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Understanding Digital Signal Processing

Gebonden Engels 2010 9780137027415
Verwachte levertijd ongeveer 9 werkdagen

Samenvatting

Understanding Digital Signal Processing, 3/e is simply the best practitioner's resource for mastering DSP technology. Richard Lyons has thoroughly updated and expanded his best-selling second edition, building on the exceptionally readable coverage that has made it a favorite of both professionals and students worldwide. Lyons achieves the perfect balance between practice and math, making DSP accessible to beginners without ever oversimplifying it, and offering systematic practical guidance for day-to-day problem-solving. Down-to-earth, intuitive, and example-rich, this book helps readers thoroughly grasp the basics and quickly move on to more sophisticated DSP techniques. Coverage includes: discrete sequences/systems, DFT, FFT, finite/infinite impulse response filters, quadrature (I/Q) processing, discrete Hilbert transforms, sample rate conversion, signal averaging, and much more. This edition adds extensive new coverage of FIR and IIR filter analysis techniques. The previous multirate processing, and binary number format, material has been significantly updated and expanded. It also provides new coverage of digital differentiators, integrators, and matched filters. Lyons has also doubled the number of DSP tips and tricks as in the previous edition including techniques even seasoned DSP professionals may have overlooked. He has also added end-of-chapter homework problems throughout to support college instruction and professional self-study.

Specificaties

ISBN13:9780137027415
Taal:Engels
Bindwijze:Gebonden

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Preface&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xv <p style="margin: 0px;">About the Author&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xxiii</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 1: Discrete Sequences and Systems&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1</p> <p style="margin: 0px;">1.1 Discrete Sequences and their Notation&nbsp;&nbsp; 2</p> <p style="margin: 0px;">1.2 Signal Amplitude, Magnitude, Power&nbsp;&nbsp; 8</p> <p style="margin: 0px;">1.3 Signal Processing Operational Symbols&nbsp;&nbsp; 10</p> <p style="margin: 0px;">1.4 Introduction to Discrete Linear Time-Invariant Systems&nbsp;&nbsp; 12</p> <p style="margin: 0px;">1.5 Discrete Linear Systems&nbsp;&nbsp; 12</p> <p style="margin: 0px;">1.6 Time-Invariant Systems&nbsp;&nbsp; 17</p> <p style="margin: 0px;">1.7 The Commutative Property of Linear Time-Invariant Systems&nbsp;&nbsp; 18</p> <p style="margin: 0px;">1.8 Analyzing Linear Time-Invariant Systems&nbsp;&nbsp; 19</p> <p style="margin: 0px;">References&nbsp;&nbsp; 21</p> <p style="margin: 0px;">Chapter 1 Problems&nbsp;&nbsp; 23</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 2: Periodic Sampling&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 33</p> <p style="margin: 0px;">2.1 Aliasing: Signal Ambiguity in the Frequency Domain&nbsp;&nbsp; 33</p> <p style="margin: 0px;">2.2 Sampling Lowpass Signals&nbsp;&nbsp; 38</p> <p style="margin: 0px;">2.3 Sampling Bandpass Signals&nbsp;&nbsp; 42</p> <p style="margin: 0px;">2.4 Practical Aspects of Bandpass Sampling&nbsp;&nbsp; 45</p> <p style="margin: 0px;">References&nbsp;&nbsp; 49</p> <p style="margin: 0px;">Chapter 2 Problems&nbsp;&nbsp; 50</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 3: