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_q2016 _bAllied Informatics, Jaipur |
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| 040 |
_bEnglish _aBSDU _cBSDU |
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| 082 |
_a621.382 2 _bBAB |
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| 100 | _aBabu, P Ramesh | ||
| 245 | 0 | _aDigital Signal Processing | |
| 250 | _a6th | ||
| 260 |
_bScitech Publications (India) Pvt. Ltd _a Chennai _c2015,c2014 |
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| 300 | _a11.75;UQ.66 | ||
| 504 | _aChapter 1 Discrete-time Signals and Linear Systems 1.1 - 1.239 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 1.2 Examples of Signals . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 1.2.1 Speech signal . . . . . . . . . . . . . . . . . . . . . . . 1.1 1.2.2 ECG signal . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 1.2.3 Electroencephalogram (EEG) signal . . . . . . . . . . . . 1.3 1.3 Classification of Signals . . . . . . . . . . . . . . . . . . . . . . . 1.3 1.3.1 Continuous-time, discrete-time and digital Signals . . . . 1.3 1.3.2 Deterministic and random signals . . . . . . . . . . . . . 1.9 1.4 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 1.4.1 Continuous-time system . . . . . . . . . . . . . . . . . . 1.11 1.4.2 Discrete-time system . . . . . . . . . . . . . . . . . . . . 1.11 1.5 Mathematical Model of Continuous-time Systems . . . . . . . . . . 1.12 1.5.1 Modeling of mechanical and electrical elements . . . . . 1.12 1.5.2 Electrical elements . . . . . . . . . . . . . . . . . . . . . 1.13 1.6 Examples of Continuous-Time System Models . . . . . . . . . . . 1.14 1.6.1 RL circuit . . . . . . . . . . . . . . . . . . . . . . . . . 1.14 1.6.2 Mass - Spring - Dashpot system . . . . . . . . . . . . . . 1.15 1.7 Examples of Discrete-Time System Models . . . . . . . . . . . . . 1.15 1.7.1 Population model . . . . . . . . . . . . . . . . . . . . . 1.15 1.7.2 Savings account . . . . . . . . . . . . . . . . . . . . . . 1.16 1.7.3 Amortization . . . . . . . . . . . . . . . . . . . . . . . . 1.16 1.8 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.18 1.9 Advantages and Limitations of Digital Signal Processing . . . . . . 1.20 1.9.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . 1.20 1.9.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 1.21 1.10 Applications of DSP . . . . . . . . . . . . . . . . . . . . . . . . . 1.21 1.11 Elementary Continuous-time Signals . . . . . . . . . . . . . . . . . 1.22 1.11.1 Unit step function . . . . . . . . . . . . . . . . . . . . . 1.22 1.11.2 Unit ramp function . . . . . . . . . . . . . . . . . . . . . 1.22 1.11.3 Impulse function . . . . . . . . . . . . . . . . . . . . . . 1.23 1.11.4 Sinusoidal signal . . . . . . . . . . . . . . . . . . . . . . 1.23 1.11.5 Real exponential signals . . . . . . . . . . . . . . . . . . 1.24 1.11.6 Complex exponential signal . . . . . . . . . . . . . . . . 1.25 1.12 Continuous-time Periodic Signals . . . . . . . . . . . . . . . . . . 1.26 1.13 Representation of Discrete-time Signals . . . . . . . . . . . . . . . 1.28 1.13.1 Graphical representation . . . . . . . . . . . . . . . . . . 1.28 1.13.2 Functional representation . . . . . . . . . . . . . . . . . 1.28 1.13.3 Tabular representation . . . . . . . . . . . . . . . . . . . 1.29 1.13.4 Sequence representation . . . . . . . . . . . . . . . . . . 1.29 1.14 Elementary Discrete-time signals . . . . . . . . . . . . . . . . . . . 1.29 1.14.1 Unit step sequence . . . . . . . . . . . . . . . . . . . . . 1.29 1.14.2 Unit ramp sequence . . . . . . . . . . . . . . . . . . . . 1.30 1.14.3 Unit-sample sequence(unit impulse sequence) . . . . . . 1.30 1.14.4 Exponential sequence . . . . . . . . . . . . . . . . . . . 1.31 1.14.5 Sinusoidal signal . . . . . . . . . . . . . . . . . . . . . . 1.31 1.14.6 Complex exponential signal . . . . . . . . . . . . . . . . 