Interpolation and decimation

Started by seb January 13, 2004
Hello,

i am looking for decimation and interpolation technique in order to,
given a sampling rate fs, obtain a new sampling rate like (a/b)*fs.

A way to to do is to decimate and then use linear interpolation...

Is there some other ways (documents) to do this ?
If so, have you got some book or url ?

Thanks
seb:

I don't know of any "new" ways to do it, but make sure that if you do it the
old way, and a<b, you LPF (or BPF is your frequency region of interest is
other than baseband) the original data prior to decimation so that folded
content is not present in downsampled data.

Jim

"seb" <germain1_fr@yahoo.fr> wrote in message
news:23925133.0401131910.7f22e0a2@posting.google.com...
> Hello, > > i am looking for decimation and interpolation technique in order to, > given a sampling rate fs, obtain a new sampling rate like (a/b)*fs. > > A way to to do is to decimate and then use linear interpolation... > > Is there some other ways (documents) to do this ? > If so, have you got some book or url ? > > Thanks
"seb" <germain1_fr@yahoo.fr> wrote in message
news:23925133.0401131910.7f22e0a2@posting.google.com...
> Hello, > > i am looking for decimation and interpolation technique in order to, > given a sampling rate fs, obtain a new sampling rate like (a/b)*fs. > > A way to to do is to decimate and then use linear interpolation... > > Is there some other ways (documents) to do this ? > If so, have you got some book or url ? > > Thanks
See www.dspguru.com on sample rate conversion
Jim Gort wrote:

> seb: > > I don't know of any "new" ways to do it, but make sure that if you do it the > old way, and a<b, you LPF (or BPF is your frequency region of interest is > other than baseband) the original data prior to decimation so that folded > content is not present in downsampled data. > > Jim > > "seb" <germain1_fr@yahoo.fr> wrote in message > news:23925133.0401131910.7f22e0a2@posting.google.com... > >>Hello, >> >>i am looking for decimation and interpolation technique in order to, >>given a sampling rate fs, obtain a new sampling rate like (a/b)*fs. >> >>A way to to do is to decimate and then use linear interpolation... >> >>Is there some other ways (documents) to do this ? >>If so, have you got some book or url ? >> >>Thanks
By upsampling first, frequencies that the final sample rate will support don't have to be removed. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
"seb" <germain1_fr@yahoo.fr> wrote in message
news:23925133.0401131910.7f22e0a2@posting.google.com...
> Hello, > > i am looking for decimation and interpolation technique in order to, > given a sampling rate fs, obtain a new sampling rate like (a/b)*fs. > > A way to to do is to decimate and then use linear interpolation... > > Is there some other ways (documents) to do this ? > If so, have you got some book or url ? > > Thanks
There have been many many discussion on this topic in comp.dsp. Use google search and look for multirate sampling. A good book for reference on this topic is Multirate Systems and Filterbanks by P.P. Vaidyanathan. Cheers Bhaskar
On Wed, 14 Jan 2004 09:49:54 -0800, "Bhaskar Thiagarajan"
<bhaskart@deja.com> wrote:

