DOCSLIB.ORG

ESE 531: Digital Signal Processing Linear Filter Design What Is A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
ESE 531: Digital Signal Processing Linear Filter Design What Is A Linear Filter Design ESE 531: Digital Signal Processing ! Used to be an art " Now, lots of tools to design optimal filters ! For DSP there are two common classes Lec 15: March 15, 2018 " Infinite impulse response IIR Design of IIR Filters " Finite impulse response FIR ! Both classes use finite order of parameters for design Penn ESE 531 Spring 2018 – Khanna Penn ESE 531 Spring 2018 – Khanna Adapted from M. Lustig, EECS Berkeley 2 What is a Linear Filter? Filter Specifications ! Attenuates certain frequencies ! Passes certain frequencies ! Affects both phase and magnitude ! What does it mean to design a filter? " Determine the parameters of a transfer function or difference equation that approximates a desired impulse response (h[n]) or frequency response (H(ejω)). Penn ESE 531 Spring 2018 – Khanna Adapted from M. Lustig, EECS Berkeley 3 Penn ESE 531 Spring 2018 - Khanna 4 What is a Linear Filter? Today ! Attenuates certain frequencies ! IIR Filter Design ! Passes certain frequencies " Impulse Invariance " Bilinear Transformation ! Affects both phase and magnitude ! Transformation of DT Filters ! FIR Filters ! IIR " Mostly non-linear phase response " Could be linear over a range of frequencies ! FIR " Much easier to control the phase " Both non-linear and linear phase Penn ESE 531 Spring 2018 – Khanna Adapted from M. Lustig, EECS Berkeley 5 Penn ESE 531 Spring 2018 - Khanna 6 1 IIR Filter Design Impulse Invariance ! Transform continuous-time filter into a discrete- ! Want to implement continuous-time system in time filter meeting specs discrete-time " Pick suitable transformation from s (Laplace variable) to z (or t to n) " Pick suitable analog Hc(s) allowing specs to be met, transform to H(z) ! We’ve seen this before… impulse invariance Penn ESE 531 Spring 2018 - Khanna 7 Penn ESE 531 Spring 2018 - Khanna 8 Impulse Invariance Impulse Invariance ! With Hc(jΩ) bandlimited, choose ! With Hc(jΩ) bandlimited, choose j ω j ω H(e ω ) = H ( j ), ω < π H(e ω ) = H ( j ), ω < π c T c T ! With the further requirement that T be chosen such ! With the further requirement that T be chosen such that that Hc ( jΩ) = 0, Ω ≥ π / T Hc ( jΩ) = 0, Ω ≥ π / T h[n] = Thc (nT ) Penn ESE 531 Spring 2018 - Khanna 9 Penn ESE 531 Spring 2018 - Khanna 10 IIR by Impulse Invariance Example ! If Hc(jΩ)≈0 for |Ωd| > π/Td, there is no aliasing jω and H(e ) = H(jω/Td), |ω|<π jω ! To get a particular H(e ), find corresponding Hc and Td for which above is true (within specs) ! Note: Td is not for aliasing control, used for frequency scaling. Penn ESE 531 Spring 2018 - Khanna 11 Penn ESE 531 Spring 2018 - Khanna 12 2 Example Example 1 eat ←⎯L→ s − a Penn ESE 531 Spring 2018 - Khanna 13 Penn ESE 531 Spring 2018 - Khanna 14 Example Example jΩ Penn ESE 531 Spring 2018 - Khanna 15 Penn ESE 531 Spring 2018 - Khanna 16 Impulse Invariance Mapping Impulse Invariance ! Let, Hc ( jΩ) = 0, Ω ≥ π / T h[n] = Thc (nT ) ! If sampling at Nyquist Rate then ∞ j ⎡ ⎛ω 2πk ⎞⎤ H(e ω ) H j = ∑ c ⎢ ⎜ − ⎟⎥ k=−∞ ⎣ ⎝T T ⎠⎦ jω ⎛ ω ⎞ H(e ) = Hc ⎜ j ⎟, |ω|<π ⎝ T ⎠ Penn ESE 531 Spring 2018 - Khanna 17 Penn ESE 531 Spring 2018 - Khanna 18 3 Impulse Invariance Impulse Invariance ! Sampling the impulse response is equivalent to mapping the ! Sampling the impulse response is equivalent