Reply by Vincent Pellissier●July 21, 20062006-07-21
Robert Orban wrote:
> In article <wkWrg.62924$fb2.42168@newssvr27.news.prodigy.net>,
> antispam_bogus@hotmail.com says...
>>
>> Hello All,
>>
>> The task is to design the multiple cascaded FIR filters to do the
>> decimation. There are tough requirements about the resultant ripples in
>> the passband; the stage-by-stage design seems to be very inefficient.
>>
>> Can you suggest a filter design software which can optimize the overall
>> response of the cascaded decimator? Also it would be nice if it can find
>> the optimal decimation ratios for every stage.
>>
>
> FilterShop will do this.
>
> http://linearx.com/products/software/FilterShop/Fshop_01.htm
>
In article <wkWrg.62924$fb2.42168@newssvr27.news.prodigy.net>,
antispam_bogus@hotmail.com says...
>
>
>Hello All,
>
>The task is to design the multiple cascaded FIR filters to do the
>decimation. There are tough requirements about the resultant ripples in
>the passband; the stage-by-stage design seems to be very inefficient.
>
>Can you suggest a filter design software which can optimize the overall
>response of the cascaded decimator? Also it would be nice if it can find
>the optimal decimation ratios for every stage.
>
On Sat, 08 Jul 2006 22:28:44 GMT, Vladimir Vassilevsky
<antispam_bogus@hotmail.com> wrote:
>Hello All,
>
>The task is to design the multiple cascaded FIR filters to do the
>decimation. There are tough requirements about the resultant ripples in
>the passband; the stage-by-stage design seems to be very inefficient.
>
>Can you suggest a filter design software which can optimize the overall
>response of the cascaded decimator? Also it would be nice if it can find
>the optimal decimation ratios for every stage.
>
>Vladimir Vassilevsky
Hello Vladimir,
I remember reading (somewhere) that it is *VERY*
difficult to find the optimum decimation factors for
a multi-stage (cascaded) decimation filter if the
number of stages is greater than two.
However, thanks to the pioneers of DSP, there
is an equation for finding the optimum
decimation factors for a two-stage (cascaded)
decimation filter. If your total desired dec factor
is D, you can design two cascaded dec filters with
the 1st filter having dec factor of D1 and the 2nd
filter having dec factor of D2. Now, D = D1*D2.
The equation for the optimum D1 (D1opt) comes from:
Crochiere, R. and Rabiner, L. "Optimum FIR Digital Implementations for
Decimation, Interpolation, and Narrow?band Filtering," IEEE Trans. on
Acoust. Speech, and Signal Proc., Vol. ASSP?23, No. 5, October 1975.
and is:
1 - sqrt[(D*F)/(2-F)]
D1opt = ------------------------
2 - F*(D + 1)
where
original desired transition region width (Hz)
F = -----------------------------------------------.
final desired stopband frequency (Hz)
Your computed D1opt probably won't be an integer so
you have to convert it to the closest integer that's
an integer submultiple of D. (Whew, what a sentence!)
For example, if D = 100 and you compute D1opt = 29.7,
then the nearest integer submultiple of 100 (nearest
to 29.7) is 25. So you assign D1 = 25.
Once you know D1, D2 is (of course)
D
D2 = ----.
D1
(I give an example of all of this in Chapter 10 of
the 2nd edition of my DSP book.)
Ya' know what you might do? You might partition your
original (high-order) dec filter into the cascade
of two separate dec filters, ... and then break each
one of those filters into two dec filters.
(My guess is that having four cascaded filters will
NOT be much more computationally efficient than
having two cascaded filters, but ya' never know.)
Good Luck,
[-Rick-]
Your friendly neighborhood DSP junkie.
Reply by decious●July 9, 20062006-07-09
Vladimir,
Is your goal to port this to hardware, or simply model something in C
or MATLAB?
Vladimir Vassilevsky wrote:
> Hello All,
>
> The task is to design the multiple cascaded FIR filters to do the
> decimation. There are tough requirements about the resultant ripples in
> the passband; the stage-by-stage design seems to be very inefficient.
>
> Can you suggest a filter design software which can optimize the overall
> response of the cascaded decimator? Also it would be nice if it can find
> the optimal decimation ratios for every stage.
>
> Vladimir Vassilevsky
>
> DSP and Mixed-Up Signal Design Consultant
>
> http://www.abvolt.com
Reply by Atmapuri●July 9, 20062006-07-09
Hi!
> The task is to design the multiple cascaded FIR filters to do the
> decimation. There are tough requirements about the resultant ripples in
> the passband; the stage-by-stage design seems to be very inefficient.
>
> Can you suggest a filter design software which can optimize the overall
> response of the cascaded decimator? Also it would be nice if it can find
> the optimal decimation ratios for every stage.
You can try out our rate converter.
www.dewresearch.com
It can convert any sampling frequency to any sampling
frequency with SNR up to 170dB with linear phase,
really short time delay and is only about 2x slower than
a 2/3 or 3/2 multirate filter with coresponding antialiasing
lowpass filter for rate conversion factors less than 2.
For conversion factors of more than 2 I am afraid it cant
be beaten with any design even if there exist a rational
number for multirate filters.
Regards!
Atmapuri
Reply by Randy Yates●July 9, 20062006-07-09
Vladimir Vassilevsky wrote:
> Also it would be nice if it can find
> the optimal decimation ratios for every stage.
Vladimir,
I'm not sure this has been "discovered" yet. I
suspect the solution might be related to some concept
in abstract algebra or finite fields, if the proper
connection could be made.
--Randy
Reply by Vladimir Vassilevsky●July 8, 20062006-07-08
Hello All,
The task is to design the multiple cascaded FIR filters to do the
decimation. There are tough requirements about the resultant ripples in
the passband; the stage-by-stage design seems to be very inefficient.
Can you suggest a filter design software which can optimize the overall
response of the cascaded decimator? Also it would be nice if it can find
the optimal decimation ratios for every stage.
Vladimir Vassilevsky
DSP and Mixed-Up Signal Design Consultant
http://www.abvolt.com