I am a little confused about the use of anti-aliasing filters. As on how I am confused, please consider the following task:
Consider a simple sampling rate conversion system with a conversion rate of 4/3. The system consists of two upsampling blocks, each by 2, and one downsampling block of 3.
The frequency spectrum has periodic repetitions at integer multiples of the sampling frequency. Therefore, upsampling creates additional - unwanted - spectral images. These can be cancelled by an anti-imaging filter:
The spectrum within the blue dotted rectangles should be my output Y_1. This output will be upsampled a second time, which I think results just having 4 spectrum repetitions until 2*pi.
But, how does downsampling work? I am given the following figure from my lecture notes:
So, apparently before downsampling we apply the anti-aliasing filter, which will result in the part of the spectrum within the blue-dotted shapes. Now, we increase Omega by a factor of 2, such that.. I don't know. What exactly happens here ?