MPA15-16 a Baseband Pulse Shaping Filter for Gaussian Minimum Shift Keying
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Moving Average Filters
CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average filter is optimal for a common task: reducing random noise while retaining a sharp step response. This makes it the premier filter for time domain encoded signals. However, the moving average is the worst filter for frequency domain encoded signals, with little ability to separate one band of frequencies from another. Relatives of the moving average filter include the Gaussian, Blackman, and multiple- pass moving average. These have slightly better performance in the frequency domain, at the expense of increased computation time. Implementation by Convolution As the name implies, the moving average filter operates by averaging a number of points from the input signal to produce each point in the output signal. In equation form, this is written: EQUATION 15-1 Equation of the moving average filter. In M &1 this equation, x[ ] is the input signal, y[ ] is ' 1 % y[i] j x [i j ] the output signal, and M is the number of M j'0 points used in the moving average. This equation only uses points on one side of the output sample being calculated. Where x[ ] is the input signal, y[ ] is the output signal, and M is the number of points in the average. For example, in a 5 point moving average filter, point 80 in the output signal is given by: x [80] % x [81] % x [82] % x [83] % x [84] y [80] ' 5 277 278 The Scientist and Engineer's Guide to Digital Signal Processing As an alternative, the group of points from the input signal can be chosen symmetrically around the output point: x[78] % x[79] % x[80] % x[81] % x[82] y[80] ' 5 This corresponds to changing the summation in Eq. -
Comparative Analysis of Gaussian Filter with Wavelet Denoising for Various Noises Present in Images
ISSN (Print) : 0974-6846 Indian Journal of Science and Technology, Vol 9(47), DOI: 10.17485/ijst/2016/v9i47/106843, December 2016 ISSN (Online) : 0974-5645 Comparative Analysis of Gaussian Filter with Wavelet Denoising for Various Noises Present in Images Amanjot Singh1,2* and Jagroop Singh3 1I.K.G. P.T.U., Jalandhar – 144603,Punjab, India; 2School of Electronics and Electrical Engineering, Lovely Professional University, Phagwara - 144411, Punjab, India; [email protected] 3Department of Electronics and Communication Engineering, DAVIET, Jalandhar – 144008, Punjab, India; [email protected] Abstract Objectives: This paper is providing a comparative performance analysis of wavelet denoising with Gaussian filter applied variouson images noises contaminated usually present with various in images. noises. Wavelet Gaussian transform filter is ais basic used filter to convert used in the image images processing. to wavelet Its response domain. isBased varying on with its kernel sizes that have also been shown in analysis. Wavelet based de-noisingMethods/Analysis: is also one of the way of removing thresholding operations in wavelet domain noise could be removed from images. In this paper, image quality matrices like PSNR andFindings MSE have been compared for the various types of noises in images for different denoising methods. Moreover, the behavior of different methods for image denoising have been graphically shown in paper with MATLAB based simulations. : In the end wavelet based de-noising methods has been compared with Gaussian basedKeywords: filter. The Denoising, paper provides Gaussian a review Filter, MSE,of filters PSNR, and SNR, their Thresholding, denoising analysis Wavelet under Transform different noise conditions. 1. Introduction is of bell shaped. -
Advanced Electronic Systems Damien Prêle
Advanced Electronic Systems Damien Prêle To cite this version: Damien Prêle. Advanced Electronic Systems . Master. Advanced Electronic Systems, Hanoi, Vietnam. 2016, pp.140. cel-00843641v5 HAL Id: cel-00843641 https://cel.archives-ouvertes.fr/cel-00843641v5 Submitted on 18 Nov 2016 (v5), last revised 26 May 2021 (v8) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. advanced electronic systems ST 11.7 - Master SPACE & AERONAUTICS University of Science and Technology of Hanoi Paris Diderot University Lectures, tutorials and labs 2016-2017 Damien PRÊLE [email protected] Contents I Filters 7 1 Filters 9 1.1 Introduction . .9 1.2 Filter parameters . .9 1.2.1 Voltage transfer function . .9 1.2.2 S plane (Laplace domain) . 11 1.2.3 Bode plot (Fourier domain) . 12 1.3 Cascading filter stages . 16 1.3.1 Polynomial equations . 17 1.3.2 Filter Tables . 20 1.3.3 The use of filter tables . 22 1.3.4 Conversion from low-pass filter . 23 1.4 Filter synthesis . 25 1.4.1 Sallen-Key topology . 25 1.5 Amplitude responses . 28 1.5.1 Filter specifications . 28 1.5.2 Amplitude response curves . -
