Geoffrey wrote:,
> These are probably ok at 96 or 192, but at 44.1/48 I think they
> will wander off at high frequencies due to warping.
> A better approach is to look for a solution which is symmetrical
> about fs/4.
If the bilinear transformation is used, then a 90 degree analogue
relative phase-shift becomes a 90-degree digital relative phase shift.
(Frequency warping will cause the roundabout to spin faster as we
approach Nyquist, but the two horses will remain 90 degrees apart !)
The "symmetrical about fs/4" design can be derived in this way. If
one starts with a set of logarithmically-spaced analogue poles and
zeroes (adjusted for end-effects a la Gerzon) and scales them to be
symmetrical about s=1, so that for each zero (or pole) at s=-k there
is another at s=-1/k, then when you take the two factors (1+s*k) and
(1+s/k), multiply them and put them through the bilinear
transformation s=(z-1)/(z+1), you find that the numerator is
(k^2+2*k+1)*z^2 - (k^2+2*k-1)
Thus there is no term in z, and the whole thing becomes a function of
z^2 only.
Hence the symmetry about fs/4. And some economy - especially if the
DSP platform can implement z^-2 can be implemented at less than twice
the cost of z^-1.
Peter
------------------------------------------------------------
Saturday, January 15, 2011, 10:38:34 AM, Geoffrey wrote:
> On 14 Jan 2011, at 17:00, sursound-requ...@music.vt.edu wrote:
>>
>> Message: 7
>> Date: Fri, 14 Jan 2011 08:52:17 +0000
>> From: Dave Malham <d...@york.ac.uk>
>> Subject: Re: [Sursound] Available UHJ encoders?
>> To: Surround Sound discussion group <sursound@music.vt.edu>
>> Message-ID: <4d300ec1.7080...@york.ac.uk>
>> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>>
>>
>>
>> On 14/01/2011 01:54, J?rn Nettingsmeier wrote:
>>>
>>> under linux, you can run jconvolver with the uhjenc plugin, sounds very
>>> good, but introduces 2048
>>> samples of latency.
>>> and fons has recently added an IIR-based uhj encoder to the AMB plugin set
>>> (with zero latency but
>>> likely some compromises in sound quality), i haven't had the chance to test
>>> it carefully, but a
>>> quick run-through showed it does the job, although i prefer the sound of
>>> the convolution one.
>>
>> D*mn, I'm just finishing off a (VST/AU) encoder myself using an IIR filter
>> set based on the analogue
>> all pass filters in the original Calrec unit (as designed by Geoffrey)-
> Nice to know something I did 30 years ago is still worth ripping off :-)
> These are probably ok at 96 or 192, but at 44.1/48 I think they
> will wander off at high frequencies due to warping.
> A better approach is to look for a solution which is symmetrical
> about fs/4. That version is only about 20 years old :-)
> Used with backwards dubbing gives partitioned convolution a run for its money.
> rgds,
> Geoffrey
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