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## Re: [Discuss-gnuradio] USRP2 Halfband filter coefficients help

 From: Jeff Brower Subject: Re: [Discuss-gnuradio] USRP2 Halfband filter coefficients help Date: Wed, 11 Nov 2009 10:02:27 -0600 (CST) User-agent: SquirrelMail/1.4.2-1

```Ilkyoung Kwoun-

> Thank you for your advice. Actually I am aware of basic characteristics of
> half band filter. It is very well explained in Rick Ryon's "Understanding
> Digital Signal Processing (2nd Ed.)" (
> http://www.amazon.com/Understanding-Digital-Signal-Processing-2nd/dp/0131089897/ref=sr_1_1?ie=UTF8&s=books&qid=1257900094&sr=8-1
>  )
>
> The thing I do not have any clue is the 'inner' and 'outer' coefficient
> things in FIR filter. I guess this is something related to the practical
> implementation issue rather than the fundamental concept. I did a simple
> googling yesterday and found a paper. (
> http://ce.et.tudelft.nl/publicationfiles/1090_509_shahbahrami_prorisc2005.pdf)
> I hope I can find a way to get started.  :-)

Here is a Hypersignal log-magnitude plot showing the frequency response of the
two halfband filters (31-tap in blue,
7-tap in red):

In the plots I used an arbitrary sampling rate of 25 MHz -- don't know what
you're using.  Note that both filters have
an approx -6 dB point at Fs/4 as would be expected due to halfband symmetry
properties.

As for "inner and outer" mention in the Verilog code, I might guess that refers
to 2 multiplies needed when filtering
a complex signal.  As for why there are two (2) filters, one is used for higher
rate up/down conversions and the other
for lower rate.  Firas' documentation has some information on this... also here
is Q&A exchange between Firas and Matt

http://old.nabble.com/Some-USRP2-Questions-td20729711.html

-Jeff

>
>> Hi
>>
>> I think Brian is just referring to the fact that you can see that the
>> HBFs are implemented as symmetric FIR filters (the coefficients).  A
>> HBF is just a special filter that is designed so that the cutoff
>> frequency will always be at fs/2, so if you filter with it and
>> decimate by 2 afterwards (which is why you would use an HBF), you
>> don't get aliasing.  Also, the decimation in the CIC filters can be
>> set to a wide range of values, so the HBF will always have to cut at
>> fs/2 regardless of the decimation in the CIC.  From what I've read,
>> Goodman and Carey came up with them so you can probably look for some
>> papers if you're interested.
>>
>> Sebastiaan
>>
>> --
>> Sebastiaan Heunis
>> Radar Remote Sensing Group, University of Cape Town, South Africa
>> Tel:  +27 72 950 9370
>>
> _______________________________________________