>
(snipped)
>> >> Is there some other ways (documents) to do this ? >> If so, have you got some book or url ? >> >> Thanks > >There have been many many discussion on this topic in comp.dsp. Use google >search and look for multirate sampling. >A good book for reference on this topic is >Multirate Systems and Filterbanks by P.P. Vaidyanathan. > >Cheers >Bhaskar
Hi Bhasker, yep, below are a few other references for seb. I'll bet he doesn't realize that a person could make a career out of learning all the theory of sample rate changing. (At least I thinkk so.) By the way, I heard that fred harris (of windows fame) is writing a book on multirate signal processing. [-Rick-] [8] Fliege, N. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets, John Wiley & Sons, 1995. [9] Crochiere, R. and Rabiner, L. Multirate Digital Signal Processing, Prentice-Hall, Upper Saddle River, New Jersey, 1983. [11] Crochiere, R. and Rabiner, L. "Decimation and Interpolation of Digital Signals-A Tutorial Review," Proceedings of the IEEE, Vol. 69, No. 3, March 1981. [12] Crochiere, R. and Rabiner, L. "Further Considerations in the Design of Decimators and Interpolators," IEEE Trans. on Acoust. Speech, and Signal Proc., Vol. ASSP?24, No. 4, August 1976. [13] Ballanger, M. et al, "Interpolation, Extrapolation, and Reduction of Computational Speed in Digital Filters," IEEE Trans. on Acoust. Speech, and Signal Proc., Vol. ASSP?22, No. 4, August 1974.
"Rick Lyons" <r.lyons@REMOVE.ieee.org> wrote in message
news:40068376.54711781@news.west.earthlink.net...
> On Wed, 14 Jan 2004 09:49:54 -0800, "Bhaskar Thiagarajan" > <bhaskart@deja.com> wrote: > > > > (snipped) > >> > >> Is there some other ways (documents) to do this ? > >> If so, have you got some book or url ? > >> > >> Thanks > > > >There have been many many discussion on this topic in comp.dsp. Use
google
> >search and look for multirate sampling. > >A good book for reference on this topic is > >Multirate Systems and Filterbanks by P.P. Vaidyanathan. > > > >Cheers > >Bhaskar > > Hi Bhasker, > yep, below are a few other references for seb. > I'll bet he doesn't realize that a person could > make a career out of learning all the theory of > sample rate changing. (At least I thinkk so.) > > By the way, I heard that fred harris (of windows > fame) is writing a book on multirate signal > processing.
That's great. I can finally have some text to go with the multiple block diagrams and pictures I have from a class he taught - really hard to decipher some of his magic more than a few months after the class. Cheers Bhaskar
> > [-Rick-] > > [8] Fliege, N. Multirate Digital Signal Processing: Multirate Systems, > Filter Banks, Wavelets, John Wiley & Sons, 1995. > > [9] Crochiere, R. and Rabiner, L. Multirate Digital Signal Processing, > Prentice-Hall, Upper Saddle River, New Jersey, 1983. > > [11] Crochiere, R. and Rabiner, L. "Decimation and Interpolation of > Digital Signals-A Tutorial Review," Proceedings of the IEEE, Vol. 69, > No. 3, March 1981. > > [12] Crochiere, R. and Rabiner, L. "Further Considerations in the > Design of Decimators and Interpolators," IEEE Trans. on Acoust. > Speech, and Signal Proc., Vol. ASSP?24, No. 4, August 1976. > > [13] Ballanger, M. et al, "Interpolation, Extrapolation, and > Reduction of Computational Speed in Digital Filters," IEEE Trans. on > Acoust. Speech, and Signal Proc., Vol. ASSP?22, No. 4, August 1974. >
r.lyons@REMOVE.ieee.org (Rick Lyons) wrote in message
news:<40068376.54711781@news.west.earthlink.net>...
> On Wed, 14 Jan 2004 09:49:54 -0800, "Bhaskar Thiagarajan" > <bhaskart@deja.com> wrote: > > > > (snipped) > >> > >> Is there some other ways (documents) to do this ? > >> If so, have you got some book or url ? > >> > >> Thanks > > > >There have been many many discussion on this topic in comp.dsp. Use google > >search and look for multirate sampling. > >A good book for reference on this topic is > >Multirate Systems and Filterbanks by P.P. Vaidyanathan. > > > >Cheers > >Bhaskar > > Hi Bhasker, > yep, below are a few other references for seb. > I'll bet he doesn't realize that a person could > make a career out of learning all the theory of > sample rate changing. (At least I thinkk so.) > > By the way, I heard that fred harris (of windows > fame) is writing a book on multirate signal > processing. > > [-Rick-] > > [8] Fliege, N. Multirate Digital Signal Processing: Multirate Systems, > Filter Banks, Wavelets, John Wiley & Sons, 1995. > > [9] Crochiere, R. and Rabiner, L. Multirate Digital Signal Processing, > Prentice-Hall, Upper Saddle River, New Jersey, 1983. > > [11] Crochiere, R. and Rabiner, L. "Decimation and Interpolation of > Digital Signals-A Tutorial Review," Proceedings of the IEEE, Vol. 69, > No. 3, March 1981. > > [12] Crochiere, R. and Rabiner, L. "Further Considerations in the > Design of Decimators and Interpolators," IEEE Trans. on Acoust. > Speech, and Signal Proc., Vol. ASSP?24, No. 4, August 1976. > > [13] Ballanger, M. et al, "Interpolation, Extrapolation, and > Reduction of Computational Speed in Digital Filters," IEEE Trans. on > Acoust. Speech, and Signal Proc., Vol. ASSP?22, No. 4, August 1974.
