Basic question on upsampling/downsampling

Hi, I am new to DSP and learning about sampling and related topics.  I have
read a book and  visited online sites but still am having problems
understanding :

1. Why do we need a filter (FIR) BEFORE we downmsample when we perform
decimation.  I understand why for upsampling we need the filtering part
but am having problems with the downsampling filter.  


2. I understand for a multirate system the filtering of both the
interpolation and decimation can be made into one, using the filter with
the lowest cutoff frquency as the only filter.  However, How do we
determine/choose the cutoff frquency for a each individual filter
(assuming ideal LP FIR filter is used for both decimation and
interpolation )?
 
3. I have read that:  "oversampling helps reduce the order of
anti-aliasingand reconstruction filter."  But why/how? 

thanks so much!!



		
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moe wrote:

> Hi, I am new to DSP and learning about sampling and related topics.  I have
> read a book and  visited online sites but still am having problems
> understanding :
> 
> 1. Why do we need a filter (FIR) BEFORE we downmsample when we perform
> decimation.  I understand why for upsampling we need the filtering part
> but am having problems with the downsampling filter.  
> 
Downsampling causes aliasing, the filter is just an ordinary old 
anti-aliasing filter.
> 
> 2. I understand for a multirate system the filtering of both the
> interpolation and decimation can be made into one, using the filter with
> the lowest cutoff frquency as the only filter.  However, How do we
> determine/choose the cutoff frquency for a each individual filter
> (assuming ideal LP FIR filter is used for both decimation and
> interpolation )?

Aliasing again -- figure out how much you can stand and design your 
filter accordingly.
>  
> 3. I have read that:  "oversampling helps reduce the order of
> anti-aliasingand reconstruction filter."  But why/how? 
> 
Because it increases the Nyquist frequency, so the reconstruction filter 
cutoff can be higher.  Note that if you oversample the data digitally 
you still need a high-order antialiasing filter; you just move the task 
into the digital domain where it's easier to control.

-- 

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

IIRC, the answer to 2) should be the bandwidth is determined as LE the
smaller of the bandwidths of the interpolation and decimation fiters.

Dirk

moe wrote:
> 1. Why do we need a filter (FIR) BEFORE we downmsample when we perform
> decimation.  I understand why for upsampling we need the filtering part
> but am having problems with the downsampling filter.

When you downsample, by definition, you reduce the sample rate.  If
the original signal has any frequency content at or above half the
new lower sample rate, which it might at the original sample rate,
then some low pass filtering is required in order to prevent aliasing.
You actually might not need any filtering if the original signal
happens to not have any frequency content high enough to cause
aliasing problems, for example if the passband during a previous
upsampling filter was low enough.  All the above comments assume
baseband content.


IMHO. YMMV.
-- 
rhn A.T. nicholson d.O.t C-o-M