The Discrete Fourier Transform&nbsp;&nbsp;&nbsp;&nbsp; 59</p> <p style="margin: 0px;">3.1 Understanding the DFT Equation&nbsp;&nbsp; 60</p> <p style="margin: 0px;">3.2 DFT Symmetry&nbsp;&nbsp; 73</p> <p style="margin: 0px;">3.3 DFT Linearity&nbsp;&nbsp; 75</p> <p style="margin: 0px;">3.4 DFT Magnitudes&nbsp;&nbsp; 75</p> <p style="margin: 0px;">3.5 DFT Frequency Axis&nbsp;&nbsp; 77</p> <p style="margin: 0px;">3.6 DFT Shifting Theorem&nbsp;&nbsp; 77</p> <p style="margin: 0px;">3.7 Inverse DFT&nbsp;&nbsp; 80</p> <p style="margin: 0px;">3.8 DFT Leakage &nbsp;&nbsp;81</p> <p style="margin: 0px;">3.9 Windows&nbsp;&nbsp; 89</p> <p style="margin: 0px;">3.10 DFT Scalloping Loss&nbsp;&nbsp; 96</p> <p style="margin: 0px;">3.11 DFT Resolution, Zero Padding, and Frequency-Domain Sampling&nbsp;&nbsp; 98</p> <p style="margin: 0px;">3.12 DFT Processing Gain&nbsp;&nbsp; 102</p> <p style="margin: 0px;">3.13 The DFT of Rectangular Functions&nbsp;&nbsp; 105</p> <p style="margin: 0px;">3.14 Interpreting the DFT Using the Discrete-Time Fourier Transform&nbsp;&nbsp; 120</p> <p style="margin: 0px;">References&nbsp;&nbsp; 124</p> <p style="margin: 0px;">Chapter 3 Problems&nbsp;&nbsp; 125</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 4: The Fast Fourier Transform&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 135</p> <p style="margin: 0px;">4.1 Relationship of the FFT to the DFT 136</p> <p style="margin: 0px;">4.2 Hints on Using FFTs in Practice 137</p> <p style="margin: 0px;">4.3 Derivation of the Radix-2 FFT Algorithm 141</p> <p style="margin: 0px;">4.4 FFT Input/Output Data Index Bit Reversal 149</p> <p style="margin: 0px;">4.5 Radix-2 FFT Butterfly Structures 151</p> <p style="margin: 0px;">4.6 Alternate Single-Butterfly Structures 154</p> <p style="margin: 0px;">References 158</p> <p style="margin: 0px;">Chapter 4 Problems 160</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 5: Finite Impulse Response Filters&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 169</p> <p style="margin: 0px;">5.1 An Introduction to Finite Impulse Response (FIR) Filters&nbsp;&nbsp; 170</p> <p style="margin: 0px;">5.2 Convolution in FIR Filters&nbsp;&nbsp; 175</p> <p style="margin: 0px;">5.3 Lowpass FIR Filter Design&nbsp;&nbsp; 186</p> <p style="margin: 0px;">5.4 Bandpass FIR Filter Design&nbsp;&nbsp; 201</p> <p style="margin: 0px;">5.5 Highpass FIR Filter Design&nbsp;&nbsp; 203</p> <p style="margin: 0px;">5.6 Parks-McClellan Exchange FIR Filter Design Method&nbsp;&nbsp; 204</p> <p style="margin: 0px;">5.7 Half-band FIR Filters&nbsp;&nbsp; 207</p> <p style="margin: 0px;">5.8 Phase Response of FIR Filters&nbsp;&nbsp; 209</p> <p style="margin: 0px;">5.9 A Generic Description of Discrete Convolution&nbsp;&nbsp; 214</p> <p style="margin: 0px;">5.10 Analyzing FIR Filters&nbsp;&nbsp; 226</p> <p style="margin: 0px;">References&nbsp;&nbsp; 235</p> <p style="margin: 0px;">Chapter 5 Problems&nbsp;&nbsp; 238</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 6: Infinite Impulse Response Filters&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 253</p> <p style="margin: 0px;">6.1 An Introduction to Infinite Impulse Response Filters&nbsp;&nbsp; 254</p> <p style="margin: 0px;">6.2 The Laplace Transform&nbsp;&nbsp; 257</p> <p style="margin: 0px;">6.3 The z-Transform&nbsp;&nbsp; 270</p> <p style="margin: 0px;">6.4 Using the z-Transform to Analyze IIR Filters&nbsp;&nbsp; 274</p> <p style="margin: 0px;">6.5 Using Poles and Zeros to Analyze IIR Filters&nbsp;&nbsp; 282</p> <p