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Re: [Discuss-gnuradio] Decimation

From: Dan Gisselquist
Subject: Re: [Discuss-gnuradio] Decimation
Date: Fri, 19 Nov 2004 15:07:54 -0700

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,


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
IIT Guwahati


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