The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing
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Home > Mathematics and Science Textbooks > Physics > Classical mechanics > Wave mechanics (vibration and acoustics) > The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing: (463 The Springer International Series in Engineering and Computer Science)
The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing: (463 The Springer International Series in Engineering and Computer Science)

The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing: (463 The Springer International Series in Engineering and Computer Science)


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About the Book

The discrete Fourier transform (DFT) is a widely used tool in many branches of engineering and science, providing information about the spectral contents of a discrete-time signal at equally-spaced discrete frequency points. A generalization of DFT introduced in this text is the nonuniform discrete Fourier transform (NDFT), which can be used to obtain frequency domain information about a signal at arbitrarily chosen frequency points. The general properties of NDFT are discussed and a number of signal processing applications of NDFT are outlined. Applications discussed include the efficient design of one- and two-dimensional FIR digital filters, and antenna arrays, and detection of dual-tone multi-frequency(DTMF) signals. Chapter 1 introduces the problem of computing frequency samples of the z-transform of a finite-length sequence, and reviews the existing techniques. Chapter 2 develops the basics of the NDFT including its definition, properties and computational aspects. The NDFT is also extended to two dimensions. The ideas introduced here are utilized to develop applications of the NDFT in the following four chapters. Chapter 3 proposes a nonuniform frequency sampling technique for designing 1-D FIR digital filters. Design examples are presented for various types of filters. Chapter 4 utilizes the idea of the 2-D NDFT to design non separable 2-D FIR filters of various types. The resulting filters are compared with those designed by other existing methods and the performances of some of these filters are investigated by applying them to the decimation of digital images. Chapter 5 develops a design technique for synthesizing antenna patterns with nulls placed at desired angles to cancel interfering signals coming from these directions.

Table of Contents:
1. Introduction.- 1.1 Overview.- 1.2 Discrete Fourier Transform.- 1.3 Chirp z-transform.- 1.4 Subband Discrete Fourier Transform.- 1.5 Computation of Nonuniformly Spaced Frequency Samples.- 1.6 Summary.- 2. The Nonuniform Discrete Fourier Transform.- 2.1 Basic Concepts.- 2.2 Properties of the NDFT.- 2.3 Computation of the NDFT.- 2.4 Subband NDFT.- 2.5 The 2-D NDFT.- 2.6 Summary.- 3. 1-D FIR Filter Design using the NDFT.- 3.1 Introduction.- 3.2 Existing Methods for Frequency Sampling Design.- 3.3 Proposed Nonuniform Frequency Sampling Design.- 3.4 Results.- 3.5 Summary.- 4. 2-D FIR Filter Design using the NDFT.- 4.1 Introduction.- 4.2 Existing Methods for 2-D Frequency Sampling.- 4.3 Proposed 2-D Nonuniform Frequency Sampling Design.- 4.4 Square Filter Design.- 4.5 Circularly Symmetric Filter Design.- 4.6 Diamond Filter Design.- 4.7 Ellipticaily-Shaped Lowpass Filter Design.- 4.8 Applications of 2-D Filters.- 4.9 Summary.- 5. Antenna Pattern Synthesis with Prescribed Nulls.- 5.1 Introduction.- 5.2 Existing Methods for Null Synthesis.- 5.3 Proposed Null Synthesis Method.- 5.4 Design Examples and Comparisons.- 5.5 Summary.- 6. Dual-Tone Multi-Frequency Signal Decoding.- 6.1 Introduction.- 6.2 Background.- 6.3 Proposed DTMF Decoding Algorithm Using the Subband NDFT.- 6.4 Results and Comparisons.- 6.5 Summary.- 7. Conclusions.- References.


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Product Details
  • ISBN-13: 9780792382812
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Edition: New edition
  • Language: English
  • Returnable: Y
  • Series Title: 463 The Springer International Series in Engineering and Computer Science
  • ISBN-10: 0792382811
  • Publisher Date: 30 Nov 1998
  • Binding: Hardback
  • Height: 235 mm
  • No of Pages: 208
  • Returnable: Y
  • Width: 155 mm


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The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing: (463 The Springer International Series in Engineering and Computer Science)
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