Jean-Laurent Puebe,
J Puebe
John Wiley & Sons
e druk, 2008
9781848210653
Fluid Mechanics
Specificaties
Gebonden, 518 blz.
|
Engels
John Wiley & Sons |
e druk, 2008
ISBN13: 9781848210653
Rubricering
Verwachte levertijd ongeveer 16 werkdagen
Samenvatting
This book examines the phenomena of fluid flow and transfer as governed by mechanics and thermodynamics. Part 1 concentrates on equations coming from balance laws and also discusses transportation phenomena and propagation of shock waves. Part 2 explains the basic methods of metrology, signal processing, and system modeling, using a selection of examples of fluid and thermal mechanics.
Specificaties
Inhoudsopgave
<p>Preface xi</p>
<p>Chapter 1. Thermodynamics of Discrete Systems 1</p>
<p>1.1. The representational bases of a material system 1</p>
<p>1.1.1. Introduction 1</p>
<p>1.1.2. Systems analysis and thermodynamics 8</p>
<p>1.1.3. The notion of state 11</p>
<p>1.1.4. Processes and systems 13</p>
<p>1.2. Axioms of thermostatics 15</p>
<p>1.2.1. Introduction 15</p>
<p>1.2.2. Extensive quantities 16</p>
<p>1.2.3. Energy, work and heat 20</p>
<p>1.3. Consequences of the axioms of thermostatics 21</p>
<p>1.3.1. Intensive variables 21</p>
<p>1.3.2. Thermodynamic potentials 23</p>
<p>1.4. Out–of–equilibrium states 29</p>
<p>1.4.1. Introduction 29</p>
<p>1.4.2. Discontinuous systems 30</p>
<p>1.4.3. Application to heat engines 45</p>
<p>Chapter 2. Thermodynamics of Continuous Media 47</p>
<p>2.1. Thermostatics of continuous media 47</p>
<p>2.1.1. Reduced extensive quantities 47</p>
<p>2.1.2. Local thermodynamic equilibrium 48</p>
<p>2.1.3. Flux of extensive quantities 50</p>
<p>2.1.4. Balance equations in continuous media 54</p>
<p>2.1.5. Phenomenological laws 57</p>
<p>2.2. Fluid statics 63</p>
<p>2.2.1. General equations of fluid statics 63</p>
<p>2.2.2. Pressure forces on solid boundaries 68</p>
<p>2.3. Heat conduction 72</p>
<p>2.3.1. The heat equation 72</p>
<p>2.3.2. Thermal boundary conditions 72</p>
<p>2.4. Diffusion 73</p>
<p>2.4.1. Introduction 73</p>
<p>2.4.2. Molar and mass fluxes 77</p>
<p>2.4.3. Choice of reference frame 80</p>
<p>2.4.4. Binary isothermal mixture 85</p>
<p>2.4.5. Coupled phenomena with diffusion 97</p>
<p>2.4.6. Boundary conditions 99</p>
<p>Chapter 3. Physics of Energetic Systems in Flow 101</p>
<p>3.1. Dynamics of a material point 101</p>
<p>3.1.1. Galilean reference frames in traditional mechanics 101</p>
<p>3.1.2. Isolated mechanical system and momentum 102</p>
<p>3.1.3. Momentum and velocity 103</p>
<p>3.1.4. Definition of force 104</p>
<p>3.1.5. The fundamental law of dynamics (closed systems) 106</p>
<p>3.1.6. Kinetic energy 106</p>
<p>3.2. Mechanical material system 107</p>
<p>3.2.1. Dynamic properties of a material system 107</p>
<p>3.2.2. Kinetic energy of a material system 109</p>
<p>3.2.3. Mechanical system in thermodynamic equilibrium the rigid solid 111</p>
<p>3.2.4. The open mechanical system 112</p>
<p>3.2.5. Thermodynamics of a system in motion 116</p>
<p>3.3. Kinematics of continuous media 119</p>
<p>3.3.1. Lagrangian and Eulerian variables 119</p>
<p>3.3.2. Trajectories, streamlines, streaklines 121</p>
<p>3.3.3. Material (or Lagrangian) derivative 122</p>
<p>3.3.4. Deformation rate tensors 129</p>
<p>3.4. Phenomenological laws of viscosity 132</p>
<p>3.4.1. Definition of a fluid 132</p>
<p>3.4.2. Viscometric flows 135</p>
<p>3.4.3. The Newtonian fluid 146</p>
<p>Chapter 4. Fluid Dynamics Equations 151</p>
<p>4.1. Local balance equations 151</p>