Hello, First, thinks for all this information I am not intend to learn all the the theory of sample rate changing. I just have a project running on a DSP on each running differents processing algorithme, each need a differents sampling rate. So, using the incoming signal, i have to do downsampling and upsampling in order to give all algorithme the rigth data. Thinks
"seb" <germain1_fr@yahoo.fr> wrote in message
news:23925133.0401151031.cb86c60@posting.google.com...
> r.lyons@REMOVE.ieee.org (Rick Lyons) wrote in message
news:<40068376.54711781@news.west.earthlink.net>...
> > On Wed, 14 Jan 2004 09:49:54 -0800, "Bhaskar Thiagarajan" > > <bhaskart@deja.com> wrote: > > > > > > > (snipped) > > >> > > >> Is there some other ways (documents) to do this ? > > >> If so, have you got some book or url ? > > >> > > >> Thanks > > > > > >There have been many many discussion on this topic in comp.dsp. Use
google
> > >search and look for multirate sampling. > > >A good book for reference on this topic is > > >Multirate Systems and Filterbanks by P.P. Vaidyanathan. > > > > > >Cheers > > >Bhaskar > > > > Hi Bhasker, > > yep, below are a few other references for seb. > > I'll bet he doesn't realize that a person could > > make a career out of learning all the theory of > > sample rate changing. (At least I thinkk so.) > > > > By the way, I heard that fred harris (of windows > > fame) is writing a book on multirate signal > > processing. > > > > [-Rick-] > > > > [8] Fliege, N. Multirate Digital Signal Processing: Multirate Systems, > > Filter Banks, Wavelets, John Wiley & Sons, 1995. > > > > [9] Crochiere, R. and Rabiner, L. Multirate Digital Signal Processing, > > Prentice-Hall, Upper Saddle River, New Jersey, 1983. > > > > [11] Crochiere, R. and Rabiner, L. "Decimation and Interpolation of > > Digital Signals-A Tutorial Review," Proceedings of the IEEE, Vol. 69, > > No. 3, March 1981. > > > > [12] Crochiere, R. and Rabiner, L. "Further Considerations in the > > Design of Decimators and Interpolators," IEEE Trans. on Acoust. > > Speech, and Signal Proc., Vol. ASSP?24, No. 4, August 1976. > > > > [13] Ballanger, M. et al, "Interpolation, Extrapolation, and > > Reduction of Computational Speed in Digital Filters," IEEE Trans. on > > Acoust. Speech, and Signal Proc., Vol. ASSP?22, No. 4, August 1974. > > > Hello, > > First, thinks for all this information > I am not intend to learn all the the theory of sample rate changing. > I just have a project running on a DSP on each running differents > processing algorithme, each need a differents sampling rate. So, using > the incoming signal, i have to do downsampling and upsampling in order > to give all algorithme the rigth data.
If you are looking for a shortcut - you are pretty much out of luck. Without learning the fundamentals of sample rate changing, you will find it pretty hard to do anything quick and dirty. There are some good tutorials on this topic though that will help you quickly learn the basics and some sample code as well that should help speed your learning. Look here http://dspguru.com/info/faqs/mrfaq.htm
> > Thinks
The fastest method of interpolation is to just use the nearest
neighbor, but this usually introduces lots of sampling jitter noise.
Slightly better, but slower by one or two multiply-adds, is 2-point
linear interpolation.

The multirate literature seems to describe lots of variations on high
quality, but much slower, N-tap windowed-sinc FIR filters, with one
or two multiply-adds per tap, depending on whether one uses a large
multi-phase table, or interpolates inside a smaller table of coefficients.

Are there methods of interpolation in between these two in performance?
e.g. if one has enough performance overhead to do more than linear
interpolation, but less than enough for a high quality 11-tap FIR filter
with a large cache-busting multi-phase coefficient table, what other
methods should one try?

Would a 3 or 4 point parabolic or cubic interpolation work?  Or would a
3 or 4 tap FIR filter with, say, a cubic approximation to the windowed
sinc be better?  Or would using 4 or 5 taps and the nearest phase
neighbor inside a small multi-phase coefficient table be sufficient?

Other options?

Thanks.

-- 
Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/ 
#include <canonical.disclaimer>        // only my own opinions, etc.