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Anti aliasing filters in JPEG compression

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DEM_

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I have built a model of JPEG encoder using Java. I implemented a simple filtering before sampling. I used couple of filtering ways:
1) simple mean value between two samples
2) tent filter (FIR with three taps 0.25, 0,5, 0.25)
3) tent filter with phase shift (FIR with four taps 1/8;3/8;3/8;1/8 )
4) lanczos2 (with and without phase shift)

I've performed some tests to check influence of filter type on PSNR ratio. I used 420 sampling mode.

I'm surprised a little bit in results. The best PSNR was achieved using simple mean value and it was comparable with Lanczos2 with phase shift. The worst results are with three tap tent filter. Basing on results I may say that the best one was achieved using filters with phase shift, because they approximate a value between pixel. But I wonder why the Lanczos filter don't improve PSNR ratio in comparison with simple mean value filter? I noticed that mean value filter pass more after nyquist frequency but also cuts less signal before nyquist freq. The Lanczos filter cuts more after nyquist frequency, but also cuts more signal before the nyquist.
the question is: How much an aliasing affects image quality (PSNR) in JPEG compression? It is required to use anti aliasing filters for sampling in JPEG? What filters are the best?
 

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