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Analog & DSP, FIR Electronic Filters - Frequency Devices

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   Filters, Linear Phase

A linear filter applies a linear operator to a time-varying input signal. Linear filters are very common in electronics and digital signal processing (see the article on electronic filters), but they can also be found in mechanical engineering and other technologies.

They are often used to eliminate unwanted frequencies from an input signal or to select a wanted frequency amongst many others. There are a wide range of types of filter and filter technologies, of which this article will present an overview.

Regardless of whether they are electronic, electrical, or mechanical, or what frequency ranges or timescales they work on, the mathematical theory of linear filters is universal.



Platinum Partners
Frequency Devices, Inc.
Bronze Partners
Aeroflex Laboratories Inc
Allen Avionics, Inc.
Alpha Components
American Trans-Coil Corp.
Anatech Electronics, Inc.
Avens Signal Equipment Corp.
AXTAL GmbH & Co. KG
Betatronics, Inc.
Chesterfield Products, Inc.
Coast Magnetics
Communication Coil Inc.
Corning Frequency Control
Curtis Industries
E G & G Optoelectronics-Reticon
EK Magnetics
Electrocom Industries
Electrocube, Inc.
Filtronetics, Inc.
Freed Transformer Company, Inc.
Hisonic, Inc.
Inductive Technologies
Integrated Microwave Corporation
Integration Assocs. Inc.
K & L Microwave, Inc.
Kappa Technologies, Inc.
KR Electronics, Inc.
Krohn-Hite Corp.
LCR Electronics, Inc.
Linear Technology Corp.
Magnetico, Inc.
Microphase Corporation
Microwave Circuits, Inc.
Microwave Filter Co., Inc.
Mitec Telecom Inc.
Netcom Inc.
North Hills Signal Processing
Pacific Instruments Inc.
Potter Production Corp.
Precision Filters, Inc.
R. C. Electronics Inc.
RCD Components, Inc.
Reactel, Inc.
RFI Corp.
RLC Electronics, Inc.
Rockwell Collins Filter Products
Signal Processing Solutions
Synetcom Digital Inc.
Toko America, Inc.
Toroid Corporation of Maryland
Transtek Magnetics
Trilithic, Inc.
TTE, Incorporated
Analog & DSP, FIR Electronic Filters - Frequency Devices

 

Books
Linear Systems, Fourier Transforms, and Optics (Wiley Series in Pure and Applied Optics)
Jack D. Gaskill

Excerpt - page 246: "... A general LSl system. (a) Depicted as cascade of amplitude filter, nonlinear phase filter, and linear phase filter. (b) Effects of the three filters on a ..."
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Low pass filters with linear phase (Technical Report-) (Technical Report-)
R. M Lerner

Principles of Adaptive Filters and Self-learning Systems (Advanced Textbooks in Control and Signal Processing)
Anthony Zaknich

Excerpt - page 48: "... Filters Three filter classes that are of special significance are linear phase filters, allpass filters and minimum phase filters. Linear phase filters are ..."
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Digital Filter Design Solutions (Artech House Microwave Library)
Jolyon M. De Freitas and Jolyon M. De Freitas

Excerpt - page 2: "... can make no assumptions about the end use of the filters. The conditions (a) to (c) are usually satisfied by linear phase filters. This class of filters is most easily designed using ..."
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Microstrip Filters for RF/Microwave Applications
Jia-Shen G. Hong and M. J. Lancaster

Excerpt - page 4: "... design with less design iterations, leading to first-pass or tuneless filters. This chapter discusses computer simulation ... using transmission line inserted inverters, linear phase filters for group delay equalization , and extracted-pole filters. These ..."
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Digital Filter Design (Topics in Digital Signal Processing)
T. W. Parks and C. S. Burrus

Excerpt - page 28: "... or will occur in complex conjugate pairs. If the FIR filter is linear phase, there are further restrictions on the possible zero locations. From ..."
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Theory and Design of Microwave Filters (Ieee Electromagnetic Waves Series)
Ian C. Hunter

Excerpt - page 9: "... in Figure I.10. Considerable research in the area of' non-minimum phase filters has resulted in so-called selective linear phase filters where a similar amplitude response to ..."
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Multirate Digital Signal Processing: Multirate Systems - Filter Banks - Wavelets
N. J. Fliege

