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In this study, the frequency spectrum of a pulse for ultra wideband impulse radio systems is assumed to be the frequency response of a real valued causal rational infinite impulse response (IIR) filter. This pulse design problem is formulated as a functional inequality constrained optimisation problem. The objective of this optimisation problem is to minimise the sum of the total passband and stopband ripple energy of the pulse. Also, the optimisation problem is subject to the stability condition of the IIR filter as well as to the specifications defined on both the maximum passband and stopband ripple magnitudes and that on the maximum time domain ripple magnitude of the pulse. If the feasible set of the optimisation problem is nonempty, then the designed pulse is guaranteed to be satisfied the specifications suggested by the Federal Communications Commission. Computer numerical simulation results show that the energy compaction performance defined in the frequency domain of the authors’ designed pulse outperforms that of existing pulses. Since the frequency spectrum of the pulse is the same as the frequency response of the designed IIR filter, the pulse can be generated via an excitation of a simple circuit.
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