style="margin: 0px;">6.6 Alternate IIR Filter Structures&nbsp;&nbsp; 289</p> <p style="margin: 0px;">6.7 Pitfalls in Building IIR Filters&nbsp;&nbsp; 292</p> <p style="margin: 0px;">6.8 Improving IIR Filters with Cascaded Structures&nbsp;&nbsp; 295</p> <p style="margin: 0px;">6.9 Scaling the Gain of IIR Filters&nbsp;&nbsp; 300</p> <p style="margin: 0px;">6.10 Impulse Invariance IIR Filter Design Method&nbsp;&nbsp; 303</p> <p style="margin: 0px;">6.11 Bilinear Transform IIR Filter Design Method&nbsp;&nbsp; 319</p> <p style="margin: 0px;">6.12 Optimized IIR Filter Design Method&nbsp;&nbsp; 330</p> <p style="margin: 0px;">6.13 A Brief Comparison of IIR and FIR Filters&nbsp;&nbsp; 332</p> <p style="margin: 0px;">References&nbsp;&nbsp; 333</p> <p style="margin: 0px;">Chapter 6 Problems&nbsp;&nbsp; 336</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 7: Specialized Digital Networks and Filters&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 361</p> <p style="margin: 0px;">7.1 Differentiators&nbsp;&nbsp; 361</p> <p style="margin: 0px;">7.2 Integrators&nbsp;&nbsp; 370</p> <p style="margin: 0px;">7.3 Matched Filters&nbsp;&nbsp; 376</p> <p style="margin: 0px;">7.4 Interpolated Lowpass FIR Filters&nbsp;&nbsp; 381</p> <p style="margin: 0px;">7.5 Frequency Sampling Filters: The Lost Art&nbsp;&nbsp; 392</p> <p style="margin: 0px;">References&nbsp;&nbsp; 426</p> <p style="margin: 0px;">Chapter 7 Problems&nbsp;&nbsp; 429</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 8: Quadrature Signals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 439</p> <p style="margin: 0px;">8.1 Why Care about Quadrature Signals?&nbsp;&nbsp; 440</p> <p style="margin: 0px;">8.2 The Notation of Complex Numbers&nbsp;&nbsp; 440</p> <p style="margin: 0px;">8.3 Representing Real Signals Using Complex Phasors&nbsp;&nbsp; 446</p> <p style="margin: 0px;">8.4 A Few Thoughts on Negative Frequency&nbsp;&nbsp; 450</p> <p style="margin: 0px;">8.5 Quadrature Signals in the Frequency Domain&nbsp;&nbsp; 451</p> <p style="margin: 0px;">8.6 Bandpass Quadrature Signals in the Frequency Domain&nbsp;&nbsp; 454</p> <p style="margin: 0px;">8.7 Complex Down-Conversion&nbsp;&nbsp; 456</p> <p style="margin: 0px;">8.8 A Complex Down-Conversion Example&nbsp;&nbsp; 458</p> <p style="margin: 0px;">8.9 An Alternate Down-Conversion Method&nbsp;&nbsp; 462</p> <p style="margin: 0px;">References&nbsp;&nbsp; 464</p> <p style="margin: 0px;">Chapter 8 Problems&nbsp;&nbsp; 465</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 9: The Discrete Hilbert Transform&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 479</p> <p style="margin: 0px;">9.1 Hilbert Transform Definition&nbsp;&nbsp; 480</p> <p style="margin: 0px;">9.2 Why Care about the Hilbert Transform?&nbsp;&nbsp; 482</p> <p style="margin: 0px;">9.3 Impulse Response of a Hilbert Transformer&nbsp;&nbsp; 487</p> <p style="margin: 0px;">9.4 Designing a Discrete Hilbert Transformer&nbsp;&nbsp; 489</p> <p style="margin: 0px;">9.5 Time-Domain Analytic Signal Generation&nbsp;&nbsp; 495</p> <p style="margin: 0px;">9.6 Comparing Analytical Signal Generation Methods&nbsp;&nbsp; 497</p> <p style="margin: 0px;">References&nbsp;&nbsp; 498</p> <p style="margin: 0px;">Chapter 9 Problems&nbsp;&nbsp; 499</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 10: Sample Rate Conversion&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 507</p> <p style="margin: 0px;">10.1 Decimation&nbsp;&nbsp; 508</p> <p style="margin: 0px;">10.2 Two-Stage Decimation&nbsp;&nbsp; 