The Fourier Transform And Its Applications PDF
Preview The Fourier Transform And Its Applications
THE FOURIER TRANSFORM AND Its APPLICATIONS RONALD No BRACEWELL Josep, Rowse, 21 Maret 176-16 May 188. (Dy permionon ofthe Bidlioueique Manieipate de Crenobl The Fourier Transform and Its Applications Third Edition Ronald N. Bracewell Levis M. Tema Prosar of Elana Enger Emi Slayer Undeey Boston Burr Ridge, Nl. Dubuque, 1A_ Madison, WL New York San Francisca St. Louis Bangkok Bogoté Caracas Tixbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto McGraw-Hill Higher Education ADs Te NeoutCngai ‘THE TOURIER TRANSFORM AND ITS APPLICATIONS. Tiverton Eons 2000 Caclsive rights Uy MeCaw-Hill Buok Co— Siegapare.forranuficure and ent Lusibook ‘cannot be reesportl Faun the cuniry to which tts suaigned by McCraw Ei ‘Cupyrght © 2000, 1986, 1978 1965 by The MeGraw-Hill Compa hs, AI rights reserved. Except as permitted under the Lnted States Coppright Act of 1976. pat oF ti, bbe repreduced or distributed in ay form o by ay means or stored in da base system, wilhuot te price weiden permission ofthe publisher 234567890 KKP UPE2 0 Library of Congress Catslogiog-in-Publication Dats ‘Bracevell, Ronald Newbold (date) ‘The Fourier ranstesm and ications /ReamlaN, Bracewell dade, pom, ISHN Oa us95e-1 1. Fourier ansfermations. 2. Transformation (Mathematics) 3. Harmonic ataiysis. 1 Tile Qaa0ss.u7 2000 51517232 9.21139 we wsbieceu ‘When ordering this tte, use ISBN O47-1N6DA3-4 Printed in Singapore Xwouv var auTHon Ml RONALD N. BRACEWELL wos bom in Australia, received his BSc, BF. and ME. degrees from the University of Sydney, and eamed a PRD. in physics from Cambridge University. Currently 1. M Terman Profesor of Bovtrical Enginece™ ing Emeritus at Stenfid Uniwrity, Dr Bracewell has an inpressive roster of pro- fessional afiations, award and publications to his edit He isa Fellow ofthe Rayal Astronomical Society, the Astronomical Society of Australia, and past Coun «lor ofthe American Astronomical Society Te is ao a life Fellow and Heireich Herts gold medals ofthe Trattue of Flecrial and Eketronie Engineers. AtStan- ford Rao Astronomy Inatitutehe designed and builrinnovative radio telescopes, fluding the first antenna with the resolution of the human eye, les than one rinute of are, and was involved in early discoveries relating 0 the cosmic back {ground radiation. Fourier analysis played s key role i his novel instrument e- Sg and. data processing, Fourier's admirable ideas also contributed to Dr. Bracewell’s advances in tomographic imaging, which led ta his election tothe fn stitute of Meslcine of he National Arademy of Sciences, to receving Sydney Uri tenity's inoogural Alumni Award for Achievement, and to being appointed sn Officer of the Onler of Australia for service to science inthe fekds of radio as- fromomy and image revonstracton. Fourier’s theorem: is not only one of the most beutiful resutis of modern analysis, but it may be said to furtish an indispensable instrument in the treatment of nearly every recondite question in madens physics. Lord Kelvin ‘To may wife Helen, those support made this edition possible. Ronald Bracewell Preface Introduction Groundwork ‘The Fourier Teanaform and Fourier’s Integeal Theorem ‘Conditions for the Existence of Fourice Tennsforms ‘Transforms in the Limit Oddiness and Everners Significance of Oddness and Fvenness ‘Complex Conjugates Cosine and Sine Transforms Interpretation of the Furmulas Convolution Examples of Convolution, Serial Products Ioerson of serial atiplation / Th seat product in maby notation Sequences os reciors Convolution by Computer ‘the Aulocoreelation Function and Pentagzam Notation the Triple Curation “The Cruse Conzelation “The Energy Spectrom. ‘Notation for Some Useful Functions Keclangle Function of Unit Height and Base, 116) ‘Triangle Function of Unit Height and Azea, A(x) ‘Various Esponentials