<p>4.1.1. Balance of an extensive quantity G 151</p>
<p>4.1.2. Interpretation of an equation in terms of the balance equation 153</p>
<p>4.2. Mass balance 154</p>
<p>4.2.1. Conservation of mass and its consequences 154</p>
<p>4.2.2. Volume conservation 160</p>
<p>4.3. Balance of mechanical and thermodynamic quantities 160</p>
<p>4.3.1. Momentum balance 160</p>
<p>4.3.2. Kinetic energy theorem 164</p>
<p>4.3.3. The vorticity equation 171</p>
<p>4.3.4. The energy equation 172</p>
<p>4.3.5. Balance of chemical species 177</p>
<p>4.4. Boundary conditions 178</p>
<p>4.4.1. General considerations 178</p>
<p>4.4.2. Geometric boundary conditions 179</p>
<p>4.4.3. Initial conditions 181</p>
<p>4.5. Global form of the balance equations 182</p>
<p>4.5.1. The interest of the global form of a balance 182</p>
<p>4.5.2. Equation of mass conservation 184</p>
<p>4.5.3. Volume balance 184</p>
<p>4.5.4. The momentum flux theorem 184</p>
<p>4.5.5. Kinetic energy theorem 186</p>
<p>4.5.6. The energy equation 187</p>
<p>4.5.7. The balance equation for chemical species 188</p>
<p>4.6. Similarity and non–dimensional parameters 189</p>
<p>4.6.1. Principles 189</p>
<p>Chapter 5. Transport and Propagation 199</p>
<p>5.1. General considerations 199</p>
<p>5.1.1. Differential equations 199</p>
<p>5.1.2. The Cauchy problem for differential equations 202</p>
<p>5.2. First order quasi–linear partial differential equations 203</p>
<p>5.2.1. Introduction 203</p>
<p>5.2.2. Geometric interpretation of the solutions 204</p>
<p>5.2.3. Comments 206</p>
<p>5.2.4. The Cauchy problem for partial differential equations 206</p>
<p>5.3. Systems of first order partial differential equations 207</p>
<p>5.3.1. The Cauchy problem for n unknowns and two variables 207</p>
<p>5.3.2. Applications in fluid mechanics 210</p>
<p>5.3.3. Cauchy problem with n unknowns and p variables 216</p>
<p>5.3.4. Partial differential equations of order n 218</p>
<p>5.3.5. Applications 220</p>
<p>5.3.6. Physical interpretation of propagation 223</p>
<p>5.4. Second order partial differential equations 225</p>
<p>5.4.1. Introduction 225</p>
<p>5.4.2. Characteristic curves of hyperbolic equations 226</p>
<p>5.4.3. Reduced form of the second order quasi–linear partial differential equation 229</p>
<p>5.4.4. Second order partial differential equations in a finite domain 232</p>
<p>5.4.5. Second order partial differential equations and their boundary conditions 233</p>
<p>5.5. Discontinuities: shock waves 239</p>
<p>5.5.1. General considerations 239</p>
<p>5.5.2. Unsteady 1D flow of an inviscid compressible fluid 239</p>
<p>5.5.3. Plane steady supersonic flow 244</p>
<p>5.5.4. Flow in a nozzle 244</p>
<p>5.5.5. Separated shock wave 248</p>
<p>5.5.6. Other discontinuity categories 248</p>
<p>5.5.7. Balance equations across a discontinuity 249</p>
<p>5.6. Some comments on methods of numerical solution 250</p>
<p>5.6.1. Characteristic curves and numerical discretization schemes 250</p>
<p>5.6.2. A complex example 253</p>
<p>5.6.3. Boundary conditions of flow problems 255</p>
<p>Chapter 6. General Properties of Flows 257</p>
<p>6.1. Dynamics of vorticity 257</p>
<p>6.1.1. Kinematic properties of the rotation vector 257</p>
<p>6.1.2. Equation and properties of the rotation vector 261</p>
<p>6.2. Potential flows 269</p>
<p>6.2.1. Introduction 269</p>
<p>6.2.2. Bernoulli s second theorem 269</p>
<p>6.2.3. Flow of compressible inviscid fluid 270</p>
<p>6.2.4. Nature of equations in inviscid flows 271</p>
<p>6.2.5. Elementary solutions in irrotational flows 273</p>
