Digital Linkwitz transform?

[Boris Bilinsky]

Hi, I would like to use some kind of digital filter to extend the bass response of my sub woofer, think it would be possible with a shelving filter and one or two parametric equalizers. So my question is if there are any receivers with this functionality? I know yamaha uses parametric eq in their YPAO calibration but those parameters seem to be impossible to edit manually. The alternative is to buy a dcx2496 to act as filter but it seems unnecessary to ad/da the signal once more especially as it has to be modded to use the highest resolution.

[Wingfeather]

The LT itself is just a 2nd-order shelf filter. So if you can find a receiver with one of those in it, that's all you need.

[Boris Bilinsky]

Hmm, the receiver market is a jungle... and most of the eq functions are only auto
Any recommendations?

It would be nice with an open source platform for receivers , and remote control by wifi for example so you don't have to mess with the lousy lcd interface.

[forr]

Hi,

I've done a lot of work on digital processors to mimic analog transforms, the Linkwitz one being only one of them. The idea I followed is quite simple, I started my reasonings in the analog domain.
("o" refers to initial, "t" to Target and "eq" to EQualisation)


Firstly,
any 2nd order filter defined by its frequency fo and Qo can be transformed to another filter with the same frequency but with another Q.

Let's suppose that a 2nd order filter, as is a driver in a closed box, at frequency fo has a Qo = 1.0.
Using a "Bell" equalisation set at Feq = fo, Qeq = 1.0, Geq = -6 dB, the transfer function of the driver+equalisation has been transformed now to fo, Q = 0.5.

Inversely, the behaviour of a driver of Qo = 0.5, can be transformed, using a bell equalisation at Feq = fo, Qeq = 1.0, Geq +6 dB, to a transfer function of fo, Q = 1.0.


Secondly,
a 2nd order filter at fo with a Qo = 0.5 can be thought as being two 1st order filters at fo in series.
Each of these 1st order filters in series can have its frequency changed by a "Shelf" equalisation.
For example, in the analog domain, to double the frequency fo to ft , the circuit shoud be a -6 dB, frequency dependent, attenuator using three components C//R & R, where
C.R = 1 / (2.pi.fc).
Using two such circuits in series (while taking impedances in consideration, it may require separating buffers), the new transfer function is now a 2nd filter at ft = 2.fo, Q = 0.5

The same reasoning applies to halve the frequency. In the analog domain, a gain of +6 dB is needed at low frequencies, the circuit C//R & R has to be included in the feedback path of an op-amp, with values such as C.R = 1 / (2.pi.ft). The new transform function is ft = fo/2, Q = 0.5.


Thirdly
now having a transfer function at the required target frequency with a Q being 0.5, this Q can be set a value suiting the needs, using a bell equalisation as explained above.


To summarize, transforming a 2nd order filter at fo, Qo to a new one at ft, Qt, one should use
. bell equalisation to get a Q = 0.5
. first shelf equalisation to get the new ft
. second shelf equalisation to get the new ft
. bell equalisation to get the required Qt


Using digital processors, this would work as intended, were the definitions of Q and Shelf equalisations standardised among the manufacturers. They are not, and this is where some difficulties happen.

I've been investigating the question with Windows free downloadable softwares for four digital processors :
BSS 366
RAM Audio LMX-244
XTA Audiocore
Yamaha SP2040
(I've been unable to do anything with the Behringer DCX software which is badly displayed on my computer)
I've also done somre real hardware and frequency tests with a BSS 366 and an RTA.

What I can say is that :
- BSS and Yamaha have the same definition of Q as in the Rane notes, RAM and XTA have not. Example of some words of caution :
http://www.laaudio.co.uk/Resources/D...anual-v1.1.pdf
- the BSS shelf algorithm does not correspond to a simple shelf R//C & R analog circuit
- playing with the BSS and the RTA, I found, almost by accident, simpler ways than as explained above to remarquably approximate analog transforms (less 0.2 dB deviations)

More to come.

[werewolf]

This is a very interesting topic to me. I'm investigating something VERY similar with yet another brand of digital EQ.

If i can summarize the last post :

1. Use a second-order EQ to move the complex poles of the driver (fo, Qo) to coincident locations on the real axis (at the same fo).
2. Use two first-order shelves to move those real, coincident poles to new real, coincident locations (corresponding to the new ft).
3. Use another second-order EQ to move the real poles (now at ft) off the real axis, corresponding to the new desired Qt.

And in all cases, of course, "moving" poles means cancellation with zeros, and re-establishing new pole locations. I think this is a fine idea

Interestingly, the digital equalizer I'm looking at offers second-order, or resonant, shelves (Rane might also offer second-order shelves, i'm not sure?) ... but the shelves use the same Q for poles & zeros. This makes life very easy, but the single-Q shelves means that I still need 2 steps:

1. Second-order EQ transforms (fo,Qo) to (fo,Qt).
2. Second-order shelf transforms (fo,Qt) to (ft,Qt).

or :

1. Second-order shelf transforms (fo,Qo) to (ft,Qo).
2. Second-order EQ transforms (ft,Qo) to (ft,Qt).

Sadly, as already mentioned, it takes some real homework to fully understand the different definition of "Q" used by different manufacturers How this has escaped standardization, also escapes my comprehension.

One must also comprehend how the boost & cut functions are implemented : symmetric, or asymmetric?

More to follow from this, also

[b_force]

More to come.

Sorry for the huge kick, but nowadays with al these affordable DSP's it would be interesting to use LT's.
I've searched for others topics, but I couldn't find the answers yet.