Re: [Discuss-gnuradio] Decimation

[Dan Gisselquist]

Any comments?  Yeah.

I had a similar conversation with my instructor two years ago.  He  
basically said that wavelets were the ideal way of breaking the world  
into time and frequency.  Be aware, however, wavelets do not divide the  
world into equal time and frequency "bins".  They are biased towards  
high frequency resolution for low frequencies, while at the same time  
achieving low time resolution for the same low frequencies.  Towards  
the higher frequency end of the scale, wavelets are often used to  
provide very precise time resolution at the expense of frequency  
resolution.  Applications for wavelets are numerous.

However (my two cents), wavelets are not as appropriate for examining  
the electromagnetic spectrum.  In particular, the assumption that  
higher frequencies need more time resolution is rendered invalid by a  
frequency agile communications system (something where the carrier  
frequency can be placed anywhere).


IMHO, decimation always requires an antialiasing low-pass filter  
coupled with the actual decimator.  Two primary implementations exist.   
The first filters and then decimates, the second couples the two  
operations together so that the only filter outputs computed are the  
valid outputs of the decimator.  The differences between these two  
approaches, in terms of computational cost, can be very dramatic.

While you could use the wavelet transform to perform the same  
operation, it would only make sense if you wanted multiple outputs as a  
result.  For example, the wavelet transform might make sense if you  
wanted to separate the input into multiple different streams at  
(likely) different rates.

Other approaches, such as those using a DFT filter banks, make a lot  
more sense when you want equally spaced frequency bins for reasons  
discussed above.  If you'd like, I can provide some really good  
references for how to do this well ...

Just my two cents,

Dan


On 11/19/2004 10:54:21 AM, Prateek Dayal wrote:
> Hi ,
>
> I saw that in GNU Radio, decimation is carried out after using an
> antialiasing low pass filter. In a discussion a professor at my
> institute suggested that we can use wavelets for decimation and
> interpolation ....
>
> any comments ???
>
> --
> Prateek Dayal
> B.Tech 4th Year
> ECE
> IIT Guwahati
>
> www.geocities.com/pmd_iitgw
>
>
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