1.32 1.15 Classification of Discrete-Time Signals . . . . . . . . . . . . . . . 1.33 1.15.1 Energy signals and power signals . . . . . . . . . . . . . 1.33 1.15.2 Periodic and aperiodic signals . . . . . . . . . . . . . . . 1.36 1.15.3 Symmetric(even) and antisymmetric (odd) signals . . . . 1.42 1.15.4 Causal and noncausal signals . . . . . . . . . . . . . . . 1.43 1.16 Operation on Signals . . . . . . . . . . . . . . . . . . . . . . . . . 1.43 1.16.1 Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.43 1.16.2 Time reversal . . . . . . . . . . . . . . . . . . . . . . . . 1.44 1.16.3 Time Scaling . . . . . . . . . . . . . . . . . . . . . . . . 1.45 1.16.4 Scalar multiplication . . . . . . . . . . . . . . . . . . . . 1.47 1.16.5 Signal multiplier . . . . . . . . . . . . . . . . . . . . . . 1.47 1.16.6 Addition operation . . . . . . . . . . . . . . . . . . . . . 1.47 1.17 Sampling and Aliasing . . . . . . . . . . . . . . . . . . . . . . . . 1.48 1.18 Discrete-Time System . . . . . . . . . . . . . . . . . . . . . . . . . 1.52 1.19 Classification of Discrete-Time systems . . . . . . . . . . . . . . . 1.52 1.19.1 Static and dynamic systems . . . . . . . . . . . . . . . . 1.52 1.19.2 Causal and noncausal systems . . . . . . . . . . . . . . . 1.53 1.19.3 Linear and non-linear systems . . . . . . . . . . . . . . . 1.54 1.19.4 Time variant and time-invariant systems . . . . . . . . . 1.56 1.20 Representation of an Arbitrary Sequence . . . . . . . . . . . . . . . 1.58 1.21 Impulse Response and Convolution Sum . . . . . . . . . . . . . . . 1.60 1.22 Properties of Convolution . . . . . . . . . . . . . . . . . . . . . . . 1.61 1.23 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.61 1.24 FIR and IIR Systems . . . . . . . . . . . . . . . . . . . . . . . . . 1.62 1.25 Stable and Unstable Systems . . . . . . . . . . . . . . . . . . . . . 1.63 1.26 Interconnection of LTI Systems . . . . . . . . . . . . . . . . . . . . 1.71 1.26.1 (i) Parallel connection of systems . . . . . . . . . . . . . 1.71 1.26.2 (ii) Cascade connection of two systems . . . . . . . . . . 1.72 1.27 Correlation of Two Sequences . . . . . . . . . . . . . . . . . . . . 1.75 1.27.1 Cross-correlation . . . . . . . . . . . . . . . . . . . . . . 1.76 1.27.2 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . 1.76 1.27.3 Properties of crosscorrelation and autocorrelation sequences 1.77 1.27.4 Computation of correlation . . . . . . . . . . . . . . . . 1.78 1.27.5 Correlation of power and periodic signals . . . . . . . . . 1.79 1.28 Inverse System and Deconvolution . . . . . . . . . . . . . . . . . . 1.80 1.28.1 Inverse system . . . . . . . . . . . . . . . . . . . . . . . 1.80 1.28.2 Deconvolution . . . . . . . . . . . . . . . . . . . . . . . 1.80 1.29 Time Response Analysis of Discrete-time Systems . . . . . . . . . 1.83 1.29.1 Natural response (zero input response) . . . . . . . . . . 1.85 1.29.2 Forced response (zero state response) . . . . . . . . . . . 1.88 1.29.3 Total response . . . . . . . . . . . . . . . . . . . . . . . 1.91 1.30 Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.93 1.31 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.99 1.32 Frequency Analysis of Discrete-Time Signals . . . . . . . . . . . . 1.100 1.33 Discrete Frequency Spectrum and Frequency Range . . . . . . . . . 1.103 1.34 Discrete-Time Fourier Transform . . . . . . . . . . . . . . . . . . . 1.107 1.34.1 Existence of discrete-time Fourier transform . . . . . . . 1.109 1.34.2 Properties of discrete-time Fourier transform . . . . . . . 1.110 1.35 Frequency Response Analysis of Discrete-time systems . . . . . . . 1.128 1.35.1 Frequency Response of First-order system . . . . . . . . 1.129 1.35.2 Frequency response of second-order system . . . . . . . 1.131 1.35.3 Transfer function . . . . . . . . . . . . . . . . . . . . . . 1.133 1.36 Steady State and Transient Response . . . . . . . . . . . . . . . . . 