Achievement of Preassigned Spectra in the Synthesis of Band-Pass   Constant-Envelope Signals by Rapidly Hopping through Discrete Frequencies
  Spread-spectrum signals are increasingly adopted in fields including communications, testing of electronic systems, Electro-Magnetic Compatibility (EMC) enhancement, ultrasonic non-destructive testing. This paper considers the synthesis of constant-envelope band-pass wave-forms with preassigned spectra via an FM technique using only a limited number of frequencies. In particular, an optimization-based approach for the selection of appropriate modulation parameters and statistical features of the modulating waveform is proposed. By example, it is shown that the design problem generally admits multiple local optima, but can still be managed with relative ease since the local optima can typically be scanned by changing the initial setting of a single parameter. 
Sergio Callegari
physics.data-an cs.IT math.IT