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" Discrete Transforms "
by Jean M. Firth.
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BL
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| Record Number
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775766
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b595762
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| Main Entry
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by Jean M. Firth.
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| Title & Author
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Discrete Transforms\ by Jean M. Firth.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1992
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| Page. NO
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(187 pages)
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| ISBN
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9401123586
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: 9789401123587
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| Contents
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1 Fourier series, integral theorem, and transforms: a review --; 1.1 Fourier series --; 1.2 Fourier exponential series --; 1.3 The Fourier integral theorem --; 1.4 Odd and even functions --; 1.5 The Fourier transform --; 1.6 The Fourier sine and cosine transforms --; 1.7 The Laplace transform --; 1.8 Laplace transform properties and pairs --; 1.9 Transfer functions and convolution --; Summary --; Problems --; 2 The Fourier transform. Convolution of analogue signals --; 2.1 Duality --; 2.2 Further properties of the Fourier transform --; 2.3 Comparison with the Laplace transform, and the existence of the Fourier transform --; 2.4 Transforming using a limit process --; 2.5 Transformation and inversion using duality and other properties --; 2.6 Some frequently occurring functions and their transforms --; 2.7 Further Fourier transform pairs --; 2.8 Graphical aspects of convolution --; Summary --; Problems --; 3 Discrete signals and transforms. The Z-transform and discrete convolution --; 3.1 Sampling, quantization and encoding --; 3.2 Sampling and 'ideal' sampling models --; 3.3 The Fourier transform of a sampled function --; 3.4 The spectrum of an 'ideally sampled' function --; 3.5 Aliasing --; 3.6 Transform and inversion sums; truncation --; 3.7 Windowing: band-limited signals and signal energy --; 3.8 The Laplace transform of a sampled signal --; 3.9 The Z-transform --; 3.10 Input-output systems and transfer functions --; 3.11 Properties of the Z-transform --; 3.12 Z-transform pairs --; 3.13 Inversion --; 3.14 Discrete convolution --; Summary --; Problems --; 4 Difference equations and the Z-transforms --; 4.1 Forward and backward difference operators --; 4.2 The approximation of a differential equation --; 4.3 Ladder networks --; 4.4 Bending in beams: trial methods of solution --; 4.5 Transforming a second-order forward difference equation --; 4.6 The characteristic polynomial and the terms to be inverted --; 4.7 The case when the characteristic polynomial has real roots --; 4.8 The case when the characteristic polynomial has complex roots --; 4.9 The case when the characteristic equation has repeated roots --; 4.10 Difference equations of order N> 2 --; 4.11 A backward difference equation --; 4.12 A second-order equation: comparison of the two methods --; Summary --; Problems --; 5 The discrete Fourier transform --; 5.1 Approximating the exponential Fourier series --; 5.2 Definition of the discrete Fourier transform --; 5.3 Establishing the inverse --; 5.4 Inversion by conjugation --; 5.5 Properties of the discrete Fourier transform --; 5.6 Discrete correlation --; 5.7 Parseval's theorem --; 5.8 A note on sampling in the frequency domain, and a further comment on window functions --; 5.9 Computational effort and the discrete Fourier transform --; Summary --; Problems --; 6 Simplification and factorization of the discrete Fourier transform matrix --; 6.1 The coefficient matrix for an eight-point discrete Fourier transform --; 6.2 The permutation matrix and bit-reversal --; 6.3 The output from four two-point discrete Fourier transforms --; 6.4 The output from two four-point discrete Fourier transforms --; 6.5 The output from an eight-point discrete Fourier transform --; 6.6 'Butterfly' calculations --; 6.7 'Twiddle' factors --; 6.8 Economies --; Summary --; Problems --; 7 Fast Fourier transforms --; 7.1 Fast Fourier transform algorithms --; 7.2 Decimation in time for an eight-point discrete Fourier transform: first stage --; 7.3 The second stage: further periodic aspects --; 7.4 The third stage --; 7.5 Construction of a flow graph --; 7.6 Inversion using the same decimation-in-time signal flow graph --; 7.7 Decimation in frequency for an eight-point discrete Fourier transform --; Summary --; Problems --; Appendix A: The Fourier integral theorem --; Appendix B: The Hartley transform --; Appendix C: Further reading.
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| Abstract
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This text provides a thorough introduction to discrete transform techniques aimed at engineering students. Worked examples and illustrations are provided throughout the text to enable readers to relate the techniques to practical engineering problems.
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Engineering.
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Mathematics.
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| LC Classification
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QA601.B954 1992
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| Added Entry
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Jean M Firth
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