1.138 1.37 Phase and Group delays . . . . . . . . . . . . . . . . . . . . . . . . 1.140 1.38 Ideal filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.141 1.39 Zero phase and linear phase transfer functions . . . . . . . . . . . . 1.144 1.40 Analog to Digital Conversion . . . . . . . . . . . . . . . . . . . . 1.146 1.40.1 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 1.146 1.40.2 Aliasing effect . . . . . . . . . . . . . . . . . . . . . . . 1.148 1.40.3 Sampling theorem . . . . . . . . . . . . . . . . . . . . . 1.149 1.40.4 Anti-Aliasing Filter . . . . . . . . . . . . . . . . . . . . 1.150 1.40.5 Sample-and-hold circuit . . . . . . . . . . . . . . . . . . 1.150 1.40.6 Quantization . . . . . . . . . . . . . . . . . . . . . . . . 1.151 1.41 Reconstruction of Analog signal . . . . . . . . . . . . . . . . . . . 1.152 1.42 Sampling of Bandpass signals . . . . . . . . . . . . . . . . . . . . 1.156 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 1.201 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 1.214 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . 1.216 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.221 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 1.225 Chapter 2 The Z-Transform 2.1 - 2.112 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 2.2 Definition of the z-Transform . . . . . . . . . . . . . . . . . . . . . 2.1 2.3 z-Transform and ROC of Finite Duration Sequences . . . . . . . . . 2.2 2.3.1 Right-hand sequence . . . . . . . . . . . . . . . . . . . . 2.2 2.3.2 Left hand sequence . . . . . . . . . . . . . . . . . . . . 2.2 2.3.3 Two-sided sequence . . . . . . . . . . . . . . . . . . . . 2.3 2.4 z-Transform and ROC of Infinite Duration Sequence . . . . . . . . 2.4 2.5 ROC of Two-sided Sequence . . . . . . . . . . . . . . . . . . . . . 2.5 2.6 Stability and ROC . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 2.7 Properties of Region of Convergence . . . . . . . . . . . . . . . . . 2.8 2.8 Properties of the z-Transform . . . . . . . . . . . . . . . . . . . . . 2.8 2.9 The system Function . . . . . . . . . . . . . . . . . . . . . . . . . 2.23 2.10 Poles and Zeros of a System Function . . . . . . . . . . . . . . . . 2.25 2.11 Stability Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.26 2.12 Relationship between the Fourier Transform and the z-Transform . . 2.27 2.13 Relationship between s-Plane and z-Plane . . . . . . . . . . . . . . 2.29 2.14 Inverse z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . 2.30 2.14.1 Long division method . . . . . . . . . . . . . . . . . . . 2.30 2.14.2 Partial fraction expansion method . . . . . . . . . . . . . 2.32 2.14.3 Residue method . . . . . . . . . . . . . . . . . . . . . . 2.40 2.14.4 Convolution Method . . . . . . . . . . . . . . . . . . . . 2.44 2.15 Solution of difference equations using one sided z-transform . . . . 2.48 2.16 Deconvolution Using z-transform . . . . . . . . . . . . . . . . . . 2.54 2.17 Simple Digital Filters . . . . . . . . . . . . . . . . . . . . . . . . . 2.66 2.17.1 Simple IIR digital Filters . . . . . . . . . . . . . . . . . 2.66 2.17.2 Highpass IIR digital filter . . . . . . . . . . . . . . . . . 2.68 2.18 Simple FIR Digital filters . . . . . . . . . . . . . . . . . . . . . . . 2.72 2.18.1 Lowpass FIR digital filters . . . . . . . . . . . . . . . . 2.72 2.18.2 Highpass FIR digital filter . . . . . . . . . . . . . . . . . 2.74 2.19 Comb Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.75 2.20 Allpass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.76 2.21 Minimum Phase, Maximum Phase and Non-minimum Phase Systems 2.79 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 2.87 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 2.92 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . 