Short-range impulse radio system by means of generalized splines

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For the impulse radio communications system connecting digital devices at very short distances, it has been clarified how to shape and detect orthogonal pulses generated through a resonance filter driven by a staircase waveform. A mathematical proof of their existence is extablished. A resulting example pulse would achieve the transmission rate to 6 billion pulses per second which is 11 times faster than the best existing one. A pair of antennas were prototyped of which operation is close to double differentiation in time.