Number of taps for a FIR

Hello all,

I am planning to introduce a decimation filter in my FPGA design in
order to reduce the sample frequency by 8. This has resulted in a 61
tap FIR filter. -It seems awfully large. Basically, I am asking , for
an FPGA implementation, what is a REASONNABLE number of taps for a FIR
filter?

(I am planning to again filter the decimation filter's output with a
cascaded structure of 4 2nd order IIR filters. In my opinion it is that
cascaded structure which is doing the REAL filtering and it happens to
be smaller and more potent. It seems a shame to ruin the compactness of
the filter modules with a huge decimation filter. P.S I have yet to
implement anything; I am just doing the planning of the required
modules for the moment so I may be completly off base in my previous
statement)

-Roger



(Filter parameters, in case they are of interest  :
Normalized Passband=0.015
Normalized StopBAnd=0.062
60dB stopband attenuation
0.1dB passband ripple
Sample frequency=1MHz
10 bits or 16 bits databus, don't know yet

"Roger Bourne" <rover8898@hotmail.com> wrote in message 
news:1143136101.823610.180860@u72g2000cwu.googlegroups.com...
> Hello all,
>
> I am planning to introduce a decimation filter in my FPGA design in
> order to reduce the sample frequency by 8. This has resulted in a 61
> tap FIR filter. -It seems awfully large. Basically, I am asking , for
> an FPGA implementation, what is a REASONNABLE number of taps for a FIR
> filter?
>
Roger,
Look at making your filter as a series of half-band FIR filters. These are 
efficient in that every other tap is zero. (Nice and easy to multiply by 
zero!) Use three, decimating by two at each stage. Your implementation 
should be a lot more compact. The later stages will probably have more taps, 
but the sample rate will be reduced, possibly allowing you to use 
distributed arithmetic.
Cheers, Syms. 

"Symon" <symon_brewer@hotmail.com> wrote in message 
news:4422e0f2$0$15787$14726298@news.sunsite.dk...
> "Roger Bourne" <rover8898@hotmail.com> wrote in message 
> news:1143136101.823610.180860@u72g2000cwu.googlegroups.com...
>> Hello all,
>>
>> I am planning to introduce a decimation filter in my FPGA design in
>> order to reduce the sample frequency by 8. This has resulted in a 61
>> tap FIR filter. -It seems awfully large. Basically, I am asking , for
>> an FPGA implementation, what is a REASONNABLE number of taps for a FIR
>> filter?
>>
> Roger,
> Look at making your filter as a series of half-band FIR filters. These are 
> efficient in that every other tap is zero. (Nice and easy to multiply by 
> zero!) Use three, decimating by two at each stage. Your implementation 
> should be a lot more compact. The later stages will probably have more 
> taps, but the sample rate will be reduced, possibly allowing you to use 
> distributed arithmetic.
> Cheers, Syms.
>
Also, check out CIC (cascaded integrator comb) filters? Although 8 may not 
be a high enough decimation factor to make this method worthwhile.
Cheers, Syms 

Symon wrote:

> "Symon" <symon_brewer@hotmail.com> wrote in message 
> news:4422e0f2$0$15787$14726298@news.sunsite.dk...
> 
>>"Roger Bourne" <rover8898@hotmail.com> wrote in message 
>>news:1143136101.823610.180860@u72g2000cwu.googlegroups.com...
>>
>>>Hello all,
>>>
>>>I am planning to introduce a decimation filter in my FPGA design in
>>>order to reduce the sample frequency by 8. This has resulted in a 61
>>>tap FIR filter. -It seems awfully large. Basically, I am asking , for
>>>an FPGA implementation, what is a REASONNABLE number of taps for a FIR
>>>filter?
>>>
>>
>>Roger,
>>Look at making your filter as a series of half-band FIR filters. These are 
>>efficient in that every other tap is zero. (Nice and easy to multiply by 
>>zero!) Use three, decimating by two at each stage. Your implementation 
>>should be a lot more compact. The later stages will probably have more 
>>taps, but the sample rate will be reduced, possibly allowing you to use 
>>distributed arithmetic.
>>Cheers, Syms.
>>
> 
> Also, check out CIC (cascaded integrator comb) filters? Although 8 may not 
> be a high enough decimation factor to make this method worthwhile.
> Cheers, Syms 
> 
> 
And keep in mind that when you decimate you don't need anti-aliasing at 
Nyquist (1/4 samples), you only need it at those frequencies where the 
energy is going to get through your IIR filters -- I see needing a 
3-stage CIC filter to do this, which with a boneheaded implementation 
only requires 24 taps.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

As Symon indicated, you should look into multi-rate filtering. 
Basically, decimate by 2 in 3 stages.  Each subsequent stage works at 
half the data rate, and the length of the earlier filters needn't be as 
long as the later filters.