2.92 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.96 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 2.99 Chapter 3 The Discrete Fourier Transform 3.1 - 3.118 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 3.2 Discrete Fourier series . . . . . . . . . . . . . . . . . . . . . . . . 3.1 3.3 Properties of the Discrete Fourier Series . . . . . . . . . . . . . . . 3.2 3.3.1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 3.3.2 Time shifting . . . . . . . . . . . . . . . . . . . . . . . . 3.3 3.3.3 Symmetry property . . . . . . . . . . . . . . . . . . . . 3.3 3.3.4 Periodic convolution . . . . . . . . . . . . . . . . . . . . 3.4 3.4 The Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . 3.5 3.4.1 Time-domain aliasing due to frequency sampling . . . . . 3.5 3.5 Relationship of The DFT to Other Transforms . . . . . . . . . . . . 3.22 3.5.1 Relationship to the Fourier transform . . . . . . . . . . . 3.22 3.5.2 Relationship to the z-transform . . . . . . . . . . . . . . 3.23 3.6 Properties of the Discrete Fourier transform . . . . . . . . . . . . . 3.25 3.6.1 Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . 3.26 3.6.2 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . 3.26 3.6.3 Circular shift of a sequence . . . . . . . . . . . . . . . . 3.26 3.6.4 Time reversal of the sequence . . . . . . . . . . . . . . . 3.31 3.6.5 Circular frequency shift . . . . . . . . . . . . . . . . . . 3.31 3.6.6 Complex conjugate property . . . . . . . . . . . . . . . . 3.32 3.6.7 Circular convolution . . . . . . . . . . . . . . . . . . . . 3.34 3.6.8 Circular correlation . . . . . . . . . . . . . . . . . . . . 3.35 3.6.9 Multiplication of two sequences . . . . . . . . . . . . . . 3.36 3.6.10 Parseval’s theorem . . . . . . . . . . . . . . . . . . . . . 3.36 3.7 Comparison between Circular Convolution and Linear Convolution . 3.41 3.8 Methods to Evaluate Circular Convolution of Two Sequences . . . . 3.42 3.8.1 Concentric circle method . . . . . . . . . . . . . . . . . 3.42 3.8.2 Matrix multiplication method . . . . . . . . . . . . . . . 3.42 3.9 Linear Convolution From Circular Convolution . . . . . . . . . . . 3.48 3.10 Filtering Long Duration Sequences . . . . . . . . . . . . . . . . . . 3.52 3.10.1 Overlap-save method . . . . . . . . . Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.60 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 4.61 Chapter 5 Infinite Impulse Response Filters 5.1 - 5.141 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 5.2 Frequency Selective Filters . . . . . . . . . . . . . . . . . . . . . . 5.1 5.3 Design of Digital Filters from Analog Filters . . . . . . . . . . . . . 5.3 5.3.1 Digital versus analog filters . . . . . . . . . . . . . . . . 5.5 5.3.2 Advantages and disadvantages of digital filters . . . . . . 5.5 5.4 Analog Lowpass Filter Design . . . . . . . . . . . . . . . . . . . . 5.6 5.5 Analog lowpass Butterworth Filter . . . . . . . . . . . . . . . . . . 5.6 5.6 Steps to Design an Analog Butterworth Lowpass Filter . . . . . . . 5.14 5.7 Analog Lowpass Chebyshev Filters . . . . . . . . . . . . . . . . . . 5.17 5.7.1 Pole locations for Chebyshev filter . . . . . . . . . . . . 5.19 5.7.2 Chebyshev Type - 2 filter . . . . . . . . . . . . . . . . . 5.22 5.8 Comparison between Butterworth Filter and Chebyshev Filter . . . 5.23 5.9 Steps to Design an Analog Chebyshev Lowpass Filter . . . . . . . . 5.23 5.10 Frequency Transformation in Analog Domain . . . . . . . . . . . . 5.29 5.10.1 Lowpass to lowpass filter . . . . . . . . . . . . . . . . . 5.29 5.10.2 Lowpass to highpass . . . . . . . . . . . . . . . . . . . . 5.29 5.10.3 Lowpass to bandpass . . . . . . . . . . . . . . . . . . . . 5.30 5.10.4 Lowpass to bandstop . . . . . . . . . . . . . . . . . . . . 5.31 5.11 Design of Highpass, Bandpass and Bandstop Filters . . . . . . . . . 5.31 5.12 Design of IIR Filters from Analog Filters . . . . . . . . . . . . . . 5.33 5.12.1 Approximation of derivatives . . . . . . . . . . . . . . . 