new book out soon will be only $50 leipzig50@gmail Written by an engineer not academic Special Topics in Numerical Analyses with Digital Applications to RADAR Systems By Douglas Colvin 2013 CHAPTER ------- CONTENT------- PAGE NUMBER 1 Pulse Shaping 7 2 The Discrete Fourier Transform (DFT) 10 2.1 DFT using Gauss-Quadrature Integration (GQI) 14 2.2 The Fast Fourier Transform (FFT) 17 2.3 Aliasing 19 3 Analog-to-Digital Converter Compensation 20 3.1 Introduction 20 3.2 ADC Review 20 3.3 Ideal Quantization 22 3.4 ADC Performance Drivers 24 3.5 Instantaneous Bandwidth 24 3.6 Instantaneous Dynamic Range 25 3.6.1 EXTENSION OF ADC DYNAMIC RANGE 25 3.7 Sample/Track-Hold Circuits 26 3.8 ADC Non-Linearity 27 3.9 Aperture Jitter 27 3.10 Flash ADC 27 3.11 Sigma-Delta ADC 28 3.12 ADC Dynamic Error Correction 30 3.13 Problem Formulation 30 3.14 Taylor Series Expansion of the Data 32 3.15 Harmonic & Intermodulation Components 33 3.16 Basis Function Representation of Error 34 3.16.1 CHOICE OF BASIS FUNCTION 35 3.17 Derivative Estimation 36 3.17.1 FINITE DIFFERENCE APPROXIMATION TO THE DERIVATIVE 36 3.17.2 DIFFERENTIATING FINITE IMPULSE RESPONSE (DFIR) FILTER 36 3.18 Solving for the Basis Function Weights, 38 3.18.1 SOLVING FOR THE BASIS FUNCTION WEIGHTS 38 3.18.2 SOLVING FOR THE BASIS FUNCTION WEIGHTS 38 3.19 Phase-Plane Description of ADCs 39 3.19.1 PHASE-PLANE DESCRIPTION FOR SINGLE-TONE TESTS 41 3.19.2 GENERATING THE ERROR TABLE 41 3.20 Example of Compensation 42 3.20.1 TEST RESULTS 43 3.21 Conclusions 45 4 Sample Rate and Aliasing 48 5 The Fractional Delay Filter 51 5.1 Introduction 51 5.2 Derivation of the FD-FIR Filter 52 6 Probability of False Alarm and Detection Based on Threshold 56 6.1 Introduction 56 6.2 Gauss-Legendre Quadrature Integration 56 6.3 Mathematics for Probabilities of False Alarm and Detection 56 7 A Summary of Statistical Distributions 60 7.1 Introduction 60 7.2 Lognormal Distribution 60 7.3 Swerling Distributions 64 7.3.1 SWERLING I DISTRIBUTION 64 7.3.2 SWERLING II DISTRIBUTION 64 7.3.3 SWERLING III DISTRIBUTION 65 7.3.4 SWERLING IV DISTRIBUTION 65 7.3.5 SWERLING V DISTRIBUTION 65 7.4 Other Distribution Functions 65 7.4.1 GAUSSIAN DISTRIBUTION 65 7.4.2 RAYLEIGH DISTRIBUTION 65 7.4.3 POISSON DISTRIBUTION 65 7.4.4 GAMMA DISTRIBUTION 66 7.4.5 RICIAN DISTRIBUTION 66 7.4.6 ERLANG DISTRIBUTION 66 7.4.7 EXPONENTIAL DISTRIBUTION 66 7.4.8 BINOMIAL DISTRIBUTION 66 7.5 Statistical Properties 66 7.5.1 AUTOCORRELATION FUNCTION (ACF) 66 7.5.2 CUMULATIVE DISTRIBUTION FUNCTION (CDF) N’TH DEGREE CHI-SQUARED 67 8 Phase-Noise and Phase-Locked-Loop 69 8.1 Narrow Band Noise 69 8.2 Phase-Locked-Loop (PLL) Transfer Function 71 8.2.1 OUTPUT PHASE NOISE 72 9 Conductivity and Resistivity 75 10 Modulation Decomposition via Polyphase Architecture 81 10.1 Z-Transform of Modulation Decomposition (MD) 81 10.2 Z-Transform of Polyphase Decomposition (PD) 84 10.3 Filtering in the Modulation and Polyphase Domains 89 11 Phased Arrays 91 11.1 Array Geometry 91 11.2 Current Distribution and the Array Factor 92 11.3 Beamsteering 94 11.4 Phase Errors and Compensation Due to Line Length Errors 94 11.5 Grating Lobes 95 11.6 Pyramidal Horn Antenna Pattern 96 11.7 Calibration 97 11.8 Phased Array Model 97 11.9 Matrix Formulation for the Phased Array Model 98 11.10 Mutual Coupling Matrix Estimation via Limited Measurements 99 11.11 Phased Array for Monopulse Direction Finding 100 11.12 DERIVATION OF OPTIMAL WEIGHTS 103 12 Method of Moments 106 13 A Broadband Multilayer CAD Tool Utilizing the Method of Continuants 121 13.1 Introduction 121 13.2 Transmission Line Equivalent Network 121 13.3 Method of Continuants 122 13.4 Transvers -Electric (TE) and Transverse-Magnetic (TM) Waves 124 13.5 Example of Application 126 13.6 Three-Dimensional Application 127 14 The Hilbert and Fourier Transform Relationship 131 14.1 Introduction 131 14.2 The Ideal Hilbert Transform 134 14.3 From the Hilbert Transform to the Low-Pass Filter 135 15 Mixer Intermodulation Products 143 15.1 Introduction 143 16 Real-Time Calibration of IF Analytic Signals 161 16.1 Introduction 161 16.2 Simplified Radar System 161 16.3 The LFM Signal 162 16.4 In-Phase and Quadrature-Phase Components (I & Q) 164 16.5 Amplitude and Phase Calibration Process 166 16.6 Phase Detection Circuit (PDC) 167 17 WIDEBAND DIGITAL RECEIVER 183 17.1 Introduction 183 17.2 Front-End Input Parameters 183 17.3 Analog-to-Digital Converter (ADC) Specifications 183 17.4 Input Power Levels and Frequencies 184 17.5 Pulse Shaping Signals and Additive Noise 184 17.6 Narrow Band Dithering 184 17.6.1 LOW PASS FILTER FOR NARROW BAND DITHERING 184 17.7 RF Band Pass Filter 185 17.8 ADC Quantized Output 185 17.9 Finite Impulse Filter with Internal Bit Rounding 186 17.10 Channel Data Convolved with the FIR Filters 186 17.11 FIR Output Bit Truncation 186 17.12 Discrete Fourier Transform (DFT) Output 186 17.13 DFT Kernel Bit Rounding 187 17.14 Application of the DFT Kernel 187 17.15 DFT Output Bit Truncation 187 17.16 Post Processing 187 17.17 Instantaneous Amplitude and Frequency Measurement 187 18 The Conjugate Gradient Method (CGM) For Solving Complex Matrix Equations 206 19 Range-Doppler Coupling 230 20 Atmospheric Refraction 243 20.1 Introduction 243 20.2 Refraction Model 244 20.3 Analysis Description 246 20.4 Brewster’s Angle 247 20.5 Critical Angle 247 20.6 Laws of Reflection and Refraction 248 20.7 Multilayer Algorithm 249 20.8 Conclusions 252 21 N-Point Scattering Center Reduction Using the FFT and CGM 265
Posted on: Sat, 08 Jun 2013 15:56:16 +0000
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