That said, 61 taps is not outrageously long, (although by using 
multi-rate, you'll be able to at least reduce the sample rate of your 
longest filter).  There is a paper by Goodman and Cary from the 70's 
that details a set of small half-band FIR filters (half the coefficients 
are zero) for decimating in multi-rate systems.  Also, the decimating 
filter sections can be reduced using polyphase decomposition so that the 
filter sections run at the output sample rate rather than at the higher 
input sample rate.  That sample rate reduction also allows you to make 
the filter physically smaller by using more than one clock per sample. 
The Goodman-Cary F8 filter is a 15 tap filter that has 5 unique non-zero 
coefficients.  Through symmetry folding and polyphase decomposition, and 
using distributed arithmetic, filter breaks down into a 4 tap filter and 
a constant multiply added together, and it provides about 65db stopband 
attenuation and a reasonably steep transition.  You'll have to work 
through the chart for you application, but you'll probably find you can 
use something like and F3, F5 and F8  filter in cascade to get 
attenuation in the aliased part of the stopband and a flat response in 
your final passband.

A CIC filter would probably not buy you much here, as it basically takes 
the place of the F3 filters in the early part of a decimation chain as 
far as response curve goes.  Where your total decimation is only by 8, 
the CIC is probably not going to buy you anything.  CIC comes in really 
handy is where you have either a high decimation ratio, or a decimation 
ratio that has to be programmable.

Your stated sample rates are actually quite low for an FPGA.  You can 
easily run the FPGA clock at around 80 MHz without any special design 
considerations and do the whole filter serial, sequential or 
serial-sequential at a considerable area savings. (serial would be using 
distributed arithmetic, in which case you need a 16x clock, sequential 
uses one multiplier to multiply and accumulate several taps: basically 
timesharing the hardware).  You may also find a FIR filter 
implementation for your final filter may be easier to deal with than an 
IIR implementation because you can generally getr by with far fewer data 
bits and the response is not subject to limit cycles and instabilities 
caused by finite precision of a fixed point implementation.

> Roger,
> Look at making your filter as a series of half-band FIR filters. These are
> efficient in that every other tap is zero. (Nice and easy to multiply by
> zero!) Use three, decimating by two at each stage. Your implementation
> should be a lot more compact.

I am new to the digital filter world. Every day I discover a new type
another type of digital filter, so perphaps (or most probably) I am
wrong in my following observation:

How can a half-band FIR filter be employed as a decimating FIR filter
for a downsampling factor of 2 ? If my limited understanding of
half-bands (Lth-bands=2) is accurate, then the stopband of the
half-band will lie above Fs/4 (Fs/2 -Fpass, where Fpass cannot exceed
Fs/4). This will violate the anti-aliasing criterion and as such will
make it non-viable to use as a decimating filter.

What am I missing?
(From what I can tell from Mr.Google, halfs-bands are very popular, so
my reasonning must be off...)

-Roger

"Roger Bourne" <rover8898@hotmail.com> wrote in message 
news:1143217383.027265.260570@g10g2000cwb.googlegroups.com...
>
>
> How can a half-band FIR filter be employed as a decimating FIR filter
> for a downsampling factor of 2 ? If my limited understanding of
> half-bands (Lth-bands=2) is accurate, then the stopband of the
> half-band will lie above Fs/4 (Fs/2 -Fpass, where Fpass cannot exceed
> Fs/4). This will violate the anti-aliasing criterion and as such will
> make it non-viable to use as a decimating filter.
>
> What am I missing?
> (From what I can tell from Mr.Google, halfs-bands are very popular, so
> my reasonning must be off...)
>
> -Roger
>
Hi Roger,
So, a lowpass half-band filter has a passband
0 to Fp where Fp is < Fs/4

The stop band is

(Fs/2 - Fp)  to Fs/2

If you use this as your specification for a filter using the Remez exchange 
algorithm for making odd order (i.e. odd number of coeffs) FIR filters, 
you'll find every second tap is zero, except for the middle tap which is 
0.5. (Unless you've scaled things somewhere)

To decimate by 8 in three stages, your first filter has a passband from

0 to Fs/32

and a stop band from

Fs*15/32 to Fs/2


As you're decimating, you can throw away every other sample that comes out 
of this filter. Then, at your new sample rate, which is half the previous 
rate so F2s = Fs/2 , your next filter has a passband from

0 to F2s/16

and a stop band from

F2s*7/16  to F2s/2

....and so on for the third stage.