5.33 5.12.2 Design of IIR filter using impulse invariance technique . . 5.35 5.12.3 Design of IIR filter using bilinear transformation . . . . . 5.44 5.12.4 The matched z-transform . . . . . . . . . . . . . . . . . 5.48 5.13 Frequency Transformation in Digital Domain . . . . . . . . . . . . 5.52 5.13.1 Lowpass to lowpass . . . . . . . . . . . . . . . . . . . . 5.52 5.13.2 Lowpass to highpass . . . . . . . . . . . . . . . . . . . . 5.52 5.13.3 Lowpass to bandpass . . . . . . . . . . . . . . . . . . . . 5.52 5.13.4 Lowpass to bandstop . . . . . . . . . . . . . . . . . . . . 5.53 5.14 Realization of Digital Filters . . . . . . . . . . . . . . . . . . . . . 5.54 5.14.1 Direct form I realization . . . . . . . . . . . . . . . . . . 5.55 5.14.2 Direct form II realization . . . . . . . . . . . . . . . . . 5.58 5.14.3 Signal flowgraph . . . . . . . . . . . . . . . . . . . . . . 5.62 5.14.4 Transposition theorem and transposed structure . . . . . . 5.63 5.14.5 Cascade form . . . . . . . . . . . . . . . . . . . . . . . 5.65 5.14.6 Parallel form structure . . . . . . . . . . . . . . . . . . . 5.67 5.14.7 Lattice structure of IIR system . . . . . . . . . . . . . . . 5.72 5.14.8 Conversion from Lattice structure to direct form . . . . . 5.74 5.14.9 Conversion from direct form to Lattice structure . . . . . 5.75 5.14.10 Lattice-Ladder structure . . . . . . . . . . . . . . . . . . 5.76 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 5.109 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 5.124 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.125 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 5.127 Chapter 6 Finite Impulse Response Filters 6.1 - 6.157 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 6.2 Linear Phase FIR Filters . . . . . . . . . . . . . . . . . . . . . . . 6.1 6.3 Frequency Response of Linear Phase FIR Filters . . . . . . . . . . . 6.5 6.4 Location of the Zeros of Linear Phase FIR Filters . . . . . . . . . . 6.13 6.5 The Fourier Series Method of Designing FIR Filters . . . . . . . . . 6.16 6.6 Design of FIR Filters using Windows . . . . . . . . . . . . . . . . 6.29 6.6.1 Rectangular window . . . . . . . . . . . . . . . . . . . 6.32 6.6.2 The Triangular or Bartlett window . . . . . . . . . . . . 6.35 6.6.3 Raised cosine window . . . . . . . . . . . . . . . . . . . 6.38 6.6.4 Hanning window . . . . . . . . . . . . . . . . . . . . . . 6.39 6.6.5 Hamming window . . . . . . . . . . . . . . . . . . . . . 6.40 6.6.6 Blackman window . . . . . . . . . . . . . . . . . . . . . 6.43 6.6.7 Kaiser window . . . . . . . . . . . . . . . . . . . . . . . 6.53 6.6.8 Summary of windows . . . . . . . . . . . . . . . . . . . 6.64 6.7 Digital Differentiator . . . . . . . . . . . . . . . . . . . . . . . . . 6.67 6.8 Hilbert Transformers . . . . . . . . . . . . . . . . . . . . . . . . . 6.74 6.9 Frequency Sampling Method of Designing FIR Filters . . . . . . . 6.80 6.9.1 Frequency sampling realization . . . . . . . . . . . . . . 6.81 6.9.2 Frequency response . . . . . . . . . . . . . . . . . . . . 6.81 6.9.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.82 6.10 Optimum Equiripple Approximation of FIR Filters . . . . . . . . . 6.99 6.11 Realization of FIR Filters . . . . . . . . . . . . . . . . . . . . . . . 6.102 6.11.1 Transversal structure . . . . . . . . . . . . . . . . . . . . 6.102 6.11.2 Linear phase realization . . . . . . . . . . . . . . . . . . 6.105 6.11.3 Lattice structure of an FIR filter . . . . . . . . . . . . . . 6.109 6.11.4 Polyphase realization of FIR filter . . . . . . . . . . . . . 6.115 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 6.129 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 6.141 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . 