Filters -> poles, order, Q, slope, bandwidth, WTF?

[CableChannel]

Vojtech, I am lost. Do you have a document about all these numbers that characterize a filter?

Specifically I am just fiddling with MBandpass (which has some misleading name, its a powerful double multimode filter if you ask me!)

I selected LP24. Now, all my life I have been thinking that this characterizes the filter completely. 24 is the order, others say 4 pole, and this describes the bandwith, or Q, which is another way of defining the bandwidth. However, you can configure that Q *in addition* to selecting the order. I am puzzled. Obviously all my filter knowledge is wrong. (Which does not surprise me, the math behind audio always defeated me in no time).

Can you please clarify for a dummy user? What is the order, that is Q?

I looked through your tutorials, but nothing seems appropriate judging from the names.


Thanks a lot!

[manducator]

I googled for 'audio filters explained' and found this:

[CableChannel]

Q not explained in the video or did I miss it?

[manducator]

http://www.rane.com/note170.html

http://en.wikipedia.org/wiki/Audio_filter

In layman's terms; Q (quality) is how narrow or wide the peak of the resonance is.

The higher the number, the smaller the peak. A Q of 3 is much more narrow than a Q of 0.5

[CableChannel]

Sorry man your links are not helping me. I need an explanation what is slope/order and Q for a LPF. Preferably with some illustration.

[Dikkop]

Maybe you should download the A-108 module document from the Doepfer site. http://www.doepfer.de/home_e.htm - choose module overview. Hope this helps.

[Tricky-Loops]

"Order" is the same as "pole" ("First Order" = "1 Pole")...
For your example: 24 db is the slope steepness: 24 db/Oct = 4 pole = 4th order

Q is *NOT* the band width; Q is the "resonance", here you see the influence of Q on the filter:

[rockstar_not]

Q IS the bandwidth of a parametric band pass or band reject filter.

To calculate Q of a band reject filter, divide the center frequency of the filter by the width; with width defined by the points to the right and left of the center frequency where the filter amplitude is -3 dB from unity gain.

For a band pass filter, same thing except for the width being the + 3dB points.

Wikipedia article: http://en.wikipedia.org/wiki/Q_factor

Perhaps Tricky-loops definition applies to HP or LP filters only, not sure - but the Q I describe above has been used for decades to describe filter width as a function of frequency.

[Tricky-Loops]

Q IS the bandwidth of a parametric band pass or band reject filter.

To calculate Q of a band reject filter, divide the center frequency of the filter by the width; with width defined by the points to the right and left of the center frequency where the filter amplitude is -3 dB from unity gain.

For a band pass filter, same thing except for the width being the + 3dB points.

Wikipedia article: http://en.wikipedia.org/wiki/Q_factor

Perhaps Tricky-loops definition applies to HP or LP filters only, not sure - but the Q I describe above has been used for decades to describe filter width as a function of frequency.

For a REAL band pass filter or band reject (notch) filter "Q" can be used instead of the band width, of course.

But in case of the MBandpass it obviously labels the resonance, not the band width.

The name "MBandpass" is confusing, anyway, as it's not a simple band pass filter but a combination of lowpass and highpass filter (which in effect *IS* some kind of band pass filter).

I have even seen peak & notch filters with "band width" controllers instead of "Q", so that's a bit confusing. Here's an example ("band width" instead of "Q"):

[Tricky-Loops]

For our mathematicians (there's even a German translation):

http://www.sengpielaudio.com/calculator-bandwidth.htm

[CableChannel]

OK so there seems to be some inconsistency about the usage of the term Q, it seems to be different in case of LP/HP vs BP.

But your picture of Q = resonance in case of LP makes sense, Tricky.

[CableChannel]

Maybe Vojtech can still say something "official" on this?

[MeldaProduction]

Hmmm, I think all was explained here. Usually Q = bandwidth = resonance, just expressed differently. I suggest checking MDynamicEq (or MAutoDynamicEq), set a band to LP or HP, then it has both order and Q parameters, so you can see what they do.

[CableChannel]

That is a good idea I will do that.

Its just a little against my intuitive understanding, I learned that resonance is sort of the height of the bump at cutoff while bandwith is how steep the rolloff is.

[MeldaProduction]

That is a good idea I will do that.

Its just a little against my intuitive understanding, I learned that resonance is sort of the height of the bump at cutoff while bandwith is how steep the rolloff is.

No no, bandwidth is basically the same thing. But note that these terms are for engineers (creators of the filters). Q is generally used for target users. Generally high Q -> low bandwidth and the filter design is based on resonance, so higher Q (also called quality) produces more resonance, because that's the only way the filter could satisfy the "low bandwidth" requirement, speaking of normal language, a little normal at least .