Sparse Representation of Signals in Hardy Space

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 H-2(D) via the compressed sensing (CS) technique with the dictionary D = {e(a):e(a) (z) = root 1-vertical bar a vertical bar(2)/1-(a) over bar z,a is an element of D}. where D denotes the unit disk. In addition, we give examples exhibiting the algorithm.