Anyway, I hope this helps, I know my posts often ramble a bit, hopefully you 
can google some of this to make more sense! It works great though.

Cheers, Syms.

p.s. You could google for scopefir, a FIR design program that you can use 
for free for a while before you buy.

p.p.s. I guess you've been here http://www.dspguru.com/info/faqs/mrfaq.htm 
? 

Roger,
The book I learnt all this from is

Multirate Digital Signal Processing
by Ronald E. Crochiere, Lawrence R. Rabiner

HTH, SYms. 

Hi Symon,

> So, a lowpass half-band filter has a passband
> 0 to Fp where Fp is < Fs/4
>
> The stop band is
>
> (Fs/2 - Fp)  to Fs/2
>
> If you use this as your specification for a filter using the Remez exchange
> algorithm for making odd order (i.e. odd number of coeffs) FIR filters,
> you'll find every second tap is zero, except for the middle tap which is
> 0.5. (Unless you've scaled things somewhere)
>
> To decimate by 8 in three stages, your first filter has a passband from
>
> 0 to Fs/32
>
> and a stop band from
>
> Fs*15/32 to Fs/2
>
>
> As you're decimating, you can throw away every other sample that comes out
> of this filter. Then, at your new sample rate, which is half the previous
> rate so F2s = Fs/2 , your next filter has a passband from
>

If the stopband is Fs*15/32 to Fs/2, then it implies that the
attenuation at frequencies around Fs/4 will be rather weak. Isn't
important that all frequencies above Fs/4 suffer a strong attenuation,
in order the Nyquist criterion be met at the post-decimation sampling
frequency (F2s=Fs/2) because we are downsampling by 2 ?
(I get the impression the solution is staring me rigth in the eyes and
I just can't see it!  ;) )

P.S I been using ScopeFiR.  

-Roger

Roger Bourne wrote:
>>Roger,
>>Look at making your filter as a series of half-band FIR filters. These are
>>efficient in that every other tap is zero. (Nice and easy to multiply by
>>zero!) Use three, decimating by two at each stage. Your implementation
>>should be a lot more compact.
> 
> 
> I am new to the digital filter world. Every day I discover a new type
> another type of digital filter, so perphaps (or most probably) I am
> wrong in my following observation:
> 
> How can a half-band FIR filter be employed as a decimating FIR filter
> for a downsampling factor of 2 ? If my limited understanding of
> half-bands (Lth-bands=2) is accurate, then the stopband of the
> half-band will lie above Fs/4 (Fs/2 -Fpass, where Fpass cannot exceed
> Fs/4). This will violate the anti-aliasing criterion and as such will
> make it non-viable to use as a decimating filter.
> 
> What am I missing?
> (From what I can tell from Mr.Google, halfs-bands are very popular, so
> my reasonning must be off...)
> 
> -Roger
> 

Roger, yes, as you point out, when the half band is used for decimate by 
  2, half of the transition band folds back on the other half of the 
transition band, so there is some aliasing in a band equal in width to 
half the width of the transition band.  This folded energy is all 
adjacent to Fs/4.  This happens because the half-band filter, by 
definition, has a symmetry about Fs/4, which means the attenuation is 
exactly 6dB at Fs/4.

If this is the only filter in your design, then, yes this would present 
a problem for decimation.  The piece you are missing is that these are 
used in conjuction with other filters in a system, and the other 
filtering removes the energy left over in the transition band. Most of 
the time, you have one or more cascaded decimate by 2 half band filters, 
followed by a filter at the lower sample rate that does the final 
passband filtering.  Each half band stage eliminates the aliased 
transition band left over from the previous halfband stage, and then 
introduces a bit of aliasing from its own transition region.  The 
(typically last) last filter in the filter chain is not a half-band 
filter and has a passband that eliminates the transition of the last 
halfband filter.