510</p> <p style="margin: 0px;">10.3 Properties of Downsampling&nbsp;&nbsp; 514</p> <p style="margin: 0px;">10.4 Interpolation&nbsp;&nbsp; 516</p> <p style="margin: 0px;">10.5 Properties of Interpolation&nbsp;&nbsp; 518</p> <p style="margin: 0px;">10.6 Combining Decimation and Interpolation&nbsp;&nbsp; 521</p> <p style="margin: 0px;">10.7 Polyphase Filters&nbsp;&nbsp; 522</p> <p style="margin: 0px;">10.8 Two-Stage Interpolation&nbsp;&nbsp; 528</p> <p style="margin: 0px;">10.9 z-Transform Analysis of Multirate Systems&nbsp;&nbsp; 533</p> <p style="margin: 0px;">10.10 Polyphase Filter Implementations&nbsp;&nbsp; 535</p> <p style="margin: 0px;">10.11 Sample Rate Conversion by Rational Factors&nbsp;&nbsp; 540</p> <p style="margin: 0px;">10.12 Sample Rate Conversion with Half-band Filters&nbsp;&nbsp; 543</p> <p style="margin: 0px;">10.13 Sample Rate Conversion with IFIR Filters&nbsp;&nbsp; 548</p> <p style="margin: 0px;">10.14 Cascaded Integrator-Comb Filters&nbsp;&nbsp; 550</p> <p style="margin: 0px;">References&nbsp;&nbsp; 566</p> <p style="margin: 0px;">Chapter 10 Problems&nbsp;&nbsp; 568</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 11: Signal Averaging&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 589</p> <p style="margin: 0px;">11.1 Coherent Averaging&nbsp;&nbsp; 590</p> <p style="margin: 0px;">11.2 Incoherent Averaging&nbsp;&nbsp; 597</p> <p style="margin: 0px;">11.3 Averaging Multiple Fast Fourier Transforms&nbsp;&nbsp; 600</p> <p style="margin: 0px;">11.4 Averaging Phase Angles&nbsp;&nbsp; 603</p> <p style="margin: 0px;">11.5 Filtering Aspects of Time-Domain Averaging&nbsp;&nbsp; 604</p> <p style="margin: 0px;">11.6 Exponential Averaging&nbsp;&nbsp; 608</p> <p style="margin: 0px;">References&nbsp;&nbsp; 615</p> <p style="margin: 0px;">Chapter 11 Problems&nbsp;&nbsp; 617</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 12: Digital Data Formats and their Effects&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 623</p> <p style="margin: 0px;">12.1 Fixed-Point Binary Formats&nbsp;&nbsp; 623</p> <p style="margin: 0px;">12.2 Binary Number Precision and Dynamic Range&nbsp;&nbsp; 632</p> <p style="margin: 0px;">12.3 Effects of Finite Fixed-Point Binary Word Length&nbsp;&nbsp; 634</p> <p style="margin: 0px;">12.4 Floating-Point Binary Formats&nbsp;&nbsp; 652</p> <p style="margin: 0px;">12.5 Block Floating-Point Binary Format&nbsp;&nbsp; 658</p> <p style="margin: 0px;">References&nbsp;&nbsp; 658</p> <p style="margin: 0px;">Chapter 12 Problems&nbsp;&nbsp; 661</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Chapter 13: Digital Signal Processing Tricks&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 671</p> <p style="margin: 0px;">13.1 Frequency Translation without Multiplication&nbsp;&nbsp; 671</p> <p style="margin: 0px;">13.2 High-Speed Vector Magnitude Approximation&nbsp;&nbsp; 679</p> <p style="margin: 0px;">13.3 Frequency-Domain Windowing&nbsp;&nbsp; 683</p> <p style="margin: 0px;">13.4 Fast Multiplication of Complex Numbers&nbsp;&nbsp; 686</p> <p style="margin: 0px;">13.5 Efficiently Performing the FFT of Real Sequences&nbsp;&nbsp; 687</p> <p style="margin: 0px;">13.6 Computing the Inverse FFT Using the Forward FFT&nbsp;&nbsp; 699</p> <p style="margin: 0px;">13.7 Simplified FIR Filter Structure&nbsp;&nbsp; 702</p> <p style="margin: 0px;">13.8 Reducing A/D Converter Quantization Noise&nbsp;&nbsp; 704</p> <p style="margin: 0px;">13.9 A/D Converter Testing Techniques&nbsp;&nbsp; 709</p> <p style="margin: 0px;">13.10 Fast FIR