A Simplified Realization for the Gaussian Filter in Surface Metrology
In X. International Colloquium on Surfaces, Chemnitz (Germany), Jan. 31 - Feb. 02, 2000, M. Dietzsch, H. Trumpold, eds. (Shaker Verlag GmbH, Aachen, 2000), p. 133. A Simplified Realization for the Gaussian Filter in Surface Metrology Y. B. Yuan(1), T.V. Vorburger(2), J. F. Song(2), T. B. Renegar(2) 1 Guest Researcher, NIST; Harbin Institute of Technology (HIT), Harbin, China, 150001; 2 National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899 USA. Abstract A simplified realization for the Gaussian filter in surface metrology is presented in this paper. The sampling function sinu u is used for simplifying the Gaussian function. According to the central limit theorem, when n approaches infinity, the function (sinu u)n approaches the form of a Gaussian function. So designed, the Gaussian filter is easily realized with high accuracy, high efficiency and without phase distortion. The relationship between the Gaussian filtered mean line and the mid-point locus (or moving average) mean line is also discussed. Key Words: surface roughness, mean line, sampling function, Gaussian filter 1. Introduction The Gaussian filter has been recommended by ISO 11562-1996 and ASME B46-1995 standards for determining the mean line in surface metrology [1-2]. Its weighting function is given by 1 2 h(t) = e−π(t / αλc ) , (1) αλc where α = 0.4697 , t is the independent variable in the spatial domain, and λc is the cut-off wavelength of the filter (in the units of t). If we use x(t) to stand for the primary unfiltered profile, m(t) for the Gaussian filtered mean line, and r(t) for the roughness profile, then m(t) = x(t)∗ h(t) (2) and r(t) = x(t) − m(t), (3) where the * represents a convolution of two functions. -
CHAPTER 3 ADC and DAC
CHAPTER 3 ADC and DAC Most of the signals directly encountered in science and engineering are continuous: light intensity that changes with distance; voltage that varies over time; a chemical reaction rate that depends on temperature, etc. Analog-to-Digital Conversion (ADC) and Digital-to-Analog Conversion (DAC) are the processes that allow digital computers to interact with these everyday signals. Digital information is different from its continuous counterpart in two important respects: it is sampled, and it is quantized. Both of these restrict how much information a digital signal can contain. This chapter is about information management: understanding what information you need to retain, and what information you can afford to lose. In turn, this dictates the selection of the sampling frequency, number of bits, and type of analog filtering needed for converting between the analog and digital realms. Quantization First, a bit of trivia. As you know, it is a digital computer, not a digit computer. The information processed is called digital data, not digit data. Why then, is analog-to-digital conversion generally called: digitize and digitization, rather than digitalize and digitalization? The answer is nothing you would expect. When electronics got around to inventing digital techniques, the preferred names had already been snatched up by the medical community nearly a century before. Digitalize and digitalization mean to administer the heart stimulant digitalis. Figure 3-1 shows the electronic waveforms of a typical analog-to-digital conversion. Figure (a) is the analog signal to be digitized. As shown by the labels on the graph, this signal is a voltage that varies over time. -
Whiguqzgdrjracxb.Pdf
Analog Filters Using MATLAB Lars Wanhammar Analog Filters Using MATLAB 13 Lars Wanhammar Department of Electrical Engineering Division of Electronics Systems Linkoping¨ University SE-581 83 Linkoping¨ Sweden [email protected] ISBN 978-0-387-92766-4 e-ISBN 978-0-387-92767-1 DOI 10.1007/978-0-387-92767-1 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2008942084 # Springer ScienceþBusiness Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer ScienceþBusiness Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer ScienceþBusiness Media (www.springer.com) Preface This book was written for use in a course at Linkoping¨ University and to aid the electrical engineer to understand and design analog filters. Most of the advanced mathematics required for the synthesis of analog filters has been avoided by providing a set of MATLAB functions that allows sophisticated filters to be designed. Most of these functions can easily be converted to run under Octave as well. -