<p>6.2.6. Surface waves in shallow water 284</p>
<p>6.3. Orders of magnitude 288</p>
<p>6.3.1. Introduction and discussion of a simple example 288</p>
<p>6.3.2. Obtaining approximate values of a solution 291</p>
<p>6.4. Small parameters and perturbation phenomena 296</p>
<p>6.4.1. Introduction 296</p>
<p>6.4.2. Regular perturbation 296</p>
<p>6.4.3. Singular perturbations 305</p>
<p>6.5. Quasi–1D flows 309</p>
<p>6.5.1. General properties 309</p>
<p>6.5.2. Flows in pipes 314</p>
<p>6.5.3. The boundary layer in steady flow 319</p>
<p>6.6. Unsteady flows and steady flows 327</p>
<p>6.6.1. Introduction 327</p>
<p>6.6.2. The existence of steady flows 328</p>
<p>6.6.3. Transitional regime and permanent solution 330</p>
<p>6.6.4. Non–existence of a steady solution 334</p>
<p>Chapter 7. Measurement, Representation and Analysis of Temporal Signals 339</p>
<p>7.1. Introduction and position of the problem 339</p>
<p>7.2. Measurement and experimental data in flows 340</p>
<p>7.2.1. Introduction 340</p>
<p>7.2.2. Measurement of pressure 341</p>
<p>7.2.3. Anemometric measurements 342</p>
<p>7.2.4. Temperature measurements 346</p>
<p>7.2.5. Measurements of concentration 347</p>
<p>7.2.6. Fields of quantities and global measurements 347</p>
<p>7.2.7. Errors and uncertainties of measurements 351</p>
<p>7.3. Representation of signals 357</p>
<p>7.3.1. Objectives of continuous signal representation 357</p>
<p>7.3.2. Analytical representation 360</p>
<p>7.3.3. Signal decomposition on the basis of functions; series and elementary solutions 361</p>
<p>7.3.4. Integral transforms 363</p>
<p>7.3.5. Time–frequency (or timescale) representations 374</p>
<p>7.3.6. Discretized signals 381</p>
<p>7.3.7. Data compression 385</p>
<p>7.4. Choice of representation and obtaining pertinent information 389</p>
<p>7.4.1. Introduction 389</p>
<p>7.4.2. An example: analysis of sound 390</p>
<p>7.4.3. Analysis of musical signals 393</p>
<p>7.4.4. Signal analysis in aero–energetics 402</p>
<p>Chapter 8. Thermal Systems and Models 405</p>
<p>8.1. Overview of models 405</p>
<p>8.1.1. Introduction and definitions 405</p>
<p>8.1.2. Modeling by state representation and choice of variables 408</p>
<p>8.1.3. External representation 410</p>
<p>8.1.4. Command models 411</p>
<p>8.2. Thermodynamics and state representation 412</p>
<p>8.2.1. General principles of modeling 412</p>
<p>8.2.2. Linear time–invariant system (LTIS) 420</p>
<p>8.3. Modeling linear invariant thermal systems 422</p>
<p>8.3.1. Modeling discrete systems 422</p>
<p>8.3.2. Thermal models in continuous media 431</p>
<p>8.4. External representation of linear invariant systems 446</p>
<p>8.4.1. Overview 446</p>
<p>8.4.2. External description of linear invariant systems 446</p>
<p>8.5. Parametric models 451</p>
<p>8.5.1. Definition of model parameters 451</p>
<p>8.5.2. Established regimes of linear invariant systems 453</p>
<p>8.5.3. Established regimes in continuous media 458</p>
<p>8.6. Model reduction 465</p>
<p>8.6.1. Overview 465</p>
<p>8.6.2. Model reduction of discrete systems 466</p>
<p>8.7. Application in fluid mechanics and transfer in flows 474</p>
<p>Appendix 1. Laplace Transform 477</p>
<p>A1.1. Definition 477</p>
<p>A1.2. Properties 477</p>
<p>A1.3. Some Laplace transforms 478</p>
<p>A1.4. Application to the solution of constant coefficient differential equations 479</p>
<p>Appendix 2. Hilbert Transform 481</p>
<p>Appendix 3. Cepstral Analysis 483</p>
<p>A3.1. Introduction 483</p>
<p>A3.2. Definitions 483</p>
<p>A3.3. Example of echo suppression 484</p>