Filtering Using the FFT&nbsp;&nbsp; 716</p> <p style="margin: 0px;">13.11 Generating Normally Distributed Random Data&nbsp;&nbsp; 722</p> <p style="margin: 0px;">13.12 Zero-Phase Filtering&nbsp;&nbsp; 725</p> <p style="margin: 0px;">13.13 Sharpened FIR Filters&nbsp;&nbsp; 726</p> <p style="margin: 0px;">13.14 Interpolating a Bandpass Signal&nbsp;&nbsp; 728</p> <p style="margin: 0px;">13.15 Spectral Peak Location Algorithm&nbsp;&nbsp; 730</p> <p style="margin: 0px;">13.16 Computing FFT Twiddle Factors&nbsp;&nbsp; 734</p> <p style="margin: 0px;">13.17 Single Tone Detection&nbsp;&nbsp; 737</p> <p style="margin: 0px;">13.18 The Sliding DFT&nbsp;&nbsp; 741</p> <p style="margin: 0px;">13.19 The Zoom FFT&nbsp;&nbsp; 749</p> <p style="margin: 0px;">13.20 A Practical Spectrum Analyzer&nbsp;&nbsp; 753</p> <p style="margin: 0px;">13.21 An Efficient Arctangent Approximation&nbsp;&nbsp; 756</p> <p style="margin: 0px;">13.22 Frequency Demodulation Algorithms&nbsp;&nbsp; 758</p> <p style="margin: 0px;">13.23 DC Removal&nbsp;&nbsp; 761</p> <p style="margin: 0px;">13.24 Improving Traditional CIC Filters&nbsp;&nbsp; 765</p> <p style="margin: 0px;">13.25 Smoothing Impulsive Noise&nbsp;&nbsp; 770</p> <p style="margin: 0px;">13.26 Efficient Polynomial Evaluation&nbsp;&nbsp; 772</p> <p style="margin: 0px;">13.27 Designing Very High-Order FIR Filters&nbsp;&nbsp; 775</p> <p style="margin: 0px;">13.28 Time-Domain Interpolation Using the FFT&nbsp;&nbsp; 778</p> <p style="margin: 0px;">13.29 Frequency Translation Using Decimation&nbsp;&nbsp; 781</p> <p style="margin: 0px;">13.30 Automatic Gain Control (AGC)&nbsp;&nbsp; 783</p> <p style="margin: 0px;">13.31 Approximate Envelope Detection&nbsp;&nbsp; 784</p> <p style="margin: 0px;">13.32 AQuadrature Oscillator&nbsp;&nbsp; 786</p> <p style="margin: 0px;">13.33 Specialized Exponential Averaging&nbsp;&nbsp; 789</p> <p style="margin: 0px;">13.34 Filtering Narrowband Noise Using Filter Nulls&nbsp;&nbsp; 792</p> <p style="margin: 0px;">13.35 Efficient Computation of Signal Variance&nbsp;&nbsp; 797</p> <p style="margin: 0px;">13.36 Real-time Computation of Signal Averages and Variances&nbsp;&nbsp; 799</p> <p style="margin: 0px;">13.37 Building Hilbert Transformers from Half-band Filters&nbsp;&nbsp; 802</p> <p style="margin: 0px;">13.38 Complex Vector Rotation with Arctangents&nbsp;&nbsp; 805</p> <p style="margin: 0px;">13.39 An Efficient Differentiating Network&nbsp;&nbsp; 810</p> <p style="margin: 0px;">13.40 Linear-Phase DC-Removal Filter&nbsp;&nbsp; 812</p> <p style="margin: 0px;">13.41 Avoiding Overflow in Magnitude Computations&nbsp;&nbsp; 815</p> <p style="margin: 0px;">13.42 Efficient Linear Interpolation&nbsp;&nbsp; 815</p> <p style="margin: 0px;">13.43 Alternate Complex Down-conversion Schemes&nbsp;&nbsp; 816</p> <p style="margin: 0px;">13.44 Signal Transition Detection&nbsp;&nbsp; 820</p> <p style="margin: 0px;">13.45 Spectral Flipping around Signal Center Frequency&nbsp;&nbsp; 821</p> <p style="margin: 0px;">13.46 Computing Missing Signal Samples&nbsp;&nbsp; 823</p> <p style="margin: 0px;">13.47 Computing Large DFTs Using Small FFTs&nbsp;&nbsp; 826</p> <p style="margin: 0px;">13.48 Computing Filter Group Delay without Arctangents&nbsp;&nbsp; 830</p> <p style="margin: 0px;">13.49 Computing a Forward and Inverse FFT Using a Single FFT&nbsp;&nbsp; 831</p> <p style="margin: 0px;">13.50 Improved Narrowband Lowpass IIR Filters&nbsp;&nbsp; 833</p> <p style="margin: 0px;">13.51 A Stable Goertzel Algorithm&nbsp;&nbsp; 838</p> <p style="margin: 