[sdiy] Digital filtering question

[Antti Huovilainen]

On Wed, 25 Aug 2010, Tom Wiltshire wrote:

> On 24 Aug 2010, at 22:33, Antti Huovilainen wrote:
> 
>> I think E-Mu used this trick to fit 32 multipole filters in a single 
>> ASIC back in the early 90s (low resolution multiplier combined with 
>> barrel shifter).
> 
> Do you mean the Morpheus, Antti? I always wondered about the internals 
> of that beastie.

Morpheus and all E-Mu samplers that had multimode filters.
Fast wide multipliers are expensive. A 24 x 24 multiplier is much more
expensive than a 8 x 24 multiplier (which can be built from three parallel 
8 x 8 multipliers).

Dave Rossum patented a method where the 2nd order filter section
coefficients are written as

H(z) = p_n(z) / p_d(z)
p(z) = 1 + t1*z^-1 + t2*z^-2
t1 = -2 + 4*2^-v1 + 2^-v2
t2 = 1 - 2^-v2

2^-v is pretty much another way of writing "multiplier followed by barrel 
shifter". You lose cutoff resolution, but you lose it evenly in _octave 
and decibel scale_ and hence the result is quite acceptable. Unless you 
have a self oscillating filter, it doesn't really matter if the filter 
tuning is off by a few cents.

Antti

"No boom today. Boom tomorrow. There's always a boom tomorrow"
   -- Lt. Cmdr. Ivanova