## Fourier and Laplace TransformsThis textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science. |

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### Contents

IV | 7 |

V | 8 |

VI | 11 |

VII | 16 |

VIII | 27 |

IX | 28 |

X | 35 |

XI | 39 |

LII | 243 |

LIII | 249 |

LIV | 253 |

LV | 256 |

LVI | 259 |

LVII | 263 |

LVIII | 267 |

LIX | 268 |

XII | 45 |

XIII | 51 |

XIV | 57 |

XV | 60 |

XVI | 61 |

XVII | 65 |

XVIII | 71 |

XIX | 72 |

XX | 76 |

XXI | 80 |

XXII | 86 |

XXIII | 89 |

XXIV | 95 |

XXV | 105 |

XXVI | 113 |

XXVII | 114 |

XXVIII | 122 |

XXIX | 138 |

XXX | 140 |

XXXI | 144 |

XXXII | 149 |

XXXIV | 156 |

XXXV | 158 |

XXXVI | 164 |

XXXVII | 165 |

XXXVIII | 172 |

XXXIX | 181 |

XL | 188 |

XLI | 189 |

XLII | 192 |

XLIII | 203 |

XLIV | 208 |

XLV | 209 |

XLVI | 217 |

XLVII | 221 |

XLVIII | 229 |

XLIX | 230 |

L | 234 |

LI | 239 |

LX | 275 |

LXI | 280 |

LXII | 288 |

LXIII | 289 |

LXIV | 291 |

LXV | 294 |

LXVI | 297 |

LXVII | 303 |

LXVIII | 310 |

LXIX | 311 |

LXX | 323 |

LXXI | 327 |

LXXII | 330 |

LXXIII | 337 |

LXXIV | 340 |

LXXV | 344 |

LXXVI | 347 |

LXXVII | 351 |

LXXVIII | 356 |

LXXIX | 362 |

LXXX | 364 |

LXXXI | 368 |

LXXXII | 375 |

LXXXIII | 380 |

LXXXIV | 383 |

LXXXV | 391 |

LXXXVI | 392 |

LXXXVII | 396 |

LXXXVIII | 400 |

LXXXIX | 404 |

XC | 407 |

XCI | 412 |

XCII | 413 |

XCIII | 419 |

XCIV | 424 |

XCV | 429 |

XCVI | 432 |

444 | |

### Other editions - View all

Fourier and Laplace Transforms R. J. Beerends,H. G. ter Morsche,J. C. van den Berg,E. M. van de Vrie No preview available - 2003 |

### Common terms and phrases

absolute convergence absolutely integrable amplitude apply arbitrary Calculate called causal function chapter complex function complex numbers consider constant continuous function continuous-time signal convolution product convolution theorem cosine defined definition derivative determine the Fourier differentiation rule discrete Fourier transform energy-content equal example exercise exists figure follows formula Fourier coefficients Fourier integral Fourier series frequency domain frequency response function f(t function with period fundamental theorem given Hence impulse response initial conditions input u(t interval Laplace transform F(s Let f(t linear time-invariant LTC-system mathematical multiplication n-domain non-periodic obtain output partial fraction expansion periodic block function periodic discrete-time signal periodic function piecewise continuous piecewise smooth piecewise smooth function polynomial power series proof rational function Re.v region of convergence result right-hand side sampling sawtooth function series converges Show sine solution step response theory time-harmonic signal tion transfer function triangle function variable verify z-transform zero