<p>A3.4. General case 485</p>
<p>Appendix 4. Eigenfunctions of an Operator 487</p>
<p>A4.1. Eigenfunctions of an operator 487</p>
<p>A4.2. Self–adjoint operator 487</p>
<p>A4.2.1. Eigenfunctions 487</p>
<p>A4.2.2. Expression of a function of f using an eigenfunction basis–set 488</p>
<p>Bibliography 489</p>
<p>Index 497</p>
<p>Chapter 1. Thermodynamics of Discrete Systems 1</p>
<p>1.1. The representational bases of a material system 1</p>
<p>1.1.1. Introduction 1</p>
<p>1.1.2. Systems analysis and thermodynamics 8</p>
<p>1.1.3. The notion of state 11</p>
<p>1.1.4. Processes and systems 13</p>
<p>1.2. Axioms of thermostatics 15</p>
<p>1.2.1. Introduction 15</p>
<p>1.2.2. Extensive quantities 16</p>
<p>1.2.3. Energy, work and heat 20</p>
<p>1.3. Consequences of the axioms of thermostatics 21</p>
<p>1.3.1. Intensive variables 21</p>
<p>1.3.2. Thermodynamic potentials 23</p>
<p>1.4. Out–of–equilibrium states 29</p>
<p>1.4.1. Introduction 29</p>
<p>1.4.2. Discontinuous systems 30</p>
<p>1.4.3. Application to heat engines 45</p>
<p>Chapter 2. Thermodynamics of Continuous Media 47</p>
<p>2.1. Thermostatics of continuous media 47</p>
<p>2.1.1. Reduced extensive quantities 47</p>
<p>2.1.2. Local thermodynamic equilibrium 48</p>
<p>2.1.3. Flux of extensive quantities 50</p>
<p>2.1.4. Balance equations in continuous media 54</p>
<p>2.1.5. Phenomenological laws 57</p>
<p>2.2. Fluid statics 63</p>
<p>2.2.1. General equations of fluid statics 63</p>
<p>2.2.2. Pressure forces on solid boundaries 68</p>
<p>2.3. Heat conduction 72</p>
<p>2.3.1. The heat equation 72</p>
<p>2.3.2. Thermal boundary conditions 72</p>
<p>2.4. Diffusion 73</p>
<p>2.4.1. Introduction 73</p>
<p>2.4.2. Molar and mass fluxes 77</p>
<p>2.4.3. Choice of reference frame 80</p>
<p>2.4.4. Binary isothermal mixture 85</p>
<p>2.4.5. Coupled phenomena with diffusion 97</p>
<p>2.4.6. Boundary conditions 99</p>
<p>Chapter 3. Physics of Energetic Systems in Flow 101</p>
<p>3.1. Dynamics of a material point 101</p>
<p>3.1.1. Galilean reference frames in traditional mechanics 101</p>
<p>3.1.2. Isolated mechanical system and momentum 102</p>
<p>3.1.3. Momentum and velocity 103</p>
<p>3.1.4. Definition of force 104</p>
<p>3.1.5. The fundamental law of dynamics (closed systems) 106</p>
<p>3.1.6. Kinetic energy 106</p>
<p>3.2. Mechanical material system 107</p>
<p>3.2.1. Dynamic properties of a material system 107</p>
<p>3.2.2. Kinetic energy of a material system 109</p>
<p>3.2.3. Mechanical system in thermodynamic equilibrium the rigid solid 111</p>
<p>3.2.4. The open mechanical system 112</p>
<p>3.2.5. Thermodynamics of a system in motion 116</p>
<p>3.3. Kinematics of continuous media 119</p>
<p>3.3.1. Lagrangian and Eulerian variables 119</p>
<p>3.3.2. Trajectories, streamlines, streaklines 121</p>
<p>3.3.3. Material (or Lagrangian) derivative 122</p>
<p>3.3.4. Deformation rate tensors 129</p>
<p>3.4. Phenomenological laws of viscosity 132</p>
<p>3.4.1. Definition of a fluid 132</p>
<p>3.4.2. Viscometric flows 135</p>
<p>3.4.3. The Newtonian fluid 146</p>
<p>Chapter 4. Fluid Dynamics Equations 151</p>
<p>4.1. Local balance equations 151</p>
<p>4.1.1. Balance of an extensive quantity G 151</p>
<p>4.1.2. Interpretation of an equation in terms of the balance equation 153</p>
<p>4.2. Mass balance 154</p>
<p>4.2.1. Conservation of mass and its consequences 154</p>
<p>4.2.2. Volume conservation 160</p>
<p>4.3. Balance of mechanical and thermodynamic quantities 160</p>
<p>4.3.1. Momentum balance 160</p>
