Help Understanding - Decimation, Anti-Alias and Accuracy !

Hi,


I have a problem, I have a oversampled (OSR =16) Digital Signal, prior
to downsampling a filter is used, a 16 Tap BandpassFIR filter wich
also have a Window.

1. Is there a document or approch how to calculate mathematically the
resolution / Accuracy after the Filter, the Window and after the
Decimation. (Filterquantisation ?) What errrors come from the Window
??

What role does the Window play (The FIR BAndpass is used to fit the
signals frequncy to allow downsampling I suppose) But for what use a
window ?


I would be happy about some help !
Thaks Sascha

"Sascha" <Sascha-78@web.de> wrote in message
news:fbc8cc04.0312170828.59845f50@posting.google.com...
> Hi,
>
>
> I have a problem, I have a oversampled (OSR =16) Digital Signal, prior
> to downsampling a filter is used, a 16 Tap BandpassFIR filter wich
> also have a Window.
>
> 1. Is there a document or approch how to calculate mathematically the
> resolution / Accuracy after the Filter, the Window and after the
> Decimation. (Filterquantisation ?) What errrors come from the Window
> ??
>
> What role does the Window play (The FIR BAndpass is used to fit the
> signals frequncy to allow downsampling I suppose) But for what use a
> window ?

Sascha,

Let's see if this doesn't help:

First, let's just stick with the window question.  The resolution / accuracy
question is quite another matter and you'll need to do some work to arrive
at reasonable answers.  This is very much dependent on your implementation
and can't be dealt with at a more abstract level really.

Let's assume that the filter is operating in the time domain - so you have
no overlap-save process associated with using fft/ifft frequency domain
multiplicative filtering.  Then we'll also assume that the data comes in a
continuous stream out of the filter.

The next step in the process is critical.  If you are going to select a
"chunk" or "temporal epoch" of the data for some sort of processing - for
example for processing by a finite-length fft - then you are perforce using
a *rectangular* window (the sequence of samples is unweighted) that has a
corresponding sin(f)/f type of frequency convolution associated with it.
sin(f)/f introduces large spectral leakage componenets and is sometimes
unacceptable.  So, instead of staying with the effects of the rectangular
window, another window is multiplied onto the data segment to get smaller
spectral leakage.  There's plenty of literature on the subject.

Fred

Fred