Patent ID: 8861327

Claim:
A method for communicating comprising: obtaining one or a plurality of input communication symbols selected from a set of communication symbols; converting the one or a plurality of input communication symbols into one or a plurality of transmittable waveforms using one or a plurality of non-periodic functions selected from a set of non-periodic functions; and transmitting the one or a plurality of transmittable waveforms over a communication channel, wherein at least one non-periodic function selected from the set of non-periodic functions has a form of equation f m ⁡ ( t ) = [ κ 0 ⁢ ⅇ ⅈω 0 ] ⁢ ⅇ [ κ 1 ⁢ ⅇ ⅈω 1 ] ⁢ ( t + t 0 ) ⁢ ⅈ [ κ 2 ⁢ ⅇ ⅈω 2 ] ⁢ ( 2 2 - m ) , wherein κ 0 is a first level amplitude coefficient, ω 0 is a first level frequency constant, i is an imaginary constant square root of minus one, κ 1 is a second level amplitude coefficient, ω 1 is a second level frequency constant, t is a time parameter, t 0 is an initial time, κ 2 is a third level amplitude coefficient, ω 2 is a third level frequency constant, and m is a waveform shape term.