<p>4.3.2. Kinetic energy theorem 164</p>
<p>4.3.3. The vorticity equation 171</p>
<p>4.3.4. The energy equation 172</p>
<p>4.3.5. Balance of chemical species 177</p>
<p>4.4. Boundary conditions 178</p>
<p>4.4.1. General considerations 178</p>
<p>4.4.2. Geometric boundary conditions 179</p>
<p>4.4.3. Initial conditions 181</p>
<p>4.5. Global form of the balance equations 182</p>
<p>4.5.1. The interest of the global form of a balance 182</p>
<p>4.5.2. Equation of mass conservation 184</p>
<p>4.5.3. Volume balance 184</p>
<p>4.5.4. The momentum flux theorem 184</p>
<p>4.5.5. Kinetic energy theorem 186</p>
<p>4.5.6. The energy equation 187</p>
<p>4.5.7. The balance equation for chemical species 188</p>
<p>4.6. Similarity and non–dimensional parameters 189</p>
<p>4.6.1. Principles 189</p>
<p>Chapter 5. Transport and Propagation 199</p>
<p>5.1. General considerations 199</p>
<p>5.1.1. Differential equations 199</p>
<p>5.1.2. The Cauchy problem for differential equations 202</p>
<p>5.2. First order quasi–linear partial differential equations 203</p>
<p>5.2.1. Introduction 203</p>
<p>5.2.2. Geometric interpretation of the solutions 204</p>
<p>5.2.3. Comments 206</p>
<p>5.2.4. The Cauchy problem for partial differential equations 206</p>
<p>5.3. Systems of first order partial differential equations 207</p>
<p>5.3.1. The Cauchy problem for n unknowns and two variables 207</p>
<p>5.3.2. Applications in fluid mechanics 210</p>
<p>5.3.3. Cauchy problem with n unknowns and p variables 216</p>
<p>5.3.4. Partial differential equations of order n 218</p>
<p>5.3.5. Applications 220</p>
<p>5.3.6. Physical interpretation of propagation 223</p>
<p>5.4. Second order partial differential equations 225</p>
<p>5.4.1. Introduction 225</p>
<p>5.4.2. Characteristic curves of hyperbolic equations 226</p>
<p>5.4.3. Reduced form of the second order quasi–linear partial differential equation 229</p>
<p>5.4.4. Second order partial differential equations in a finite domain 232</p>
<p>5.4.5. Second order partial differential equations and their boundary conditions 233</p>
<p>5.5. Discontinuities: shock waves 239</p>
<p>5.5.1. General considerations 239</p>
<p>5.5.2. Unsteady 1D flow of an inviscid compressible fluid 239</p>
<p>5.5.3. Plane steady supersonic flow 244</p>
<p>5.5.4. Flow in a nozzle 244</p>
<p>5.5.5. Separated shock wave 248</p>
<p>5.5.6. Other discontinuity categories 248</p>
<p>5.5.7. Balance equations across a discontinuity 249</p>
<p>5.6. Some comments on methods of numerical solution 250</p>
<p>5.6.1. Characteristic curves and numerical discretization schemes 250</p>
<p>5.6.2. A complex example 253</p>
<p>5.6.3. Boundary conditions of flow problems 255</p>
<p>Chapter 6. General Properties of Flows 257</p>
<p>6.1. Dynamics of vorticity 257</p>
<p>6.1.1. Kinematic properties of the rotation vector 257</p>
<p>6.1.2. Equation and properties of the rotation vector 261</p>
<p>6.2. Potential flows 269</p>
<p>6.2.1. Introduction 269</p>
<p>6.2.2. Bernoulli s second theorem 269</p>
<p>6.2.3. Flow of compressible inviscid fluid 270</p>
<p>6.2.4. Nature of equations in inviscid flows 271</p>
<p>6.2.5. Elementary solutions in irrotational flows 273</p>
<p>6.2.6. Surface waves in shallow water 284</p>
<p>6.3. Orders of magnitude 288</p>
<p>6.3.1. Introduction and discussion of a simple example 288</p>
<p>6.3.2. Obtaining approximate values of a solution 291</p>
<p>6.4. Small parameters and perturbation phenomena 296</p>
<p>6.4.1. Introduction 296</p>
<p>6.4.2. Regular perturbation 296</p>