6.142 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.144 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 6.146 Chapter 7 Finite Word Length Effects in Digital Filters 7.1 - 7.72 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 7.2 Number Representation . . . . . . . . . . . . . . . . . . . . . . . . 7.2 7.3 Types of Number Representation . . . . . . . . . . . . . . . . . . . 7.3 7.3.1 Fixed point representation . . . . . . . . . . . . . . . . . 7.3 7.3.2 Sign-magnitude form . . . . . . . . . . . . . . . . . . . 7.3 7.3.3 One’s-complement form . . . . . . . . . . . . . . . . . . 7.3 7.3.4 Two’s-complement form . . . . . . . . . . . . . . . . . . 7.4 7.3.5 Addition of two fixed point numbers . . . . . . . . . . . 7.5 7.3.6 Multiplication in fixed point arithmetic . . . . . . . . . . 7.7 7.4 Floating Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . 7.7 7.4.1 Comparison of fixed point and floating point arithmetic . 7.8 7.5 Block Floating Point Numbers . . . . . . . . . . . . . . . . . . . . 7.9 7.6 Quantization Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 7.6.1 Truncation . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 7.6.2 Rounding . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10 7.6.3 Error due to truncation and rounding . . . . . . . . . . . 7.10 7.7 Input Quantization Error . . . . . . . . . . . . . . . . . . . . . . . 7.15 7.7.1 Steady state input noise power . . . . . . . . . . . . . . . 7.16 7.7.2 Steady state output noise power . . . . . . . . . . . . . . 7.18 7.8 Product Quantization Error . . . . . . . . . . . . . . . . . . . . . . 7.21 7.9 Coefficient Quantization error . . . . . . . . . . . . . . . . . . . . 7.29 7.10 Zero-input Limit Cycle Oscillations . . . . . . . . . . . . . . . . . 7.30 7.10.1 Dead band . . . . . . . . . . . . . . . . . . . . . . . . . 7.31 7.11 Overflow Limit Cycle Oscillations . . . . . . . . . . . . . . . . . . 7.32 7.12 Signal Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.33 7.13 Quantization in Floating Point Realization of IIR Digital Filters . . . 7.37 7.14 Finite Word Length Effects in FIR Digital Filters . . . . . . . . . . 7.41 7.15 Quantization Effects in the Computation of the DFT . . . . . . . . . 7.43 7.16 Quantization Errors in FFT Algorithms . . . . . . . . . . . . . . . 7.45 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 7.59 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 7.68 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . 7.68 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.71 Chapter 8 Multirate Signal Processing 8.1 - 8.54 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 8.2 Down Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 8.3 Spectrum of the Down Sampled Signal . . . . . . . . . . . . . . . . 8.2 8.4 Upsampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9 8.5 Spectrum of the Up-sampled Signal . . . . . . . . . . . . . . . . . 8.11 8.6 Anti-imaging Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12 8.7 Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.15 8.7.1 First identity . . . . . . . . . . . . . . . . . . . . . . . . 8.15 8.7.2 Second identity . . . . . . . . . . . . . . . . . . . . . . 8.15 8.7.3 Third identity . . . . . . . . . . . . . . . . . . . . . . . 8.16 8.7.4 Fourth identity . . . . . . . . . . . . . . . . . . . . . . . 8.17 8.7.5 Fifth identity . . . . . . . . . . . . . . . . . . . . . . . . 8.17 8.7.6 Sixth identity . . . . . . . . . . . . . . . . . . . . . . . . 8.18 8.8 Cascading Sample Rate Converters . . . . . . . . . . . . . . . . . . 8.19 8.9 Efficient Transversal Structure for Decimator . . . . . . . . . . . . 8.24 8.10 Efficient Transversal Structure for Interpolator . . . . . . . . . . . . 8.26 8.11 Polyphase Structure of Decimator . . . . . . . . . . . . . . . . . . 8.28 8.12 Polyphase Decimation using the z-transform . . . . . . . . . . . . . 8.31 8.13 Polyphase Structure of Interpolator . . . . . . . . . . . . . . . . . . 8.31 8.14 Polyphase Interpolation using the z-transform . . . . . . . . . . . . 