[SOLVED] Half band filters and perfect reconstruction condition

[Sonia1234]

Hello,

I've tried to search for this topic online and even tried to look the book wavelets and filterbanks by strang it didn't help much to develop my understanding of how half-band filters are uniquely identified. Hence I'm posting here to know your perspective of how would determine them.
Lets initiate from here, for instance, if I have two filters p(0) and p(1) both of which are equivalent to 1, how would determine that these are half band filters?

Thanks

 

[albbg]

Your question is not clear to me. Could you elaborate it a little bit more ?

 

[Sonia1234]

I'm asking for better explanation of the characteristics of half band filters which are basically the condition for perfect reconstruction. So for instance, can you please explain me how would I determine if the filter: p(0)=p(1)=1 is half band filter?

 

[axcdd]

You get something wrong here....

To get 'perfect reconstruction signal' you need to sample it with as least twice its band frequency.

Halfband filters are special group of FIR filters that got passband frequency equall to 0.5 of they normalized frequency

 

[albbg]

You get something wrong here....

To get 'perfect reconstruction signal' you need to sample it with as least twice its band frequency.

Halfband filters are special group of FIR filters that got passband frequency equall to 0.5 of they normalized frequency

Halfband filter are resampling filter and they are used when you want to oversample the signal by a factor 2 and then go back to the "normal" rate (dividing by 2), in order to eliminate (or better, reduce) the aliasing. In this way you can do a (ideally) perfect reconstruction of the signal. So it's correct at reception they cut half the bandwidth of the oversampled signal.
They are used on both side: transmission, before the oversampling and reception, after undersampling.