Re: [Discuss-gnuradio] Pulse shaping filter advice needed

[Linus Gasser]

On Mardi, 5 Août 2003 16.55, Ian Wraith wrote:
> Hello Linus
>             Many thanks for taking the time for writing such a detailed
> response to my question. However I have another question for you ..
>
>   Am I correct in thinking I should downsample my I & Q channels down
> to 18 KHz after I have put each channel through the root raised
> cosine filter ? Or should I downsample each channel to 18 KHz and then
> put them through that filter.

The first option. I draw some more graphics ;)

Let this be the FFT of your input-signal y, oversampled by a factor of 2:

    |Y|
     ^
     I__
    /I I 
 ^ / I I ^
-----+-----> f

The two ^ at the right and the left of the signal denote some adjascent signal 
that is not wanted. Now, if you filter first, you suppress this not-wanted 
signal, and you get:

    |Y1|
     ^
     I__
    /I I 
   / I I  
-----+-----> f

and then you downsample

    |Y2|
     ^
    _I____
  _/ I   I 
 /   I   I  
-----+-----> f

Now, the stairy thing to the left should be a normal slope. Anyway, now your 
signal is clean, downsampled, and you use the full bandwith which reduces the 
mathematical complexity of any decoding (theoretically you don't need to 
downsample at all. It's just more convenient because then 1 sample = 1 
symbol...)

OK, let's do the downsampling first:

    |Y1'|
     ^
    _I_^__
  ^/ I   I 
 /   I   I  
-----+-----> f

What happened is that the adjascent signal overlapped with the original signal 
and thus introduces some additional noise that can make it impossible to 
retrieve your original signal. As you see, there is no possibility to take 
out this noise by any filter.
 This is why you have to filter first, to clear out the other half of the 
spectrum, then downsample. Or you don't downsample and get some method to 
decode using 2 samples = 1 symbol...

I hope it helped a bit,

Linus

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