An edition of DSP for MATLAB and LabVIEW (2008)

DSP for MATLAB and LabVIEW

Discrete frequency transforms

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An edition of DSP for MATLAB and LabVIEW (2008)

DSP for MATLAB and LabVIEW

Discrete frequency transforms

  • 1 Want to read

This book is Volume II of the series DSP for MATLAB and LabVIEW. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z-Transform (including definition and properties, the inverse z-transform, frequency response via z-transform, and alternate filter realization topologies including Direct Form, Direct Form Transposed, Cascade Form,Parallel Form, and Lattice Form), and the Discrete Fourier Transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair, DFT of common signals, bin width, sampling duration, and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT).^

The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form (available via the internet at http://www.morganclaypool.com/page/isen) will run on both MATLAB and LabVIEW. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEW Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer screen.^

Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion, and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter 4 of Volume I, in particular, provides an intuitive or "first principle" understanding of how digital filtering and frequency transforms work, preparing the reader for the present volume (Volume II).^

Volume III of the series covers digital filter design (FIR design using Windowing, Frequency Sampling, and Optimum Equiripple techniques, and Classical IIR design) and Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications.

Publish Date
Language
English

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Edition Availability
Cover of: DSP for MATLAB and LabVIEW
DSP for MATLAB and LabVIEW: Discrete frequency transforms
2008, Morgan & Claypool Publishers
electronic resource / in English

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Book Details


Table of Contents

The discrete time Fourier transform
Overview
In the previous volume
In this volume
In this chapter
Software for use with this book
Introduction to transform families
Fourier family (constant unity-magnitude correlators)
Laplace family (time-varying-magnitude correlators)
The DTFT
Inverse DTFT
A few properties of the DTFT
Linearity
Conjugate symmetry for real x[n]
Periodicity
Shift of frequency
Convolution
Even and odd components
Multiplication by a ramp
Frequency response of an LTI system
From impulse response
From difference equation
References
Exercises
The z-transform
Overview
Software for use with this book
Definition & properties
The z-transform
The inverse z-transform
Convergence criteria
Summary of ROC facts
Trivial poles and zeros
Basic properties of the z-transform
Common z-transforms
Transfer functions, poles, and zeros
Pole location and stability
^
Conversion from z-domain to time domain
Difference equation
Table lookup
Partial fraction expansion
Contour integration in the complex plane
Transient and steady-state responses
Frequency response from z-transform
For generalized transfer function
Relation to DTFT
Finite impulse response (FIR)
Infinite impulse response (IIR) single pole
Cascaded single-pole filters
Off-unit-circle zeros and decaying signals
Transfer function & filter topology
Direct form
Direct form transposed
Cascade form
Parallel form
Lattice form
References
Exercises
The DFT
Overview
Software for use with this book
Discrete Fourier series
Sampling in the z-domain
From DFS to DFT
DFT-IDFT pair
Definition-forward transform (time to frequency)
Definition-inverse transform (frequency to time)
Magnitude and phase
N, scaling constant, and DFT variants
MathScript implementation
A few DFT properties
^
^^
General considerations and observations
Bin values
Periodicity in n and k
Frequency multiplication in time domain
Computation of DFT via matrix
DFT of common signals
Frequency resolution
Bin width and sample rate
The FFT
N-pt DFT from two N/2-pt DFTs
Decimation-in-time
Reassembly via butterfly
Algorithm execution time
Other algorithms
The Goertzel algorithm
Via single-pole
Using complex conjugate poles
Magnitude only output
Linear, periodic, and circular convolution and the DFT
Cyclic/periodic convolution
Circular convolution
DFT convolution theorem
Linear convolution using the DFT
Summary of convolution facts
The overlap-add method
DFT leakage
On-bin/off-bin: DFT leakage
Avoiding DFT leakage-windowing
Inherent windowing by a rectangular window
A few common window types
DFT leakage v. window type
Additional window use
DTFT via padded DFT
The inverse DFT (IDFT)
^
^^
Computation of IDFT via matrix
IDFT via DFT
IDFT phase descrambling
Phase zeroing
Phase shifting
Equalization using the DFT
References
Exercises.
^^

Edition Notes

Part of: Synthesis digital library of engineering and computer science.

Title from PDF t.p. (viewed on January 8, 2009).

Series from website.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat reader.

Published in
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA)
Series
Synthesis lectures on signal processing -- # 5
Other Titles
Discrete frequency transforms., Synthesis digital library of engineering and computer science.

Classifications

Dewey Decimal Class
621.3822
Library of Congress
TK5102.9 .I8332 2008

The Physical Object

Format
[electronic resource] /

Edition Identifiers

Open Library
OL27033312M
ISBN 13
9781598298949, 9781598298932

Work Identifiers

Work ID
OL19844242W

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