LEADER 05155nam 2200625 a 450 001 9910829925503321 005 20230617035827.0 010 $a1-282-37214-9 010 $a9786612372148 010 $a3-527-61856-2 010 $a3-527-61857-0 035 $a(CKB)1000000000687364 035 $a(EBL)482174 035 $a(OCoLC)609855545 035 $a(SSID)ssj0000304391 035 $a(PQKBManifestationID)11256742 035 $a(PQKBTitleCode)TC0000304391 035 $a(PQKBWorkID)10278942 035 $a(PQKB)10059425 035 $a(MiAaPQ)EBC482174 035 $a(EXLCZ)991000000000687364 100 $a20041014d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA new twist to Fourier transforms$b[electronic resource] /$fHamish D. Meikle 210 $aWeinheim $cWiley-VCH$dc2004 215 $a1 online resource (240 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40441-4 320 $aIncludes bibliographical references and index. 327 $aA New Twist to Fourier Transforms; Table of Contents; Introduction; Conventions; Symbols; Acknowledgments; 1 The Fourier Transform and the Helix; 1.1 Fourier Transform Conventions; 1.1.1 Fourier Transforms in Physics; 1.1.2 Fourier Transform in Electrical Engineering; 1.1.3 Fourier Transform in Statistics; 1.2 The Fourier Transform and the Helical Functions; 1.3 Radar and Sonar Echo Signals; 1.4 Colour Television Signals; 1.5 Modulation and Demodulation; 1.6 Communications; 1.7 Circularly Polarised Waves; 1.8 Noise; 1.9 Other Forms of the Fourier Transform; 2 Spiral and Helical Functions 327 $a2.1 Complex Arithmetic2.1.1 Unary Operations; 2.1.2 Vector Addition and Subtraction; 2.1.3 Vector Multiplication; 2.1.4 Division; 2.1.5 Powers of Vectors; 2.2 Unbalanced Polyphase Voltages and Currents; 3 Fourier Transforms; 3.1 From Fourier Series to Fourier Transform; 3.1.1 Fourier Series; 3.1.2 Period of Integration for a Fourier Series; 3.1.3 Fourier Transform; 3.1.4 Inverse Transform; 3.2 Three of the Conventions for Fourier Transforms; 3.3 Fourier Transforms and Spatial Spirals; 3.4 Properties of Fourier Transforms; 3.4.1 Addition, Subtraction, and Scaling - Linearity 327 $a3.4.2 Multiplication of Transforms3.4.3 Division; 3.4.4 Differentiation; 3.4.5 Moments; 3.5 Special Functions used for Fourier Transforms; 3.6 Summary of Fourier Transform Properties; 3.7 Examples of Fourier Transforms; 3.7.1 Cosine and Sine Waveforms; 3.7.2 Rectangular Pulse; 3.7.3 Triangular Pulse; 3.7.4 Ramp Pulse; 3.7.5 Gaussian Pulse; 3.7.6 Unequally Spaced Samples; 4 Continuous, Finite, and Discrete Fourier Transforms; 4.1 Finite Fourier Transforms - Limited in Time or Space; 4.2 Discrete Fourier Transforms; 4.2.1 Cyclic Nature of Discrete Transforms 327 $a4.2.2 Other Forms of the Discrete Fourier Transform4.2.3 Summary of Properties; 4.3 Sampling; 4.3.1 Sampling Errors; 4.3.2 Sampling of Polyphase Voltages; 4.4 Examples of Discrete Fourier Transforms; 4.4.1 Finite Impulse Response Filters and Antennae; 4.4.2 The z-transform; 4.4.3 Inverse Fourier Transforms, a Lowpass Filter; 4.4.4 Inverse Fourier Transforms, a Highpass Filter; 4.4.5 Inverse Fourier Transforms, Bandpass and Bandstop Filters; 4.4.6 Arrays of Sensors, Linear Antennae; 4.4.7 Pattern Synthesis, the Woodward-Levinson Sampling Method 327 $a4.5 Conversion of Analogue Signals to Digital Words4.5.1 Dynamic Range; 4.5.2 Dynamic Range in Vector Systems; 4.5.3 Quantisation Noise; 4.5.4 Conversion Errors; 4.5.5 Image Frequency or Negative Phase Sequence Component Power; 5 Tapering Functions; 5.1 Conventions and Normalisation; 5.2 Parameters used with Tapering Functions; 5.2.1 Parameters A and C; 5.2.2 Efficiency Parameter ?; 5.2.3 Noise Width; 5.2.4 Half-power Width; 5.2.5 Parameters D and G; 5.2.6 Root Mean Square (rms) Width in Terms of p ?; 5.2.7 Root Mean Square (rms) Width in Terms of p ?; 5.2.8 First Sidelobe or Sideband Height 327 $a5.2.9 Fall-off 330 $aMaking use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, o 606 $aFourier transformations 606 $aSignal processing 615 0$aFourier transformations. 615 0$aSignal processing. 676 $a515.723 676 $a515/.723 676 $a621.38223 700 $aMeikle$b Hamish$01608860 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829925503321 996 $aA new twist to Fourier transforms$93935828 997 $aUNINA