| Description |
1 online resource (xvi, 217 pages) : illustrations |
| Series |
Synthesis lectures on signal processing, 1932-1694 ; # 5 |
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Synthesis lectures on signal processing (Online) ; #5.
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| 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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references |
| SUBJECT |
MATLAB. http://id.loc.gov/authorities/names/n92036881
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LabVIEW. http://id.loc.gov/authorities/names/n94038111
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LabVIEW fast |
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MATLAB fast |
| Subject |
Signal processing -- Digital techniques.
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Transformations (Mathematics)
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COMPUTERS -- Information Theory.
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TECHNOLOGY & ENGINEERING -- Signals & Signal Processing.
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Signal processing -- Digital techniques
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Transformations (Mathematics)
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| Form |
Electronic book
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| ISBN |
9781598298949 |
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1598298941 |
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9783031025297 |
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3031025296 |
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