The difference between even length and odd length FIR ?

I got this question asked in an interview.
The question is quoated "what is the difference between even length and
odd length FIR " .
It's a confusing question. Anyone has a good answer to it?
Thanks a lot ~

"daka" <miranda.wu@gmail.com> wrote in message 
news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
>I got this question asked in an interview.
> The question is quoated "what is the difference between even length and
> odd length FIR " .
> It's a confusing question. Anyone has a good answer to it?
> Thanks a lot ~
>

Hello Daka,


Your interviewer probably made an assumption that your filter was linear 
phase. Then you can make some general statements. I.e., the delay is 
(N+1)/2, so odd length filters have integral delay. And even length filters 
have an extra 1/2 sample delay.  Linear phase also means can can have two 
types of symmetry among the coefficients. Namely symmetric and 
antisymmetric. Antisymmtric filters add a 90 degree phase shift in addition 
to the delay afforded by (N+1)/2 samples.

Also some constraints happen to the magnitude repsonse.

sym, odd length -> no constraints

sym, even length -> response at 1/2 sample rate must be zero.

asym, odd length -> response at 0 and 1/2 sample rate must be zero

asym, even length -> response at 0 must be zero


IHTH,
Clay

"Clay S. Turner" <Physics@Bellsouth.net> writes:

> "daka" <miranda.wu@gmail.com> wrote in message 
> news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
>>I got this question asked in an interview.
>> The question is quoated "what is the difference between even length and
>> odd length FIR " .
>> It's a confusing question. Anyone has a good answer to it?
>> Thanks a lot ~
>>
>
> Hello Daka,
>
>
> Your interviewer probably made an assumption that your filter was linear 
> phase. Then you can make some general statements. I.e., the delay is 
> (N+1)/2, 

Counterexample: h[n] = delta[n] has N = 1 and a delay of zero. 

Should be (N-1)/2. 
-- 
%  Randy Yates                  % "And all that I can do
%% Fuquay-Varina, NC            %  is say I'm sorry, 
%%% 919-577-9882                %  that's the way it goes..."
%%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
http://home.earthlink.net/~yatescr

"Randy Yates" <yates@ieee.org> wrote in message 
news:ek9dyv3e.fsf@ieee.org...
> "Clay S. Turner" <Physics@Bellsouth.net> writes:
>
>> "daka" <miranda.wu@gmail.com> wrote in message
>> news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
>>>I got this question asked in an interview.
>>> The question is quoated "what is the difference between even length and
>>> odd length FIR " .
>>> It's a confusing question. Anyone has a good answer to it?
>>> Thanks a lot ~
>>>
>>
>> Hello Daka,
>>
>>
>> Your interviewer probably made an assumption that your filter was linear
>> phase. Then you can make some general statements. I.e., the delay is
>> (N+1)/2,
>
> Counterexample: h[n] = delta[n] has N = 1 and a delay of zero.
>
> Should be (N-1)/2.
> -- 

Thanks. Yes (N-1)/2 is correct for the delay. However I believe my other 
comments are true. Of course my fingers get ahead of my brain sometimes and 
mistakes result.

Clay

"Clay S. Turner" <Physics@Bellsouth.net> wrote in message 
news:_VxHe.1209$jq.798@bignews3.bellsouth.net...
>
> "daka" <miranda.wu@gmail.com> wrote in message 
> news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
>>I got this question asked in an interview.
>> The question is quoated "what is the difference between even length and
>> odd length FIR " .
>> It's a confusing question. Anyone has a good answer to it?
>> Thanks a lot ~
>>
>
> Hello Daka,
>
>
> Your interviewer probably made an assumption that your filter was linear 
> phase. Then you can make some general statements. I.e., the delay is 
> (N+1)/2, so odd length filters have integral delay. And even length 
> filters have an extra 1/2 sample delay.  Linear phase also means can can 
> have two types of symmetry among the coefficients. Namely symmetric and 
> antisymmetric. Antisymmtric filters add a 90 degree phase shift in 
> addition to the delay afforded by (N+1)/2 samples.
>
> Also some constraints happen to the magnitude repsonse.
>
> sym, odd length -> no constraints
>
> sym, even length -> response at 1/2 sample rate must be zero.
>
> asym, odd length -> response at 0 and 1/2 sample rate must be zero
>
> asym, even length -> response at 0 must be zero

Clay,

I don't follow the last two ...

