FOURIER TRANSFORMS IN RADAR AND SIGNAL PROCESSING
CONTENTS INTRODUCTION AIM OF THE WORK ORIGIN OF THE RULES AND PAIRS METHOD FOR FOURIER TRANSFORMS OUTLINE OF THE RULES AND PAIRS METHOD THE FOURIER TRANSFORM AND GENERALIZED FUNCTIONS COMPLEX WAVEFORMS AND SPECTRA IN SIGNAL PROCESSING OUTLINE OF THE CONTENTS REFERENCES RULES AND PAIRS NOTATION FOURIER TRANSFORM AND INVERSE FOURIER TRANSFORM RECT AND SINC D-FUNCTION AND STEP FUNCTION REP AND COMB CONVOLUTION THREE ILLUSTRATIONS NARROWBAND WAVEFORMS PARSEVAL’S THEOREM THE WIENER-KHINCHINE RELATION APPENDIX 2A: PROPERTIES OF THE SINC FUNCTION APPENDIX 2B: BRIEF DERIVATIONS OF THE RULES AND PAIRS PULSE SPECTRA SYMMETRICAL TRAPEZOIDAL PULSE SYMMETRICAL TRIANGULAR PULSE ASYMMETRICAL TRAPEZOIDAL PULSE RAISED COSINE PULSE ROUNDED PULSES GENERAL ROUNDED TRAPEZOIDAL PULSE REGULAR TRAIN OF IDENTICAL RF PULSES CARRIER GATED BY A REGULAR PULSE TRAIN PULSE DOPPLER RADAR TARGET RETURN SUMMARY SAMPLING THEORY BASIC TECHNIQUE WIDEBAND SAMPLING UNIFORM SAMPLING MINIMUM SAMPLING RATE GENERAL SAMPLING RATE HILBERT SAMPLING QUADRATURE SAMPLING BASIC ANALYSIS LOW IF ANALYTIC SIGNAL SAMPLING HIGH IF SAMPLING APPENDIX 4A: THE HILBERT TRANSFORM INTERPOLATION FOR DELAYED WAVEFORM TIME SERIES SPECTRUM INDEPENDENT INTERPOLATION MINIMUM SAMPLING RATE SOLUTION OVERSAMPLING AND THE SPECTRAL GATING CONDITION THREE SPECTRAL GATES RESULTS AND COMPARISONS LEAST SQUARED ERROR INTERPOLATION METHOD OF MINIMUM RESIDUAL ERROR POWER POWER SPECTRA AND AUTOCORRELATION FUNCTIONS ERROR POWER LEVELS APPLICATION TO GENERATION OF SIMULATED GAUSSIAN CLUTTER DIRECT GENERATION OF GAUSSIAN CLUTTER WAVEFORM EFFICIENT CLUTTER WAVEFORM GENERATION USING INTERPOLATION RESAMPLING EQUALIZATION BASIC APPROACH RAMP AND SNCR FUNCTIONS SIMPLE EXAMPLE OF AMPLITUDE EQUALIZATION EQUALIZATION FOR BROADBAND ARRAY RADAR SUM BEAM EQUALIZATION DIFFERENCE BEAM EQUALIZATION ARRAY BEAMFORMING BASIC PRINCIPLES UNIFORM LINEAR ARRAYS DIRECTIONAL BEAMS LOW SIDELOBE PATTERNS SECTOR BEAMS NONUNIFORM LINEAR ARRAYS