to mapping the s-plane to the z-plane using: s-plane to the z-plane using: st0 jω st0 jω " z = e = r e " z = e = r e ! The entire Ω axis of the s-plane wraps around the unit circle ! The entire Ω axis of the s-plane wraps around the unit circle of the z-plane an infinite number of times of the z-plane an infinite number of times ! The left half s-plane maps to the interior of the unit circle and the right half plane to the exterior Penn ESE 531 Spring 2018 - Khanna 19 Penn ESE 531 Spring 2018 - Khanna 20 Review: S-plane and stability Impulse Invariance Mapping jΩ σ Penn ESE 531 Spring 2018 - Khanna 21 Penn ESE 531 Spring 2018 - Khanna 22 Impulse Invariance Impulse Invariance Mapping ! Sampling the impulse response is equivalent to mapping the s-plane to the z-plane using: st0 jω " z = e = r e ! The entire Ω axis of the s-plane wraps around the unit circle of the z-plane an infinite number of times ! The left half s-plane maps to the interior of the unit circle and the right half plane to the exterior ! This means stable analog filters (poles in LHP) will transform to stable digital filters (poles inside unit circle) ! This is a many-to-one mapping of strips of the s-plane to regions of the z-plane " Not a conformal mapping st0 " The poles map according to z = e , but the zeros do not always Penn ESE 531 Spring 2018 - Khanna 23 Penn ESE 531 Spring 2018 - Khanna 24 4 Impulse Invariance Mapping Impulse Invariance ! Limitation of Impulse Invariance: overlap of images of the frequency response. This prevents it from being used for high-pass filter design Penn ESE 531 Spring 2018 - Khanna 25 Penn ESE 531 Spring 2018 - Khanna 26 Bilinear Transformation Bilinear Transformation ! The technique uses an algebraic transformation between the variables s and z that maps the entire jΩ-axis in the s-plane to one revolution of the unit circle in the z-plane. ω ! Substituting s = σ+ j Ω and z = ej Penn ESE 531 Spring 2018 - Khanna 27 Penn ESE 531 Spring 2018 - Khanna 28 Bilinear Transformation Bilinear Transformation ω ! Substituting s = σ+ j Ω and z = ej Penn ESE 531 Spring 2018 - Khanna 29 Penn ESE 531 Spring 2018 - Khanna 30 5 Bilinear Transformation Example: Notch Filter ! The continuous time filter with: s2 +Ω2 H (s) 0 a = 2 2 s + Bs +Ω0 Penn ESE 531 Spring 2018 - Khanna 31 Penn ESE 531 Spring 2018 - Khanna 32 Simple Band-Stop (Notch) Filter Transformation of DT Filters Z −1 = G(z−1) Hlp(Z) ! Z – complex variable for the LP filter ! z – complex variable for the transformed filter ! Map Z-plane#z-plane with transformation G Penn ESE 531 Spring 2018 – Khanna Adapted from M. Lustig, EECS Berkeley 33 Penn ESE 531 Spring 2018 - Khanna 34 Transformation of DT Filters Example 1: ! Lowpass#highpass " Shift frequency by π −1 −1 Z = G(z ) Z −1 z−1 Hlp(Z) = − ! Map Z-plane#z-plane with transformation G Penn ESE 531 Spring 2018 - Khanna 35 Penn ESE 531 Spring 2018 - Khanna 36 6 Example 1: Example 2: ! Lowpass#highpass ! Lowpass#bandpass " Shift frequency by π Z −1 = −z−2 1 1 H (z) = ⎯⎯→ H (z) = lp −1 bp −2 Z −1 = −z−1 1− az 1+ az Pole at z=a Pole at z=±j√a Penn ESE 531 Spring 2018 - Khanna 37 Penn ESE 531 Spring 2018 - Khanna 38 Example 2: Transformation Constraints on G(z-1) ! Lowpass#bandpass ! If Hlp(Z) is the rational system function of a causal −1 −2 and stable system, we naturally require that the Z = −z transformed system function H(z) be a rational 1 1 H (z) H (z) function and that the system also be causal and lp = 1 ⎯⎯→ bp = 2 1− az− 1+ az− stable. -l -1 Pole at z=a Pole at z=±j√a " G(Z ) must be a rational function of z " The inside of the unit circle of the Z-plane must map to ! Lowpass#bandstop the inside of the unit circle of the z-plane " The unit circle of the Z-plane must map onto the unit −1 −2 Z = z circle of the z-plane. 