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THE MATHEMATICAL TREATMENT OF
WORKED UNCERTAINTY FUNCTION EXAMPLES
6 other sections not shown
amplitude area of uncertainty bandwidth Changing the dummy co-ordinates complex analytic signal constant carrier frequency convolution theorem corresponding defined definition delay-Doppler coupling delta function discussed in Section dispersion factor Doppler offset Doppler precision dummy variable duty cycle equal evaluated exponential expression fa(t Fourier transform calculator Fourier transform receiver Fresnel integrals gives oo Hilbert transform illustrated by Fig impulse response integral in Equation Ix(t large values leads linear FM matched filter receiver mathematical modulation multiplier notation number of pulses obtained one-sided oo oo oo optimum output waveform Parseval's theorem peak signal-to-noise ratio phase plane Proof of Equation properties prove Equation pulse repetition frequency Re(p real signal receiver output rectangular pulse relationship RF envelope Section 3.2 shown in Section shows sidelobes signal processing spectra spectrum strip of convergence target term transfer function transmitted signal two-sided Laplace transform uncertainty function velocity precision waveform zero