8.33 8.15 Multistage Implementation of Sampling Rate Conversion . . . . . . 8.34 8.16 Implementation of Narrow Band Lowpass Filter . . . . . . . . . . . 8.35 8.17 Filter Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.35 8.17.1 Analysis filter bank . . . . . . . . . . . . . . . . . . . . 8.36 8.17.2 Synthesis filter bank . . . . . . . . . . . . . . . . . . . . 8.36 8.17.3 Subband coding filter bank . . . . . . . . . . . . . . . . 8.36 8.18 Quadrature - Mirror Filter (QMF) Bank . . . . . . . . . . . . . . . 8.37 8.18.1 Alias free filter bank . . . . . . . . . . . . . . . . . . . . 8.40 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 8.44 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 8.46 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . 8.46 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 8.48 Chapter 9 Statistical Digital Signal Processing 9.1 - 9.45 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 9.2 Random processes . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 9.3 Random Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 9.4 Random variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 9.5 Discrete-time Random Signals . . . . . . . . . . . . . . . . . . . . 9.3 9.6 Statistical Properties of Random Signal . . . . . . . . . . . . . . . 9.4 9.6.1 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 9.6.2 Mean square . . . . . . . . . . . . . . . . . . . . . . . . 9.6 9.6.3 Variance . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 9.6.4 Autocorrelation of random process . . . . . . . . . . . . 9.7 9.6.5 Autocovariance of random process . . . . . . . . . . . . 9.7 9.6.6 Crosscorrelation of random processes . . . . . . . . . . . 9.7 9.6.7 Crosscovariance of random processes . . . . . . . . . . . 9.7 9.7 Wide-sense Stationary Random Process . . . . . . . . . . . . . . . 9.8 9.7.1 Power in a random signal . . . . . . . . . . . . . . . . . 9.11 9.7.2 Ergodic process . . . . . . . . . . . . . . . . . . . . . . 9.12 9.8 Power Density Spectrum . . . . . . . . . . . . . . . . . . . . . . . 9.12 9.9 The DTFT of the Crosscorrelation Sequence . . . . . . . . . . . . . 9.13 9.10 White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.14 9.11 Response of LTI System Due to Random Signals . . . . . . . . . . 9.14 9.12 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.20 9.13 Estimation of Autocorrelation . . . . . . . . . . . . . . . . . . . . 9.23 9.14 The Periodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.24 9.14.1 Average value of IN (ω) . . . . . . . . . . . . . . . . . . 9.25 9.14.2 Variance of the periodogram . . . . . . . . . . . . . . . . 9.26 9.15 The Use of DFT in Power Spectrum Estimation . . . . . . . . . . . 9.31 9.16 Performance Characteristics of Nonparametric Power Spectrum Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.32 9.16.1 Periodogram . . . . . . . . . . . . . . . . . . . . . . . . 9.32 9.16.2 Bartlett’s power spectrum estimate . . . . . . . . . . . . 9.33 9.16.3 Welch power spectrum estimate . . . . . . . . . . . . . . 9.34 9.17 Computational Requirements of Nonparametric Power Spectrum Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.36 9.17.1 Bartlett’s method . . . . . . . . . . . . . . . . . . . . . . 9.37 9.17.2 Welch’s method (50% overlap) . . . . . . . . . . . . . . 9.37 9.17.3 Blackman-Tukey method . . . . . . . . . . . . . . . . . 9.38 9.18 Advantages and Disadvantages of Nonparametric Power Spectrum Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.39 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 9.42 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 9.43 MATLAB Programs . . . . . . . . . . . . . . . . . . . . . . . . . 