Comments on "A Convolution and Product Theorem for the Linear Canonical Transform"

A recent letter proposed a new convolution structure for the linear canonical transform [1], and claimed that theirs was clearly easier to implement in the designing of filters than the one suggested earlier in [2]. However, we find that the two kinds of filtering methods are essentially the same through the theoretic deduction. That is to say, the two kinds of filtering methods can obtain the same effect through the same filtering steps. Taking digital signal processing into account, we analyze further the computation complexity according to the steps of multiplicative filter.