Chapter 3 FILTERS
Chapter 3 FILTERS Most images are a®ected to some extent by noise, that is unexplained variation in data: disturbances in image intensity which are either uninterpretable or not of interest. Image analysis is often simpli¯ed if this noise can be ¯ltered out. In an analogous way ¯lters are used in chemistry to free liquids from suspended impurities by passing them through a layer of sand or charcoal. Engineers working in signal processing have extended the meaning of the term ¯lter to include operations which accentuate features of interest in data. Employing this broader de¯nition, image ¯lters may be used to emphasise edges | that is, boundaries between objects or parts of objects in images. Filters provide an aid to visual interpretation of images, and can also be used as a precursor to further digital processing, such as segmentation (chapter 4). Most of the methods considered in chapter 2 operated on each pixel separately. Filters change a pixel's value taking into account the values of neighbouring pixels too. They may either be applied directly to recorded images, such as those in chapter 1, or after transformation of pixel values as discussed in chapter 2. To take a simple example, Figs 3.1(b){(d) show the results of applying three ¯lters to the cashmere ¯bres image, which has been redisplayed in Fig 3.1(a). ² Fig 3.1(b) is a display of the output from a 5 £ 5 moving average ¯lter. Each pixel has been replaced by the average of pixel values in a 5 £ 5 square, or window centred on that pixel. -
Electronic Filters Design Tutorial - 3
Electronic filters design tutorial - 3 High pass, low pass and notch passive filters In the first and second part of this tutorial we visited the band pass filters, with lumped and distributed elements. In this third part we will discuss about low-pass, high-pass and notch filters. The approach will be without mathematics, the goal will be to introduce readers to a physical knowledge of filters. People interested in a mathematical analysis will find in the appendix some books on the topic. Fig.2 ∗ The constant K low-pass filter: it was invented in 1922 by George Campbell and the Running the simulation we can see the response meaning of constant K is the expression: of the filter in fig.3 2 ZL* ZC = K = R ZL and ZC are the impedances of inductors and capacitors in the filter, while R is the terminating impedance. A look at fig.1 will be clarifying. Fig.3 It is clear that the sharpness of the response increase as the order of the filter increase. The ripple near the edge of the cutoff moves from Fig 1 monotonic in 3 rd order to ringing of about 1.7 dB for the 9 th order. This due to the mismatch of the The two filter configurations, at T and π are various sections that are connected to a 50 Ω displayed, all the reactance are 50 Ω and the impedance at the edges of the filter and filter cells are all equal. In practice the two series connected to reactive impedances between cells. -
Memristor-Based Approximation of Gaussian Filter
Memristor-based Approximation of Gaussian Filter Alex Pappachen James, Aidyn Zhambyl, Anju Nandakumar Electrical and Computer Engineering department Nazarbayev University School of Engineering Astana, Kazakhstan Email: [email protected], [email protected], [email protected] Abstract—Gaussian filter is a filter with impulse response of fourth section some mathematical analysis will be provided to Gaussian function. These filters are useful in image processing obtained results and finally the paper will be concluded by of 2D signals, as it removes unnecessary noise. Also, they could stating the result of the done work. be helpful for data transmission (e.g. GMSK modulation). In practice, the Gaussian filters could be approximately designed II. GAUSSIAN FILTER AND MEMRISTOR by several methods. One of these methods are to construct Gaussian-like filter with the help of memristors and RLC circuits. A. Gaussian Filter Therefore, the objective of this project is to find and design Gaussian filter is such filter which convolves the input signal appropriate model of Gaussian-like filter, by using mentioned devices. Finally, one possible model of Gaussian-like filter based with the impulse response of Gaussian function. In some on memristor designed and analysed in this paper. sources this process is also known as the Weierstrass transform [2]. The Gaussian function is given as in equation 1, where µ Index Terms—Gaussian filters, analog filter, memristor, func- is the time shift and σ is the scale. For input signal of x(t) tion approximation the output is the convolution of x(t) with Gaussian, as shown in equation 2. -
