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The DFT

The DFT
An Owners' Manual for the Discrete Fourier Transform

$80.00

  • Date Published: March 1995
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898713428

$ 80.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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  • Just as a prism separates white light into its component bands of colored light, so the discrete Fourier transform (DFT) is used to separate a signal into its constituent frequencies. Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect. In fact, by analyzing the component frequencies of a signal or any system, the DFT can be used in an astonishing variety of problems. Among the applications of the DFT are digital signal processing, oil and gas exploration, medical imaging, aircraft and spacecraft guidance, and the solution of differential equations of physics and engineering. The DFT: An Owner's Manual for the Discrete Fourier Transform explores both the practical and theoretical aspects of the DFT, one of the most widely used tools in science and engineering.

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    Product details

    • Date Published: March 1995
    • format: Paperback
    • isbn: 9780898713428
    • length: 450 pages
    • dimensions: 255 x 173 x 23 mm
    • weight: 0.76kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. Introduction. A Bit of History
    An Application
    Problems
    2. The Discrete Fourier Transform (DFT). Introduction
    DFT Approximation to the Fourier Transform
    The DFT-IDFT pair
    DFT Approximations to Fourier Series Coefficients
    The DFT from Trigonometric Approximation
    Transforming a Spike Train
    Limiting Forms of the DFT-IDFT Pair
    Problems
    3. Properties of the DFT. Alternate Forms for the DFT
    Basic Properties of the DFT
    Other Properties of the DFT
    A Few Practical Considerations
    Analytical DFTs
    Problems
    4. Symmetric DFTs. Introduction
    Real sequences and the Real DFT (RDFT)
    Even Sequences and the Discrete Cosine Transform (DST)
    Odd Sequences and the Discrete Sine Transform (DST)
    Computing Symmetric DFTs
    Notes
    Problems
    5. Multi-dimensional DFTs. Introduction
    Two-dimensional DFTs
    Geometry of Two-Dimensional Modes
    Computing Multi-Dimensional DFTs
    Symmetric DFTs in Two Dimensions
    Problems
    6. Errors in the DFT. Introduction
    Periodic, Band-limited Input
    Periodic, Non-band-limited Input
    Replication and the Poisson Summation Formula
    Input with Compact Support
    General Band-Limited Functions
    General Input
    Errors in the Inverse DFT
    DFT Interpolation - Mean Square Error
    Notes and References
    Problems
    7. A Few Applications of the DFT. Difference Equations - Boundary Value Problems
    Digital Filtering of Signals
    FK Migration of Seismic Data
    Image Reconstruction from Projections
    Problems
    8. Related Transforms. Introduction
    The Laplace Transform
    The z- Transform
    The Chebyshev Transform
    Orthogonal Polynomial Transforms
    The Discrete Hartley Transform (DHT)
    Problems
    9. Quadrature and the DFT. Introduction
    The DFT and the Trapezoid Rule
    Higher Order Quadrature Rules
    Problems
    10. The Fast Fourier Transform (FFT). Introduction
    Splitting Methods
    Index Expansions (One ---> Multi-dimensional)
    Matrix Factorizations
    Prime Factor and Convolution Methods
    FFT Performance
    Notes
    Problems
    Glossary of (Frequently and Consistently Used) Notations
    References.

  • Authors

    William L. Briggs

    Van Emden Henson

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