Design of UWB pulses by spline approximation

The present paper discusses a new construction of UWB pulses within the framework of soft-spectrum adaptation. The employed basis functions are B-splines having the following properties: (i) the B-splines are time-limited piecewise polynomials; (ii) the first-order B-splines are rectangular pulses and they converge band-limited functions at the limit that their order tends to infinity; (iii) there is an analog circuit and a fast digital filter for the generation of B-splines. A constrained approximation technique is proposed for adaptively designing pulses so that they approximate target frequency characteristics. At the cost of using eleven shifted B-splines, an example set of four pulses conforming to the FCC spectral mask is obtained.