and Gaussian and Rayleigh Curves Heaviside’s Unit Step Function, Hs) “The Sign Function, sgn x ‘The Filtering or Interpolating Function, sine» Pictorial Representation Summary of Special Symbols conTtEeNTS Ml Contents The Impulse Symbol ” ‘The Sifting Property ™ “The Sampling or Keplicoting Syenbal TK.) ot ‘The Feen and Od Topule Pairs n(x) and tts) 8 Derivatives ofthe Impulse Syabol ‘Null Functions e Some Funcburs in Two or More Dimensions co ‘The Concept of Generalized Function 2 Ponizilety wal-tchcoo! fonts / Reguler voquemes f Conealiced fowtion: £ Algehne of gemeuted fusions 7 Difrontiaian of dinar fanctions The Basic Theorems 106 ‘A Bow Teansfonme for Mustration 105, ‘Simian Theorem 108 Addition Theorem ne Shift There m Modulation Theozera a3 Convolution Thearem us Rayleigh’. Theosern up Power Thoorem 0 ‘Autecorrelation Theorem iw Derivative Theorem ot Derivative of a Convolution knteg 16 ‘The Transform of a Generalized Puration ur Pras of Theorems 3 ‘Skniarity nl shi themes / Dercaicetheren 7 Power thee Suramary of Theorers 19 Obtaining Transforms 136 Integration in Closed Form 137 “Numeral Force Temslortion. 10 The Slow Fourier Transform Program we ‘Generation of Teansforrs by Theorers 5 “Applicaties vf the Derivative Theswm te Segmented Functions MS Measurement of Spectea “ Radlofenuency spectral aval / Optical Faxver transform spectroscopy ‘The Two Domains 11 Daft Fteyral 152 ‘ie First Moment 383 Centtoid 15 Moment of Inertio (Seruned Moment) 156 Moments wr Mean-Square Abscissa 18 Radi of Cyration 10 Contents Variance Smeothress ond Compsctness ‘Smoothness under Convolution “Asymprotic Behavior Tquivalent Width Autocorrelation Width ‘Mean Square Widths Sampling, and Replication Connie Some Inepsites per tints le ontinle an slope / Schurz’ inepality ‘he Uncertainty Keaton. rss of urcrksinty relation 7 Example of uncertainty relation ‘The Finite Pitfrence Running Means ‘Cental Limit Theorent ‘Summary af Correspondenees in the Twe Domains 9 Waveforms, Spectra, Fillers, and Linearity lectrcal Waveforns ara! Shen Bhs Gencraity of Lines Fi Tiga ling Interpolation of Theorems ‘Siar hare Aiton teore £ Shift ore /Metlstion theorem / Caner of medion tere Lineatity and Tine fnvaviance Feviodiity Theory 10 Sampling and Series Sampling Theorem Interpolation Rectengular Fitring in Hrequency Demain Smoothing by Rinneing, Means LUndersampling ‘Ordinate and Slope Saenpling Interlaced Sampling Sage in the Presence of Noise Fourier Series Gibbs phenomenon / Finite Foner tronsforms f Fourier copies Impulse Trains That Are Periodic The Shal Symbol Is ts Oven Fourier Transform A The Discrete Fourier Transform and the FFT ‘The Discrete Trsforos Formula Cyclic Convolution ‘samples of Dincate Fourier Transforms ai R Reciprocal Property (Oddness snd Evenness KEeinples with Special Symentty Complex Conjugates Reversal Property Adkltion Theron ‘Shift Theorem Convelition Theorem Product Theoron (Crese-Conreation Autocorrelation ‘Sum of Sequence First Yolue Generalized Parseval Rayleigh Theorem Packing Theor Sonitanty These, Examples Using MATLAB ‘The Fast Fourier ranstor, Practical Considerations le fhe Discrete Fourier Transform Correct? “Applications ofthe FFI “Timing Diagrams When N is Not a Power of ‘TwoDimensional Dats Power Spectra ‘The Discrete Hartley Transform ‘A Strietly Reciprocal Real Transform ‘Notation and Example ‘The Discrete Hanley Transform Exomples of DHT Tiscussion ‘A Convolution of Algosithm in One and Two Dimensions “Two Dimensions The CosCan Teanafou, ‘Thecrems “The Diserete Sine and Cosine transforms ewndary sales prees/ Data compression: aplicoton Computing (Goring a Feel foe Numeric Tarsfomes The Complex Flaneg Tansforrs Physical Aspect of the Hartley Transformation ‘The Fast Hatley Trnstorm The Fast Algorithm Running lime ; H USSUSSSIVSERRSRRRR 295 SegRRe SeRREES
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