criterion
[1]
7. 7
Adaptive filter
• Because of complexity of the optimizing algorithms
most adaptive filters are digital filters that perform
digital signal processing
• When processing
analog signals,
the adaptive filter
is then preceded
by A/D and D/A
convertors. [1]
8. 8
Adaptive filter
• The generalization to adaptive IIR filters leads to
stability problems
• It’s common to use
a FIR digital filter
with adjustable
coefficients.
[1]
9. 9
LMS Algorithm
• Most popular adaptation algorithm is LMS
Define cost function as mean-squared error
• Based on the method of steepest descent
Move towards the minimum on the error surface to
get to minimum
gradient of the error surface estimated at every
iteration
signal
error
vector
input
tap
parameter
rate
-
learning
vector
weight
-
tap
of
value
old
vector
weigth
-
tap
of
value
update
[2]
11. 11
Stability of LMS
• The LMS algorithm is convergent in the mean square
if and only if the step-size parameter satisfy
• Here max is the largest eigenvalue of the correlation
matrix of the input data
• More practical test for stability is
• Larger values for step size
– Increases adaptation rate (faster adaptation)
– Increases residual mean-squared error
max
2
0
power
signal
input
2
0
[2]
12. 12
Applications of Adaptive Filters:
Identification
• Used to provide a linear model of an unknown plant
• Applications:
– System identification [2]
13. 13
Applications of Adaptive Filters:
Inverse Modeling
• Used to provide an inverse model of an unknown
plant
• Applications:
– Equalization (communications channels)
[2]
14. 14
Applications of Adaptive Filters:
Prediction
• Used to provide a prediction of the present value of a
random signal
• Applications:
– Linear predictive coding
[2]
15. 15
Applications of Adaptive Filters:
Interference Cancellation
• Used to cancel unknown interference from a primary
signal
• Applications:
– Echo / Noise cancellation
hands-free carphone, aircraft headphones etc [2]
17. 17
A new work
• Novel Adaptive IIR Filter for Frequency
Estimation and Tracking
In many applications we may want to estimate (track)
the signal’s fundamental frequency as well as any
harmonic frequencies
In this article, we present a novel adaptive harmonic IIR
notch filter with a single adaptive coefficient to
efficiently perform frequency estimation and tracking
in a harmonic frequency environment [3]
18. 18
Structure
frequency estimation of a measured signal x(n)
V(n) is a white Gaussian noise
• To estimate frequency in such a harmonic frequency
environment, a IIR notch filter presented for the
case of M=3 (the fundamental and
two harmonics)
[3]
19. 19
Pole zero plot
• Parameter r is chosen to be close to, but less than,
one to achieve narrowband notches and avoid any
filter stability problems [3]
20. 20
Transfer function
• the transfer function has only one adaptive coefficient
• Our objective, then, is to minimize the power of the
last subfilter output
[3]
21. 21
MSE
• we could determine a frequency capture range based
on the plotted MSE function [3]
23. 23
PROGRAM: HIGH PASS FIR FILTER DESIGN USING WINDOW METHOD
clc; clear all;
close all;
n=20;
fp=300; f
q=200;
fs=1000;
fn=2*fp/fs;
window=blackman(n+1);
b=fir1(n,fn,'high',window);
[H W]=freqz(b,1,128);
subplot(2,1,1);
plot(W/pi,abs(H));
title('mag res of hpf’);
ylabel('gain in db-------->’);
xlabel('normalized frequency------>’);
subplot(2,1,2); plot(W/pi,angle(H));
title('phase res of lpf'); ylabel('angle-------->’);
xlabel('normalized frequency------>')