Excerpt - page 57: "... e-jSt(N-1)12. (2.61) The amplitude frequency response of the causal complementary filter, 1 - A(ei~2), is the ... the complementary filter is a linear-phase filter with group delay (N - 1)/2. The high-pass/low-pass and ..."
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Simplified Design of Filter Circuits (EDN Series for Design Engineers)
John D. Lenk and Lenk

Excerpt - page 16: "... or Thompson Figure 1-24 shows the amplitude-response curves for Bessel filters of various orders. Figure 1-25 ... Bessel filter is an approximately linear phase shift. All filters show phase shift that varies with frequency. ..."
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Linear Algebra for Signal Processing (The IMA Volumes in Mathematics and its Applications)
Adam Bojanczyk and George Cybenko

Excerpt - page 102: "... P(z) function [21]. Set C contains the solutions where all filters are linear phase, first examined in [47]. The earliest examples of perfect reconstruction ..."
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Digital Filters and Signal Processing... with MATLAB Exercises
Leland B. Jackson

Excerpt - page 115: "... H(z), then 1/z* also. Therefore, the zeros of a linear-phase filter either must lie on the unit circle or must occur ..."
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DSP System Design: Complexity Reduced IIR Filter Implementation for Practical Applications
Artur Krukowski and Izzet Kale

Excerpt - page 6: "... cosine function in (10) corresponding to the frequencies of the filter zeros and. Those phase jumps can be seen in the filter stopband in Figure 1-3. Linear- phase requirement is very important in the design of digital ..."
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Design of High Frequency Integrated Analogue Filters (Iee Circuits, Devices and Systems Series, 14)
Yichuang Sun

Excerpt - page 18: "... ladder simulation methods 131, 671. As another example, an nth-order linear phase filter with two real zeros' gain boost used in computer hard ..."
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Design and Analysis of Analog Filters - A Signal Processing Perspective (The Kluwer International Series in Engineering and Computer Science, Volume 617) ... Series in Engineering and Computer Science)
Larry D. Paarmann

Excerpt - page 16: "... (2) where the primary concern is constant time delay / linear phase. General Filter Design Papoulis introduced filters with a maximum magnitude slope at ..."
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Spectral Analysis and Filter Theory in Applied Geophysics
Burkhard Buttkus

Excerpt - page 318: "... even impulse response functions, the phase spectra 6(f) of causal filters always differ from zero, i.e., causal filters always introduce phase shifts. 13.6.2 Filters with a linear phase spectrum Assume the signal x(t) has the following spectrum: ..."
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Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications
Alfred Mertins

Excerpt - page 157: "... 17I = 1 in order to be both power-complementary and linear-phase. In other words, power-complementary linear-phase filters cannot have more than two coefficients . ..."
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Selective Linear-Phase Switched-Capacitor and Digital Filters (The International Series in Engineering and Computer Science)
Hussein Baher

Introduction to Digital Signal Processing and Filter Design
B. A. Shenoi

Excerpt - page 24: "... mentioned above, we can realize the following characteristics from digital filters: 1. Transition bands much smaller ... tolerances on the magnitude and phase responses over adjacent passbands are ... impulse response and filters with linear phase. Neither of these characteristics can be achieved by analog ..."
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Signal Processing and Linear Systems
B. P. Lathi

Excerpt - page 270: "... which is not readily apparent to the human eye. The phase distortion (nonlinear phase), on the ... versa. 4.5 Ideal and practical filters Ideal filters allow distortionless transmission ... in Fig. 4.27a has a linear phase of slope -td, which results in a time delay ..."
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Linear minimum-variance filters applied to phase-lock loops, (Charles Stark Draper Laboratory. [Report]) (Charles Stark Draper Laboratory. [Report])
Donald Eugene Gustafson

The Circuits and Filters Handbook, Second Edition
Wai-Kai Chen

Excerpt - page 116: "... was derived by passing the input through an 8-tap FIR filter, which serves as the model ... white pseudo-noise with a 32-tap linear phase FIR noise-coloring filter to produce an input autocorrelation eigenvalue ratio ..."
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Adaptive Filter Theory (3rd Edition)
Simon S. Haykin and Simon Haykin

