Interchanging FIR and Decimation operation

"tarangdadia@gmail.com" wrote:
> 
> Jim,
> 
> HPF that I am using is [1 -2 1]. I need to have that in place because
> systems engineer asked me to ;-). It may not be the best HPF but I
> believe systems engineers word for it that will be good enough for our
> system.


Your original question was and apparently still is how can I optimize
the process of filtering with a high pass filter, then a low pass
filter, then decimate? My suggestion ignores your question and
introduces a fresh idea - why don't you try your proccess in an
unoptimized form first to see if its really does what you want. Or,
better yet why don't you just consider what happens when you first apply
a high pass filter and then a low pass filter. The fact that you have
anything left at all will be because the filters are not very good. That
seems to me to be more of an accident rather than a matter of design.

-jim

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Bhaskar,

I had used that phrase that it is given by system designer cos that is
kind of fixed part in the circuit. As I had earlier mentioned that the
input samples are all singel bit long and filter is [1 -2 1]. It is
just used to readjust the level of the signal and more specifically for
error correction. I am talking about multi stage sigma-delta modulator.
The output  has to be error corrected using [1 -2 1] filter ( or in
other word a HPF). My specific band of interest is 0 -> Fs/24. This
filter will essentially remove the noise from my pass band and I will
have less noise and hence higher SNR in my required bandwidth.

I actually was calling AAF as low pass filter, but I did not quite
understand why it is not common to call LPF as AAF. Are there any other
function other than anti-aliasing? I would appreciate little more
insight into this notation.

Thanks a lot.
Tarang

Jim,

I wanted to optimize the operation such that I can complete the
operation with minimum number of computation. I wanted to know whether
I can decimate first and then pass it thru filter.

But from the responses I have got so far I think this is what I have to
do now.

My Input is still 64K long. I will have 2 FIR filters, I will convolve
them and get another filter.

Finally I will get my output samples by computing the taps only which I
need at output.

I wanted to do something mentioned in this article, using noble
identity, but I think with the HPF filter of [1 -2 1] I will not be
able to do that.

figure 2 in http://cnx.rice.edu/content/m10432/latest/

My aim is not to optimize the filter structure itself but to optimize
the whole operation for minimum number of computation.

Thanks for ur inputs.
Tarang

My 2 cents on the discussion:

The high pass filter has a sine-square shape, peaking at omega== pi.
This is indeed a high pass filter. according to my calculation its
3-db point is at 2-radians or 114 degrees approximately. You need a
lowpass filter which cuts off anything above pi/8. So combining the
two filter is a peculiar thing, as you are  not even reaching the
pass-band of your HPF.
Anyway, assuming that your application does need sine-square frequency
shaped data, you CAN combine the two filters in any order you like.
As both the filters are LTI systems, 
---hpf---lpf--->
is equivalent to 
---lpf---hpf--->
And they are as equivalent as anything can be (except for the finite
precision effects).
However, you can not commute the downsampling operation anywhere, as
it is not a LTI system (sigh).
So you can try 3 cases:
two as mentioned above, and third: convolve the two filters.
You will have to watch out for finite precision effects.

Regards
Manish

"tarangdadia@gmail.com" <tarangdadia@gmail.com> wrote in message news:<1113267384.021960.171490@l41g2000cwc.googlegroups.com>...
> Bhaskar,
> 
> I had used that phrase that it is given by system designer cos that is
> kind of fixed part in the circuit. As I had earlier mentioned that the
> input samples are all singel bit long and filter is [1 -2 1]. It is
> just used to readjust the level of the signal and more specifically for
> error correction. I am talking about multi stage sigma-delta modulator.
> The output  has to be error corrected using [1 -2 1] filter ( or in
> other word a HPF). My specific band of interest is 0 -> Fs/24. This
> filter will essentially remove the noise from my pass band and I will
> have less noise and hence higher SNR in my required bandwidth.
> 
> I actually was calling AAF as low pass filter, but I did not quite
> understand why it is not common to call LPF as AAF. Are there any other
> function other than anti-aliasing? I would appreciate little more
> insight into this notation.
> 
> Thanks a lot.
> Tarang