05155nam 2200625 a 450 991082992550332120230617035827.01-282-37214-997866123721483-527-61856-23-527-61857-0(CKB)1000000000687364(EBL)482174(OCoLC)609855545(SSID)ssj0000304391(PQKBManifestationID)11256742(PQKBTitleCode)TC0000304391(PQKBWorkID)10278942(PQKB)10059425(MiAaPQ)EBC482174(EXLCZ)99100000000068736420041014d2004 uy 0engur|n|---|||||txtccrA new twist to Fourier transforms[electronic resource] /Hamish D. MeikleWeinheim Wiley-VCHc20041 online resource (240 p.)Description based upon print version of record.3-527-40441-4 Includes bibliographical references and index.A 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 Functions2.1 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 - Linearity3.4.2 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 Transforms4.2.2 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 Method4.5 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 η; 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 Height5.2.9 Fall-offMaking 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, oFourier transformationsSignal processingFourier transformations.Signal processing.515.723515/.723621.38223Meikle Hamish1608860MiAaPQMiAaPQMiAaPQBOOK9910829925503321A new twist to Fourier transforms3935828UNINA