# DWT architecture using filter bank

I am studying this paper.

In one of the figures in the paper (Fig 5.b and Fig 5.c) DWT architecture is given using db2 and filter bank.

I don't understand how Lo_D and Hi_D have size half of input image size? If we see the figures there is no downsampler. Then how the size of the Lo_D and Hi_D have half the size of image (either row wise or column wise)?

Please explain me how single level DWT is implemented using filter banks? How the size of the decomposition values is half of the input (i.e. image) when filter banks are used to implement DWT?

I understand they implement the convolution by Lo and Hi db2 filters given after the sentence:

Rather, we propose to use db2 filters. The filter coefficients for the db2 filter are represented as

I have not seen in the paper a claim that Lo_D and Hi_D in Figures 5b and 5c should be half-size. They are low-pass and high-pass branches. However, they should be followed by a downsampling to implement a one level-DWT, or at least something similar.

There are different ways for implementing a one level of a standard critically sampled DWT: direct, lattice, lifting, polyphase, Fourier. They should end up all with the same number of samples as the original signal (away from the borders).

• Thanks Laurent for the answer. I had this doubt whether downsampler is following the filter or not. By your answer it got clarified. – kushi May 22 '16 at 3:42
• @kushi Could you tell by "vote" or "accept" whether your question requires additional clarification? – Laurent Duval Jul 21 '16 at 13:14