1 1 Hlp (z) = ⎯⎯→ Hbs (z) = 1− az−1 1− az−2 Penn ESE 531 Spring 2018 - Khanna Pole at z=±√a 39 Penn ESE 531 Spring 2018 - Khanna 40 Transformation Constraints on G(z-1) Transformation Constraints on G(z-1) ! Respective unit circles in both planes ! Respective unit circles in both planes Z −1 = G(z−1) e− jθ = G(e− jω ) − jω e− jθ = G(e− jω ) e j∠G(e ) Penn ESE 531 Spring 2018 - Khanna 41 Penn ESE 531 Spring 2018 - Khanna 42 7 Transformation Constraints on G(z-1) Transformation Constraints on G(z-1) ! Respective unit circles in both planes ! General form that meets all constraints: " ak real and |ak|<1 Z −1 = G(z−1) e− jθ = G(e− jω ) − jω e− jθ = G(e− jω ) e j∠G(e ) j 1= G(e− ω ) −θ = ∠G(e− jω ) Penn ESE 531 Spring 2018 - Khanna 43 Penn ESE 531 Spring 2018 - Khanna 44 General Transformation General Transformation ! Lowpass#lowpass ! Lowpass#lowpass ! Changes passband/stopband edge frequencies ! Changes passband/stopband edge frequencies Penn ESE 531 Spring 2018 - Khanna 45 Penn ESE 531 Spring 2018 - Khanna 46 General Transformation General Transformations ! Lowpass#lowpass ! Changes passband/stopband edge frequencies Penn ESE 531 Spring 2018 - Khanna 47 Penn ESE 531 Spring 2018 - Khanna 48 8 Reminder: Simple Low Pass Filter What is a Linear Filter? ! Attenuates certain frequencies ! Passes certain frequencies ! Affects both phase and magnitude H(e jω ) ! IIR 1 " Mostly non-linear phase response 1 2 " Could be linear over a range of frequencies ω ω ! c π FIR " Much easier to control the phase " Both non-linear and linear phase Penn ESE 531 Spring 2018 – Khanna Penn ESE 531 Spring 2018 – Khanna Adapted from M. Lustig, EECS Berkeley 49 Adapted from M. Lustig, EECS Berkeley 50 FIR GLP: Type I and II FIR GLP: Type III and IV Penn ESE 531 Spring 2018 – Khanna Penn ESE 531 Spring 2018 – Khanna Adapted from M.
Load more

Recommended publications
  • Linear Filtering of Random Processes
    Linear Filtering of Random Processes Lecture 13 Spring 2002 Wide-Sense Stationary A stochastic process X(t) is wss if its mean is constant E[X(t)] = µ and its autocorrelation depends only on τ = t1 − t2 ∗ Rxx(t1,t2)=E[X(t1)X (t2)] ∗ E[X(t + τ)X (t)] = Rxx(τ) ∗ Note that Rxx(−τ)=Rxx(τ)and Rxx(0) = E[|X(t)|2] Lecture 13 1 Example We found that the random telegraph signal has the autocorrelation function −c|τ| Rxx(τ)=e We can use the autocorrelation function to find the second moment of linear combinations such as Y (t)=aX(t)+bX(t − t0). 2 2 Ryy(0) = E[Y (t)] = E[(aX(t)+bX(t − t0)) ] 2 2 2 2 = a E[X (t)] + 2abE[X(t)X(t − t0)] + b E[X (t − t0)] 2 2 = a Rxx(0) + 2abRxx(t0)+b Rxx(0) 2 2 =(a + b )Rxx(0) + 2abRxx(t0) −ct =(a2 + b2)Rxx(0) + 2abe 0 Lecture 13 2 Example (continued) We can also compute the autocorrelation Ryy(τ)forτ =0. ∗ Ryy(τ)=E[Y (t + τ)Y (t)] = E[(aX(t + τ)+bX(t + τ − t0))(aX(t)+bX(t − t0))] 2 = a E[X(t + τ)X(t)] + abE[X(t + τ)X(t − t0)] 2 + abE[X(t + τ − t0)X(t)] + b E[X(t + τ − t0)X(t − t0)] 2 2 = a Rxx(τ)+abRxx(τ + t0)+abRxx(τ − t0)+b Rxx(τ) 2 2 =(a + b )Rxx(τ)+abRxx(τ + t0)+abRxx(τ − t0) Lecture 13 3 Linear Filtering of Random Processes The above example combines weighted values of X(t)andX(t − t0) to form Y (t).