Fred 

Fred Marshall wrote:
> "Clay S. Turner" <Physics@Bellsouth.net> wrote in message
> news:_VxHe.1209$jq.798@bignews3.bellsouth.net...
> >
> > "daka" <miranda.wu@gmail.com> wrote in message
> > news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
> >>I got this question asked in an interview.
> >> The question is quoated "what is the difference between even length and
> >> odd length FIR " .
> >> It's a confusing question. Anyone has a good answer to it?
> >> Thanks a lot ~
> >>
> >
> > Hello Daka,
> >
> >
> > Your interviewer probably made an assumption that your filter was linear
> > phase. Then you can make some general statements. I.e., the delay is
> > (N+1)/2, so odd length filters have integral delay. And even length
> > filters have an extra 1/2 sample delay.  Linear phase also means can can
> > have two types of symmetry among the coefficients. Namely symmetric and
> > antisymmetric. Antisymmtric filters add a 90 degree phase shift in
> > addition to the delay afforded by (N+1)/2 samples.
> >
> > Also some constraints happen to the magnitude repsonse.
> >
> > sym, odd length -> no constraints
> >
> > sym, even length -> response at 1/2 sample rate must be zero.
> >
> > asym, odd length -> response at 0 and 1/2 sample rate must be zero
> >
> > asym, even length -> response at 0 must be zero
>
> Clay,
>
> I don't follow the last two ...

If a FIR filter is antisymmetric, the coefficients add up to 0.
So the DC coefficient in the transfer function is 0.

Rune

daka wrote:

> I got this question asked in an interview.
> The question is quoated "what is the difference between even length and
> odd length FIR " .
> It's a confusing question. Anyone has a good answer to it?
> Thanks a lot ~
> 
I was going to say "an even length filter has a number of elements that
can be divided by 2" -- but I mostly deal with motion control, and
consequently IIR filters.

I've found it very effective when interviewing for work (because I've
found it very disarming when interviewing for workers) to come out
point-blank and say "gee, I don't know that" when asked a question that
completely stumps me.  I'll usually ask for a bit of explanation.  If
they can explain part of it and I can guess the rest then I get a few
points.  If they start explaining it and I can say "Oh!  What you're
calling the Gnorbnitz equation is what I learned as the Lagrabnabber
Transform!" then I earn almost as many points as if I just started
rattling on.

The principal here is that if it was some go/no-go thing then you blew
it when you walked into the interview without that knowledge.  If you
try to spread BS about something you don't know then you'll lose
credibility with everything else.  If you're up front about what you
don't know then you'll gain points for being a straightforward kind of guy.

-- 

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

"Tim Wescott" <tim@seemywebsite.com> wrote in message 
news:11ev4mn6r0l363@corp.supernews.com...
> "Oh!  What you're calling the Gnorbnitz equation is what I learned as
> the Lagrabnabber Transform!"

I found that sentence amusing!  (My spellchecker has no suggestions for those 
words.) 

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message 
news:1122971699.302236.5890@o13g2000cwo.googlegroups.com...
>
> Fred Marshall wrote:
>> "Clay S. Turner" <Physics@Bellsouth.net> wrote in message
>> news:_VxHe.1209$jq.798@bignews3.bellsouth.net...
>> >
>> > "daka" <miranda.wu@gmail.com> wrote in message
>> > news:1122933805.795462.212060@o13g2000cwo.googlegroups.com...
>> >>I got this question asked in an interview.
>> >> The question is quoated "what is the difference between even length 
>> >> and
>> >> odd length FIR " .
>> >> It's a confusing question. Anyone has a good answer to it?
>> >> Thanks a lot ~
>> >>
>> >
>> > Hello Daka,
>> >
>> >
>> > Your interviewer probably made an assumption that your filter was 
>> > linear
>> > phase. Then you can make some general statements. I.e., the delay is
>> > (N+1)/2, so odd length filters have integral delay. And even length
>> > filters have an extra 1/2 sample delay.  Linear phase also means can 
>> > can
>> > have two types of symmetry among the coefficients. Namely symmetric and
>> > antisymmetric. Antisymmtric filters add a 90 degree phase shift in
>> > addition to the delay afforded by (N+1)/2 samples.
>> >
>> > Also some constraints happen to the magnitude repsonse.
>> >
>> > sym, odd length -> no constraints
>> >
>> > sym, even length -> response at 1/2 sample rate must be zero.
>> >
>> > asym, odd length -> response at 0 and 1/2 sample rate must be zero
>> >
>> > asym, even length -> response at 0 must be zero
>>
>> Clay,
>>
>> I don't follow the last two ...
>
> If a FIR filter is antisymmetric, the coefficients add up to 0.
> So the DC coefficient in the transfer function is 0.
>
> Rune

Rune,

When writing, I switched in midstream from thinking that "asym" meant 
asymmetric instead of antisymmetric.  So, of course .... we agree.

Now what about the zero at fs/2?

Fred 

Hello Fred,

Sorry about my cryptic shorthand. I was in a rush to a photoclub
meeting when I wrote that.

Rune hit the nail on the head that at DC, your signal is simply
...,1,1,1,1,1,1,1,1,1,1,... so passing this thru an FIR filter you are
in effect just adding up all of the FIR's coefs..

Now for fs/2 your signal is ...,-1,1,-1,1,-1,1,-1,1,-1,...

And an odd length antisymmtric FIR filter's coefs can be written as

...,-c,-b,-a,0,a,b,c, ...

so the resulting convolution ends up being simply zero.

For an even length antisymmetric linear FIR filter, there is no
restriction at fs/2

IHTH,
Clay