9.44 Chapter 10 Applications of Digital Signal Processing 10.1 - 10.12 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 10.2 Speech Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 10.3 Speech Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 10.4 Speech Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 10.5 Subband coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 10.6 Channel Vocoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 10.7 Homomorphic Vocoder . . . . . . . . . . . . . . . . . . . . . . . . 10.8 10.8 Digital Processing of Audio Signals . . . . . . . . . . . . . . . . . 10.9 10.9 Radar Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 10.10 10.10DSP Based Measurement System . . . . . . . . . . . . . . . . . . . 10.11 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12 Chapter 11 Digital Signal Processors 11.1 - 11.76 11.1 Overview of Digital Signal Processors . . . . . . . . . . . . . . . . 11.1 11.2 Selecting Digital Signal Processors . . . . . . . . . . . . . . . . . . 11.5 11.3 Applications of PDSPs . . . . . . . . . . . . . . . . . . . . . . . . 11.6 11.3.1 Communications systems . . . . . . . . . . . . . . . . . 11.6 11.3.2 Audio signal processing . . . . . . . . . . . . . . . . . . 11.7 11.3.3 Control and data acquisition . . . . . . . . . . . . . . . . 11.7 11.3.4 Biometric Information Processing . . . . . . . . . . . . . 11.8 11.3.5 Image/video processing . . . . . . . . . . . . . . . . . . 11.8 11.4 Von Neumann Architecture . . . . . . . . . . . . . . . . . . . . . . 11.8 11.5 Harvard Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 11.9 11.6 VLIW Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 11.10 11.7 Multiply Accumulate Unit (MAC) . . . . . . . . . . . . . . . . . . 11.11 11.8 Pipelining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13 11.9 Architecture of TMS320C50 . . . . . . . . . . . . . . . . . . . . . 11.15 11.9.1 Bus structure . . . . . . . . . . . . . . . . . . . . . . . . 11.16 11.9.2 Central processing unit . . . . . . . . . . . . . . . . . . 11.17 11.9.3 On-chip memory . . . . . . . . . . . . . . . . . . . . . . 11.21 11.9.4 On-chip peripherals . . . . . . . . . . . . . . . . . . . . 11.23 11.10 Addressing modes . . . . . . . . . . . . . . . . . . . . . . . . . . 11.25 11.10.1 Immediate addressing . . . . . . . . . . . . . . . . . . . 11.26 11.10.2 Indirect addressing . . . . . . . . . . . . . . . . . . . . . 11.26 11.10.3 Register addressing . . . . . . . . . . . . . . . . . . . . 11.26 11.10.4 Memory mapped register addressing . . . . . . . . . . . 11.27 11.10.5 Direct addressing mode . . . . . . . . . . . . . . . . . . 11.27 11.10.6 Circular addressing mode . . . . . . . . . . . . . . . . . 11.28 11.11 Instruction Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.28 11.11.1 Summary of instructions . . . . . . . . . . . . . . . . . . 11.28 11.11.2 Classification of instructions . . . . . . . . . . . . . . . . 11.34 11.12 Simple Assembly Language Programs . . . . . . . . . . . . . . . . 11.48 11.13 Architecture of TMS320C54x . . . . . . . . . . . . . . . . . . . . 11.60 11.13.1 Internal memory organization . . . . . . . . . . . . . . . 11.60 11.13.2 Overflow handling . . . . . . . . . . . . . . . . . . . . . 11.63 11.13.3 The carry bit . . . . . . . . . . . . . . . . . . . . . . . . 11.64 11.13.4 Dual 16-bit mode . . . . . . . . . . . . . . . . . . . . . 11.64 11.14 Accumulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.64 Questions and Answers . . . . . . . . . . . . . . . . . . . . . . . 11.72 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 11.75 Appendix A Mathematical Identities A.1 - A.2 A.1 Infinite Summation Formulas . . . . . . . . . . . . . . . . . . . . . A.1 A.2 Finite Summation Formulas . . . . . . . . . . . . . . . . . . . . . A.1 A.3 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 A.4 Complex Variables . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 A.5 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . A.2 | ||
| 650 | _aElectronics | ||
| 942 |
_2ddc _cBK |
||