    [Show full text]
  • 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.
    [Show full text]
  • A Multidimensional Filtering Framework with Applications to Local Structure Analysis and Image Enhancement
    Linkoping¨ Studies in Science and Technology Dissertation No. 1171 A Multidimensional Filtering Framework with Applications to Local Structure Analysis and Image Enhancement Bjorn¨ Svensson Department of Biomedical Engineering Linkopings¨ universitet SE-581 85 Linkoping,¨ Sweden http://www.imt.liu.se Linkoping,¨ April 2008 A Multidimensional Filtering Framework with Applications to Local Structure Analysis and Image Enhancement c 2008 Bjorn¨ Svensson Department of Biomedical Engineering Linkopings¨ universitet SE-581 85 Linkoping,¨ Sweden ISBN 978-91-7393-943-0 ISSN 0345-7524 Printed in Linkoping,¨ Sweden by LiU-Tryck 2008 Abstract Filtering is a fundamental operation in image science in general and in medical image science in particular. The most central applications are image enhancement, registration, segmentation and feature extraction. Even though these applications involve non-linear processing a majority of the methodologies available rely on initial estimates using linear filters. Linear filtering is a well established corner- stone of signal processing, which is reflected by the overwhelming amount of literature on finite impulse response filters and their design. Standard techniques for multidimensional filtering are computationally intense. This leads to either a long computation time or a performance loss caused by approximations made in order to increase the computational efficiency. This dis- sertation presents a framework for realization of efficient multidimensional filters. A weighted least squares design criterion ensures preservation of the performance and the two techniques called filter networks and sub-filter sequences significantly reduce the computational demand. A filter network is a realization of a set of filters, which are decomposed into a structure of sparse sub-filters each with a low number of coefficients.
    [Show full text]
  • Signal Processing with Scipy: Linear Filters
    PyData CookBook 1 Signal Processing with SciPy: Linear Filters Warren Weckesser∗ F Abstract—The SciPy library is one of the core packages of the PyData stack. focus on a specific subset of the capabilities of of this sub- It includes modules for statistics, optimization, interpolation, integration, linear package: the design and analysis of linear filters for discrete- algebra, Fourier transforms, signal and image processing, ODE solvers, special time signals. These filters are commonly used in digital signal functions, sparse matrices, and more. In this chapter, we demonstrate many processing (DSP) for audio signals and other time series data of the tools provided by the signal subpackage of the SciPy library for the design and analysis of linear filters for discrete-time signals, including filter with a fixed sample rate. representation, frequency response computation and optimal FIR filter design. The chapter is split into two main parts, covering the two broad categories of linear filters: infinite impulse response Index Terms—algorithms, signal processing, IIR filter, FIR filter (IIR) filters and finite impulse response (FIR) filters. Note. We will display some code samples as transcripts CONTENTS from the standard Python interactive shell. In each interactive Python session, we will have executed the following without Introduction....................1 showing it: IIR filters in scipy.signal ..........1 IIR filter representation.........2 >>> import numpy as np >>> import matplotlib.pyplot as plt Lowpass filter..............3 >>> np.set_printoptions(precision=3, linewidth=50) Initializing a lowpass filter.......5 Bandpass filter..............5 Also, when we show the creation of plots in the transcripts, we Filtering a long signal in batches....6 won’t show all the other plot commands (setting labels, grid Solving linear recurrence relations...6 lines, etc.) that were actually used to create the corresponding FIR filters in scipy.signal ..........7 figure in the paper.
