Reply to comments on a convolution and product theorem for the linear canonical transform

In this letter, we reply to the comment regarding our recent report on filtering. The authors found that two kinds of filtering methods are essentially the same . However, we will demonstrate that the multiplicative filter in the linear canonical transform (LCT) domain is carried out easily using our convolution structure. Considering the designing of filter, firstly, we can easily convert the multiplicative filter in the LCT domain to the time domain using our formula. Secondly, we can easily implement with hardware unit though our filtering model. Lastly, we present a simple example to illustrate the advantage of our convolution structure.