0px;">References&nbsp;&nbsp; 840</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix A: The Arithmetic of Complex Numbers&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 847</p> <p style="margin: 0px;">A.1 Graphical Representation of Real and Complex Numbers&nbsp;&nbsp; 847</p> <p style="margin: 0px;">A.2 Arithmetic Representation of Complex Numbers&nbsp;&nbsp; 848</p> <p style="margin: 0px;">A.3 Arithmetic Operations of Complex Numbers&nbsp;&nbsp; 850</p> <p style="margin: 0px;">A.4 Some Practical Implications of Using Complex Numbers&nbsp;&nbsp; 856</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix B: Closed Form of a Geometric Series&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 859</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix C: Time Reversal and the DFT&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 863</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix D: Mean, Variance, and Standard Deviation&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 867</p> <p style="margin: 0px;">D.1 Statistical Measures&nbsp;&nbsp; 867</p> <p style="margin: 0px;">D.2 Statistics of Short Sequences &nbsp;&nbsp;870</p> <p style="margin: 0px;">D.3 Statistics of Summed Sequences&nbsp;&nbsp; 872</p> <p style="margin: 0px;">D.4 Standard Deviation (RMS) of a Continuous Sinewave&nbsp;&nbsp; 874</p> <p style="margin: 0px;">D.5 Estimating Signal-to-Noise Ratios&nbsp;&nbsp; 875</p> <p style="margin: 0px;">D.6 The Mean and Variance of Random Functions&nbsp;&nbsp; 879</p> <p style="margin: 0px;">D.7 The Normal Probability Density Function&nbsp;&nbsp; 882</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix E: Decibels (DB and DBM)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 885</p> <p style="margin: 0px;">E.1 Using Logarithms to Determine Relative Signal Power&nbsp;&nbsp; 885</p> <p style="margin: 0px;">E.2 Some Useful Decibel Numbers&nbsp;&nbsp; 889</p> <p style="margin: 0px;">E.3 Absolute Power Using Decibels&nbsp;&nbsp; 891</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix F: Digital Filter Terminology&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 893</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix G: Frequency Sampling Filter Derivations&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 903</p> <p style="margin: 0px;">G.1 Frequency Response of a Comb Filter&nbsp;&nbsp; 903</p> <p style="margin: 0px;">G.2 Single Complex FSF Frequency Response&nbsp;&nbsp; 904</p> <p style="margin: 0px;">G.3 Multisection Complex FSF Phase&nbsp;&nbsp; 905</p> <p style="margin: 0px;">G.4 Multisection Complex FSF Frequency Response&nbsp;&nbsp; 906</p> <p style="margin: 0px;">G.5 Real FSF Transfer Function&nbsp;&nbsp; 908</p> <p style="margin: 0px;">G.6 Type-IV FSF Frequency Response&nbsp;&nbsp; 910</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix H: Frequency Sampling Filter Design Tables&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 913</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Appendix I: Computing Chebyshev Window Sequences&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 927</p> <p style="margin: 0px;">I.1 Chebyshev Windows for FIR Filter Design&nbsp;&nbsp; 927</p> <p style="margin: 0px;">I.2 Chebyshev Windows for Spectrum Analysis&nbsp;&nbsp; 929</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">Index&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 931</p>

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        Understanding Digital Signal Processing