    [Show full text]
  • Filters CW100322-01
    PHY3128 Electronics for Measurement Systems Linear Filters Linear Filters Introduction A linear filter is a circuit with an output Vout that is a linear function of its input Vin and that is intended to remove unwanted parts of a signal. Such filters are often described by specifying how they modify the amplitude and phase of each frequency component of the signal with a transfer function € € 2 Vout (ω) a0 + a1ω + a2ω + ... G(ω) = = 2 . (1) Vin (ω) b0 + b1ω + b2ω + ... This quotient of two polynomials is known as a Padé function and is usually expressed as the product of its complex poles and zeros, e.g. € (ωz0 + jω) × (ωz1 + jω) × ... G(ω) = (2) (ωp0 + jω) × (ωp1 + jω) × ... Much cryptic engineering-jargon arises from this convention. For example a ‘single-pole op-amp’ is one with an open-loop gain accurately described by € a A(ω ) = 0 (3) ω 0 + jω which has a single complex pole at ω = jω0 . In principle, designing a filter is a straightforward matter – one uses a computer and/or creates a chain of stages until the desired transfer function is obtained. However, non-trivial designs often do not work well; they tend to require extremely precise component values that are not available in practice. There are many of types of filter; the most commonly encountered include: Butterworth (maximum flatness in pass-band), Chebyshev (sharpest transition from pass-band to stop-band), Bessel (best linear phase vs frequency response). General Remarks In the context of test and measurement systems, filters irreversibly remove information from the signal and should be used sparingly, particularly if it would be possible to post-process signals digitally.
    [Show full text]
  • Convention Paper 7997 Presented at the 128Th Convention 2010 May 22–25 London, UK
    Audio Engineering Society Convention Paper 7997 Presented at the 128th Convention 2010 May 22–25 London, UK The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio nd Engineering Society, 60 East 42 Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society. Modeling Distortion Effects in Class-D 8094 Amplifier Filter Inductors Arnold Knott1, Tore Stegenborg-Andersen 1, Ole C. Thomsen 1, Dominik Bortis 2, Johann W. Kolar 2 Gerhard Pfaffinger3 and Michael A.E. Andersen1 1Technical University of Denmark, 2800 Kgs. Lyngby, Denmark 2ETH Zurich / Power Electronics System Laboratory, CH-8092 Zurich, Switzerland 3Harman/Becker Automotive Systems GmbH, 94315 Straubing, Germany Correspondence should be addressed to Arnold Knott ([email protected]) ABSTRACT Distortion is generally accepted as a quantifier to judge the quality of audio power amplifiers. In switch- mode power amplifiers various mechanisms influence this performance measure. After giving an overview of those, this paper focuses on the particular effect of the nonlinearity of the output filter components on the audio performance. While the physical reasons for both, the capacitor and the inductor induced distortion are given, the practical in depth demonstration is done for the inductor only.
    [Show full text]
  • The Scientist and Engineer's Guide to Digital Signal Processing
    CHAPTER 14 Introduction to Digital Filters Digital filters are used for two general purposes: (1) separation of signals that have been combined, and (2) restoration of signals that have been distorted in some way. Analog (electronic) filters can be used for these same tasks; however, digital filters can achieve far superior results. The most popular digital filters are described and compared in the next seven chapters. This introductory chapter describes the parameters you want to look for when learning about each of these filters. Filter Basics Digital filters are a very important part of DSP. In fact, their extraordinary performance is one of the key reasons that DSP has become so popular. As mentioned in the introduction, filters have two uses: signal separation and signal restoration. Signal separation is needed when a signal has been contaminated with interference, noise, or other signals. For example, imagine a device for measuring the electrical activity of a baby's heart (EKG) while still in the womb. The raw signal will likely be corrupted by the breathing and heartbeat of the mother. A filter might be used to separate these signals so that they can be individually analyzed. Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to better represent the sound as it actually occurred. Another example is the deblurring of an image acquired with an improperly focused lens, or a shaky camera. These problems can be attacked with either analog or digital filters. Which is better? Analog filters are cheap, fast, and have a large dynamic range in both amplitude and frequency.
