Discrete Wavelets - Question on decimation of high pass
Hi, I'm trying to grasp the concept of discrete wavelets and can't seem to find an answer to my question.
In the decomposition of a signal using wavelets filter banks, the signal goes through a low pass and high pass filter. The output of the low pass and high pass is decimated by 2. I can understand the low pass output being decimated by 2 since only the lower half of the bandwidth is kept. However, how is it possible to decimate the high pass output by 2 given Nyquist theory? I'm imagining if the original signal was sampled at a rate slightly higher than twice the highest frequency in the signal, the output of the high pass filter bank can't be downsampled without losing the high frequency information. Can anyone help me see this clearly? Thanks alot