Sampling and Reconstruction
Sampling and reconstruction COMP 575/COMP 770 Spring 2016 • 1 Sampled representations • How to store and compute with continuous functions? • Common scheme for representation: samples write down the function’s values at many points [FvDFH fig.14.14b / Wolberg] [FvDFH fig.14.14b / • 2 Reconstruction • Making samples back into a continuous function for output (need realizable method) for analysis or processing (need mathematical method) amounts to “guessing” what the function did in between [FvDFH fig.14.14b / Wolberg] [FvDFH fig.14.14b / • 3 Filtering • Processing done on a function can be executed in continuous form (e.g. analog circuit) but can also be executed using sampled representation • Simple example: smoothing by averaging • 4 Roots of sampling • Nyquist 1928; Shannon 1949 famous results in information theory • 1940s: first practical uses in telecommunications • 1960s: first digital audio systems • 1970s: commercialization of digital audio • 1982: introduction of the Compact Disc the first high-profile consumer application • This is why all the terminology has a communications or audio “flavor” early applications are 1D; for us 2D (images) is important • 5 Sampling in digital audio • Recording: sound to analog to samples to disc • Playback: disc to samples to analog to sound again how can we be sure we are filling in the gaps correctly? • 6 Undersampling • What if we “missed” things between the samples? • Simple example: undersampling a sine wave unsurprising result: information is lost surprising result: indistinguishable from -
Deconvolution
Pulses and Parameters in the Time and Frequency Domain David A Humphreys National Physical Laboratory ([email protected]) Signal Processing Seminar 30 November 2005 Structure • Introduction • Waveforms and parameters • Instruments • Waveform metrology and correction Waveforms and parameters Parameters for a pulse waveform Signal Time Why use parameters? • Convenient way to compare information • Reduce data complexity • Specification of instruments • IEEE Standard on Transitions, Pulses, and Related Waveforms, IEEE Std 181, 2003 • These documents standardise how to characterise a waveform but do not specify units Measuring and characterising a signal Determine parameters that describe a signal or response I. Instrument capabilities II. Waveform metrology and correction III. Parameter analysis and extraction Assumptions • In practice we want to define a response in terms of single parameters such as width or risetime or bandwidth • Assume oscilloscope response has smooth bell-shaped e.g. Gaussian Simple analytically Can calculate frequency response, convolution simply, reasonably realistic Only 3 parameters – width/risetime; amplitude and position Instruments Instrumentation • Time-domain Frequency Real-time oscilloscope Time High-speed A/D converter Memory subsystem e.g. 32 Msamples X(t) A/D Memory Instrumentation • Time-domain Frequency Real-time oscilloscope Time Sample rates up to 40Gsamples/s Multiple high-speed A/D converters X(t) A/D Memory Fast memory subsystem A/D Memory Memory architecture may limit the length of trace A/D Memory e.g. 1 Msamples A/D Memory Resolution typically 8 bits Instrumentation • Time-domain Frequency Real-time oscilloscope Time Sampling oscilloscope Requires a repetitive waveform Sampling X(t) High-speed >70 GHz Gate Short trace length (e.g. -
3D Profile Filter Algorithm Based on Parallel Generalized B-Spline Approximating Gaussian
CHINESE JOURNAL OF MECHANICAL ENGINEERING ·148· Vol. 28,aNo. 1,a2015 DOI: 10.3901/CJME.2014.1106.163, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn 3D Profile Filter Algorithm Based on Parallel Generalized B-spline Approximating Gaussian REN Zhiying1, 2, GAO Chenghui1, 2, *, and SHEN Ding3 1 School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China 2 Tribology Research Institute, Fuzhou University, Fuzhou 350108, China 3 Fujian Institute of Metrology, Fuzhou 35000, China Received January 24, 2014; revised September 10, 2014; accepted November 6, 2014 Abstract: Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, these methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters (t1, t2), and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form. Finally, the approximation filter of Gaussian filter is obtained. In order to verify