    [Show full text]
  • An ON–OFF Log Domain Circuit That Recreates Adaptive Filtering in the Retina Kareem A
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 1, JANUARY 2005 99 An ON–OFF Log Domain Circuit That Recreates Adaptive Filtering in the Retina Kareem A. Zaghloul and Kwabena A. Boahen Abstract—We introduce a new approach to synthesizing Class fore, to obtain the derivative of the voltage, divide the derivative AB log-domain filters that satisfy dynamic differential-mode of the signal, , by the signal, . That is to say, divide the and common-mode constraints simultaneously. Whereas the current you wish to supply to the capacitor by the current made dynamic differential-mode constraint imposes the desired fil- tering behavior, the dynamic common-mode constraint solves by the transistor whose gate (or base) is connected to it. Intu- the zero-dc-gain problem, a shortcoming of previous approaches. itively, this division compensates for the slope of the exponential Also, we introduce a novel push–pull circuit that serves as a at the transistor’s operating point, such that its current changes current-splitter; it rectifies a differential signal into the ON and at a constant rate. Current-division is readily realized with log- OFF paths in our log-domain filter. As an example, we synthesize a arithmic elements by exploiting the translinear principle [8]. first-order low-pass filter, and, to demonstrate the rejection of dc signals, we implement an adaptive filter by placing this low-pass In theory, log-domain filters have limitless dynamic range; in circuit in a variable-gain negative-feedback path. Feedback gain is practice, dynamic range is limited by the bias current.
    [Show full text]
  • Design of a 100 Mhz, 5 Order Elliptic, Low-Pass Switched Capacitor Filter
    1 Design of a 100 MHz, 5th Order Elliptic, Low-Pass Switched Capacitor Filter Jon Guerber, ECE 626, Student Member, IEEE TABLE I Abstract—The design and simulation of an Elliptic switched FILTER DESIGN SPECIFICATIONS capacitor filter with modeled non-idealities will be discussed and analyzed. The complete design procedure starting with Parameter Specified Value specifications will be shown. Non-idealities such as finite bandwidth, charge injection, slew rate, offset, finite gain and real world opamps have been incorporated into this study and their Sampling Frequency 100 MHz effect will be demonstrated though simulation. Finally dynamic DC Gain 0 dB range scaling and chip area scaling will be examined for optimal Passband Frequency 0-5 MHz design. Ripple in Passband < 0.2 dB I. INTRODUCTION Stopband Frequency 10-50 MHz ince the dawn of the electronics, the physical laws of Gain in Stopband < -50 dB Snature have necessitated a way to remove unwanted noise Minimum Capacitor Size 0.05 pF from a desired signal. The filter was created to mitigate this problem and has evolved from crude passive device configurations to highly modeled continuous and discrete time integrated blocks. Currently, many low frequency filters With use of Matlab filter design tools, we can quickly employ switched capacitor methods due to the high compare the relative order of the filter for the specifications predictability, reduced cost, and ease of design. above. These filter order results are shown in Table 2. In this paper, a switched capacitor filter with a sampling TABLE II frequency of 100 MHz has been designed. This filter is FILTER ORDER REQUIREMENTS designed without phase considerations, assuming that its use will be in delay tolerant systems or will be followed by an all- Filter Type Minimum Order pass phase correcting filter.
