Trends in Digital Signal Processing

June 16, 2015 13:40 PSP Book - 9in x 6in 08-Yong-Ching-Lim-c08

Dictionary Approaches 281

(Vaidyanathan and Pal, 2014). A dictionary is simply a fat matrix A

of size N × M where M >> N.EachoftheM columns is a periodic

signal, and is called a (periodic) atom. Given an N-vector x (signal

x(n) with N samples), the representation takes the form

x = A



N×M

d (8.38)

Since M >> N, columns with all periods in the range 1 ≤ q ≤ N can

be accommodated in the dictionary, as in the first Ramanujan sum

representation (Eq. (8.4)). Furthermore, for each period q,wecan

accommodate a number of columns in A representing that period.

Thus an entire subspace can be used to ...