[sdiy] Vocoder dabblings

[ASSI]

On Thursday 29 November 2012, 21:54:53, Tom Wiltshire wrote:
> Thanks, I was aware of that. What I meant was "why use that in particular
> rather than something else?" but I obviously didn't express it very
> clearly.

Any Hilbert transformer/filter critically depends on keeping the quadrature 
error between the I and Q part of the signal very small.  You can interpret 
the operation in question as the distance between two phasors at 90° offset: 
hence a geometrical addition is needed.  The method of approximating it with 
absolutes would compute the Manhattan distance and the quadrature would be 
lost quickly.  For the final part of the envelope follower that same 
precision is probably not necessary, but that depends a lot on what you do 
with that result later on.

> As Richie said, the square root operation is expensive, so there
> needs to be some decent reason to include it - I was wondering what that
> reason was, since it isn't immediately apparent to me.

Square roots can actually be computed very efficiently with Newton-Raphson 
iteration when you have pipelined multiplies.  If your CPU can't do that, 
the most efficient method (in terms of cycles) is usually a table-lookup 
followed up by an iteration.  There are literally hundreds of algorithms for 
computing square roots that take advantage of any thinkable arcana of the 
used number system and computational resources available.  Start here:

https://en.wikipedia.org/wiki/Methods_of_computing_square_roots
http://mathworld.wolfram.com/SquareRootAlgorithms.html


Regards,
Achim.
-- 
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