    [Show full text]
  • Filter Design Considerations for High Performance
    FILTER DESIGN CONSIDERATIONS FOR HIGH PERFORMANCE CONTINUOUS-TIME LOW-PASS SIGMA-DELTA ADC A Thesis by VENKATA VEERA SATYA SAIR GADDE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE December 2009 Major Subject: Electrical Engineering FILTER DESIGN CONSIDERATIONS FOR HIGH PERFORMANCE CONTINUOUS-TIME LOW-PASS SIGMA-DELTA ADC A Thesis by VENKATA VEERA SATYA SAIR GADDE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved by: Chair of Committee, Jose Silva-Martinez Committee Members, Shankar P. Bhattacharyya Aydin I. Karsilayan Jay Porter Head of Department, Costas N. Georghiades December 2009 Major Subject: Electrical Engineering iii ABSTRACT Filter Design Considerations for High Performance Continuous-time Low-pass Sigma- delta ADC. (December 2009) Venkata Veera Satya Sair Gadde, B. E., Birla Institute of Technology & Science, Pilani Chair of Advisory Committee: Dr. Jose Silva-Martinez Continuous-time filters are critical components in the implementation of large bandwidth, high frequency, and high resolution continuous-time (CT) sigma-delta (ΣΔ) analog-to-digital converters (ADCs). The loop filter defines the noise-transfer function (NTF) and hence the quantization noise-shaping behavior of the ΣΔ modulator, and becomes the most critical performance determining part in ΣΔ ADC. This thesis presents the design considerations for the loop filter in low-pass CT ΣΔ ADC with 12-bits resolution in 25MHz bandwidth and low power consumption using 0.18μm CMOS technology. Continuous-time filters are more suitable than discrete-time filters due to relaxed amplifier bandwidth requirements for high frequency ΣΔ ADCs.
    [Show full text]
  • Chapter 3 Linear Filters
    Chapter 3 Linear Filters Mikael Olofsson — 2003–2007 A signal is a - normally time-varying - measure of some kind, and filters are devices that manipulate signals. We use mathematical descriptions to model our filters and signals. It should be emphasized that those mathematical descriptions are precisely that - models. How well such a model describes reality has to do with how detailed the model is, what frequencies we are interested in, or in what way input signals are limited. The same model can be good in one situation and bad in another, by which we mean how well it predicts the outcome of an experiment. Linear filters belong to the class of linear systems. However, before we can say anything about systems, we need to start our presentation with signals as functions of time. After that, we continue to describe systems and their properties in the time domain, followed by both signals and systems described in terms of frequencies. Last, standard characterizations of filters are given. 3.1 Signals First of all, a signal is represented as a function of time, where we usually let t denote time. In the practical situation, signals can be almost any physical measures, such as currents, voltages, preassures, positions, and so forth. In telecommunication systems, however, most often we are dealing with voltages and currents, but also electromagnetic phenomena like radio waves and light. Mostly, we are interested in signals that represent some information. In some situations, e.g. when recording sound, the signal can be that information in itself. In other situations, a signal can represent some particular information, e.g.
    [Show full text]
  • APPLICATION BULLETIN Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S
    ®APPLICATION BULLETIN Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S. Tucson Blvd. • Tucson, AZ 85706 Tel: (602) 746-1111 • Twx: 910-952-111 • Telex: 066-6491 • FAX (602) 889-1510 • Immediate Product Info: (800) 548-6132 FAST SETTLING LOW-PASS FILTER By Rod Burt and R. Mark Stitt (602) 746-7445 Noise reduction by filtering is the most commonly used V method for improving signal-to-noise ratio. The increase in IN 1 settling time, however, can be a serious disadvantage in some applications such as high-speed data acquisition sys- R1 tems. The nonlinear filter described here is a simple way to 10kΩ 2 get a four-to-one improvement in settling time as compared VOUT to a conventional filter. C1* 3 To understand the circuit, first consider the dynamics of a single-pole RC filter (Figure 1). Filtering reduces broadband or “white” noise by the square root of the bandwidth reduc- * For 10kHz, C1 = 1592pF. tion as shown by the following calculation: f = 1/(2 • π • R • C ) 4 –3dB 1 1 f f 2 2 FIGURE 1. Conventional Single-Pole RC Filter. e 2 = e 2 df = e 2 • f n B B f f 1 1 VIN 1/2 en = eB (f2 – f1) Diodes Where: R1 10kΩ 1N4148 en = total noise (Vrms) e = broadband noise (V/√Hz) 6 B VOUT f1, f2 = frequency range of interest (Hz) C1* In other words, if the frequency range (f2 – f1) is reduced by a factor of 100, the total noise would be reduced by a factor 7 of 10.
    [Show full text]