🚀 go-pugleaf

wilf@sce.carleton.ca (Wilf Leblanc) writes:

>jbuck@galileo.berkeley.edu (Joe Buck) writes:

>>[deleted]

>>Example of CD salespeak: pushing oversampling as an advanced technical
>>feature.  Oversampling is simply inserting zeros between the digital
>>samples and thus increasing the sampling rate.  It's used because then you
>>can use cheaper, less complex analog filters; it reduces the system cost.
>>Still, some sales critters think it's an advanced technical extra.

>This kills me too.  Especially 8x oversampling !
>(I always thought oversampling was used because analog filters usually
>have a horrible phase response near the cutoff.  However, if you want
>to spend enough money, you can get very near linear phase response
>with an analog filter.  So, you are right).

> ... [ stuff deleted ] ...

>--
>Wilf LeBlanc                                 Carleton University
>Internet: wilf@sce.carleton.ca               Systems & Computer Eng.
>    UUCP: ...!uunet!mitel!cunews!sce!wilf    Ottawa, Ont, Canada, K1S 5B6

---
  Let me first point out that I'm not very familiar with CD players, so
please forgive me if this posting is not compatible with contemprary CD
technology.
---

  The reason for oversampling is, as mentioned above, that analog filters
with very sharp cutoff are expensive and/or have a horrible phase response.
With oversampling it's possible to use (generaliszed) linear phase discrete
time filters prior to the D/A conversion. As a result of this operation one
can use much cheaper analog filters on the output. 

This media is not ideal for graphical illustrations, but I'll try anyway.

Let:       fs  - sampling frequency ( 44 kHz )
           Fs  - new sampling frequency ( L*44 kHz )

Consider the following amplitude spectrum on a CD:

                             ^  
        --           --------|--------           --
           \       /         |         \       /
             \   /           |           \   /
        -------+-------------+-------------+--------->  
             -fs/2                       fs/2

Reconstruction of this signal require an analog filter with a
sharp cutoff frequency at fs/2.

After insertion of (L-1) 0's between the samples we get:

                             ^  
--     -----     -----     --|--     -----     -----     -----
  \   /     \   /     \   /  |  \   /     \   /     \   /     \ 
   \ /       \ /       \ /   |   \ /       \ /       \ /       \
---------+--------------+----+----+--------------+--------------->
       -Fs/2          -fs/2     fs/2            Fs/2

Now ... use a discrete time filter (generalized linear phase) with a
sharp cutoff frequency at fs/2 (i.e at fs/Fs - normalized frequency).

This operation will give us the following spectrum:
(which is a copy of the first one except for the difference that the
lobes are furter apart)

                             ^ 
                           --|--  
                          /  |  \ 
                         /   |   \
---------+--------------+----+----+--------------+--------------->
       -Fs/2          -fs/2     fs/2            Fs/2


Reconstruction of this signal is much "cheaper" since the analog
filter on the output could have a much wider transition region. 


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