Excerpt - page 86: "... the case of a special class of filters known as minimum-phase filters, the magnitude response and phase ... The minimum-phase property of a linear time-invariant filter places restrictions of its own on possible locations ..."
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Digital Filters: Basics and Design
Dietrich Schlichtharle

Excerpt - page 6: "... (dB). The negative argument of the frequency response is the phase response of the system. b(w) ... in the passband of the filter; this is equivalent to a linear-phase behaviour. This guarantees that all parts of the spectrum experience ..."
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CRC Handbook of Electrical Filters
John Taylor and Qiuting Huang

Excerpt - page 16: "... lead to greater maximum deviations.'' Compared with special nonrecursive digital filters with strictly linear phase functions even in the stopbands, the result presented is of ..."
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Continuous-Time Active Filter Design
T. Deliyannis, Yichuang Sun, and J.K. Fidler

Excerpt - page 6: "... an ideal time delayer. In practice the phase can be linear, within an acceptable error, up to a certain frequency (o, For frequencies below w, the allpass filter operates as a delayer. It is useful in phase equalization. It should be noted that allpass filters are not ..."
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Multidimensional Filter Banks and Wavelets: Basic Theory and Cosine Modulated Filter Banks
Sankar Basu and Bernard C. Levy

Excerpt - page 20: "... diamond-shaped H0(z) and F0(z) such that Ho(z)Fo(z) is a Nyquist(Q) filter. 2.1.2. Design of Ho(z) and ... this case are FIR and linear-phase. McClellan transformation. This transformation was proposed by McClellan in 1976 ..."
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Digital Signal Processing: Spectral Computation and Filter Design (The Oxford Series in Electrical and Computer Engineering)
Chi-Tsong Chen

Excerpt - page 253: "... be extended periodically with period 27r to all w. The filter has magnitude 1 and a linear phase -(ono for lwl _< co, and zero magnitude and unspecified ..."
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Phase-Locked Loop Circuit Design (Prentice Hall Advanced Reference Series)
Dan H. Wolaver

Excerpt - page 28: "... design of a PLL. This chapter deals with the loop filter, and the next two chapters deal with the phase detector and the VCO. The linear model of the PLL in Fig. 3-3 has already been ..."
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Linear IC Applications, A Designer's Handbook
Joseph Carr

Excerpt - page 287: "... The Bessel filter also shows a phase shift over the passband, but it is nearly linear. A useful feature of this characteristic is that it allows ..."
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Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms (Stability and Control: Theory, Methods and Applications)
F A Aliev and V B Larin

Excerpt - page 48: "... 48 OPTIMIZATION OF LINEAR CONTROL SYSTEMS filtering problems (Kalman filter design) for the systems, the phase coordinates of which are registered in different time intervals (see ..."
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Theory of the Non-linear Analog Phase Locked Loop (Lecture Notes in Control and Information Sciences)
Nikolaos I. Margaris

Binary Polynomial Transforms and Non-linear Digital Filters (Pure and Applied Mathematics (Marcel Dekker))
S. Agaian, Jaakko Astola, and Karen Egiazarian

Signals and Systems: Analysis of Signals Through Linear Systems
M. J. Roberts

Excerpt - page 398: "... its magnitude is not constant with frequency. But an ideal filter is distortionless within its passband. That is, its transfer function magnitude is constant within the passband and its transfer function phase is linear within the passband. There are four commonly defined types of ..."
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Phase-Locked Loops
John L. Stensby

Excerpt - page 18: "... 18 PHASE-LOCKED LOOPS: THEORY AND APPLICATIONS defines the loop filter. This equation is linear, and it has constant coefficients . Furthermore, it has a ..."
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Practical Analog And Digital Filter Design (Artech House Microwave Library)
Les Thede

Excerpt - page 7: "... passband, but a smooth, ever-decreasing gain in the stopband. The phase distortion produced by these filters is not as severe as ... 1.4. It provides the most linear phase response of any approximation technique discussed in this text. ..."
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Intuitive Analog Circuit Design
Marc Thompson

Excerpt - page 387: "... association the group delay' response) affects the transient response of filters. An ide- al filter has a linear phase shift with frequency, and hence constant group delay as in ..."
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