<p>6.4.3. Singular perturbations 305</p>
<p>6.5. Quasi–1D flows 309</p>
<p>6.5.1. General properties 309</p>
<p>6.5.2. Flows in pipes 314</p>
<p>6.5.3. The boundary layer in steady flow 319</p>
<p>6.6. Unsteady flows and steady flows 327</p>
<p>6.6.1. Introduction 327</p>
<p>6.6.2. The existence of steady flows 328</p>
<p>6.6.3. Transitional regime and permanent solution 330</p>
<p>6.6.4. Non–existence of a steady solution 334</p>
<p>Chapter 7. Measurement, Representation and Analysis of Temporal Signals 339</p>
<p>7.1. Introduction and position of the problem 339</p>
<p>7.2. Measurement and experimental data in flows 340</p>
<p>7.2.1. Introduction 340</p>
<p>7.2.2. Measurement of pressure 341</p>
<p>7.2.3. Anemometric measurements 342</p>
<p>7.2.4. Temperature measurements 346</p>
<p>7.2.5. Measurements of concentration 347</p>
<p>7.2.6. Fields of quantities and global measurements 347</p>
<p>7.2.7. Errors and uncertainties of measurements 351</p>
<p>7.3. Representation of signals 357</p>
<p>7.3.1. Objectives of continuous signal representation 357</p>
<p>7.3.2. Analytical representation 360</p>
<p>7.3.3. Signal decomposition on the basis of functions; series and elementary solutions 361</p>
<p>7.3.4. Integral transforms 363</p>
<p>7.3.5. Time–frequency (or timescale) representations 374</p>
<p>7.3.6. Discretized signals 381</p>
<p>7.3.7. Data compression 385</p>
<p>7.4. Choice of representation and obtaining pertinent information 389</p>
<p>7.4.1. Introduction 389</p>
<p>7.4.2. An example: analysis of sound 390</p>
<p>7.4.3. Analysis of musical signals 393</p>
<p>7.4.4. Signal analysis in aero–energetics 402</p>
<p>Chapter 8. Thermal Systems and Models 405</p>
<p>8.1. Overview of models 405</p>
<p>8.1.1. Introduction and definitions 405</p>
<p>8.1.2. Modeling by state representation and choice of variables 408</p>
<p>8.1.3. External representation 410</p>
<p>8.1.4. Command models 411</p>
<p>8.2. Thermodynamics and state representation 412</p>
<p>8.2.1. General principles of modeling 412</p>
<p>8.2.2. Linear time–invariant system (LTIS) 420</p>
<p>8.3. Modeling linear invariant thermal systems 422</p>
<p>8.3.1. Modeling discrete systems 422</p>
<p>8.3.2. Thermal models in continuous media 431</p>
<p>8.4. External representation of linear invariant systems 446</p>
<p>8.4.1. Overview 446</p>
<p>8.4.2. External description of linear invariant systems 446</p>
<p>8.5. Parametric models 451</p>
<p>8.5.1. Definition of model parameters 451</p>
<p>8.5.2. Established regimes of linear invariant systems 453</p>
<p>8.5.3. Established regimes in continuous media 458</p>
<p>8.6. Model reduction 465</p>
<p>8.6.1. Overview 465</p>
<p>8.6.2. Model reduction of discrete systems 466</p>
<p>8.7. Application in fluid mechanics and transfer in flows 474</p>
<p>Appendix 1. Laplace Transform 477</p>
<p>A1.1. Definition 477</p>
<p>A1.2. Properties 477</p>
<p>A1.3. Some Laplace transforms 478</p>
<p>A1.4. Application to the solution of constant coefficient differential equations 479</p>
<p>Appendix 2. Hilbert Transform 481</p>
<p>Appendix 3. Cepstral Analysis 483</p>
<p>A3.1. Introduction 483</p>
<p>A3.2. Definitions 483</p>
<p>A3.3. Example of echo suppression 484</p>
<p>A3.4. General case 485</p>
<p>Appendix 4. Eigenfunctions of an Operator 487</p>
<p>A4.1. Eigenfunctions of an operator 487</p>
<p>A4.2. Self–adjoint operator 487</p>
<p>A4.2.1. Eigenfunctions 487</p>
<p>A4.2.2. Expression of a function of f using an eigenfunction basis–set 488</p>
<p>Bibliography 489</p>
<p>Index 497</p>