New sampling formulae related to linear canonical transform

Digital computation of the complex linear canonical transform

“…(5) is consistent with the results for real parameters [11][12][13]19]. We assume that the function gðξÞ is concentrated in a circular area with radius r, i.e., that it is zero outside this area, as shown in Fig.…”

“…The sampling issues for LCTs with real parameters have been discussed in detail in many references [11][12][13][14][15][16][17][18][19]. When the parameters become complex, however, the output domain variable must in general be dealt with as a complex variable.…”

Fast linear canonical transforms

“…While Stern approached reconstruction as simply multiplying by a rect function in the appropriate domain, Deng et al explicitly derived the time-domain reconstruction formula. Recently, Li et al [36] published a proof of Ding's theorem similar to that in [33].…”

The ambiguity function associated with the linear canonical transform

“…With the rapid developments of the modern signal processing technology, the classical concepts and theories in the FT domain have been studied extensively in the LCT domain, for example, the uniform and nonuniform sampling theories [32][33][34], the convolution and product theorems [14,15], the uncertainty principles [35][36][37] have been well studied and investigated in the LCT domain.…”