Mathematically, signals can be seen as functions in certain spaces. And processing is more efficient in a sparse representation where few coefficients reveal the information. Such representations are constructed by decomposing signals into elementary waveforms. A set of all elementary waveforms is called a dictionary. In this chapter, we introduce a new kind of sparse representation of signals in Hardy space  H²(D)via the compressed sensing (CS) technique with the dictionary D={ea:ea(z)=1−|a|2√1−a¯z,a∈D}.D={ea:ea(z)=1−|a|21−a¯z,a∈D}.

where ⅅ denotes the unit disk. In addition, we give examples exhibiting the algorithm.