Haar Filter for QMF

Hi,
 Its known that Haar filter is the only FIR filter achieves the perfect
reconstruction when used in QMF filter. Then why is it not used? Why do
people go for longer length filters and pseudo QMF? What are the
disadvantages of Haar filter that it cannot be used in QMF filter?

Thanks in advance.

vasindagi wrote:
> 
> Hi,
>  Its known that Haar filter is the only FIR filter achieves the perfect
> reconstruction when used in QMF filter. Then why is it not used? Why do
> people go for longer length filters and pseudo QMF? What are the
> disadvantages of Haar filter that it cannot be used in QMF filter?


The reason the Haar filters work is because the aliasing which is
considerable cancels out in the end. So if all you were doing was
separating the signal into to channels followed by reconstruction that
is the best way to do it. But if you modify the channels before
reconstructing the signal then the aliases will no longer cancel and
you get noise. For instance if you quantize the high band you get more
noise than just the quantization in the high band. You also get noise
in the low band from aliases that are no longer canceled. 

	If you could construct a pair of mirror filters with a perfect brick
wall frequency response you would also get perfect reconstruction.
That is when the frequency responses were squared and summed it would
add to a flat response. That would also mean you wouldn't be relying
on the aliases to cancel for perfect reconstruction. 
	You can't make perfect filters but you can try to get close.

-jim




> 
> Thanks in advance.


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