[PD] dac object question

[Lex Ein]

Frank Barknecht wrote:

>Hallo,
>
>first: thanks a lot for explaining the DC effects to you and to Lex. I
>did however ask my question slightly ambivalent. I also would be interested
>in why and how a [hip~ 5] filter removes a DC offset. 
>  
>
It's convenient to look at DSP in the time domain to answer this.

A factory worker (a signal processor) is tasked to:
- grab an audio sample (a card with a number) off a conveyor belt
at the sample rate (as fast as they're delivered),
 - perform simple arithmetic,
 - erase and write the answer on the card,
 - drop the card on the output conveyor belt.
The worker only thinks about the current number and
the last number before it was crossed out..
Numbers range in value from -1 to +1.

In a two-sample crude lowpass:
   Sout = (Sample1 + Sample0)/2
This sums current (Sample1) and previous (Sample0) input samples
and divides by 2 (otherwise this filter would have a gain of 2).
This preserves DC because any two adjacent identical samples are output
without alteration.

What about:
   Sout = (Sample1 - Sample0)/2
( We still divide by 2 because 1 -(-1) gives a peak amplitude of 2.)
This subtracts any two adjacent samples.  Identical adjacent samples
cancel each other out, so only changing signals make it out.  The more
rapidly the signal changes, the more amplitude it will have. This creates
a high pass filter. DC is effectively removed, or more accurately, 
restored to 0.

Questions for the reader, and MOVING THIS DISCUSSION TO PD-OT,
These examples make for weird filters. In the real world, nobody makes
filters this simplistically. For example: frequencies at half the sample 
rate are nulled.
 - Why?
 - What happens to frequencies above 1/2 the sample rate? 
    - Ooh, that's bad, isn't it?
 - Can you get rid of DC by performing a forward FFT, then an inverse FFT?
    - Why does _that_ work?
    - Is it a good idea?


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