help with hz to octave conversion for dsp

B

BJ James

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Jan 11, 2011
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I got some nice numbers from yorkville for my recent trade in U215. Now my problen is that yorkville lists the width in hz and the dsp wants the numbers in octave bandwidth. I have looked for a conversion table online but have not had luck. How do I calculate this?
Thanks,
BJ
 
Re: help with hz to octave conversion for dsp

BJ James said:
I got some nice numbers from yorkville for my recent trade in U215. Now my problen is that yorkville lists the width in hz and the dsp wants the numbers in octave bandwidth. I have looked for a conversion table online but have not had luck. How do I calculate this?
Thanks,
BJ
Click to expand...

Q factor bandwidth in octaves filter calculator formula bandwidth - quality factor Q to bandwidth per octave width convert filter BW octave mastering slope dB/oct steepness - sengpielaudio Sengpiel Berlin

Is this what you're looking for? Sorry for the hit and run reply if it's not......
 
Re: help with hz to octave conversion for dsp

Dick Rees said:
Q factor bandwidth in octaves filter calculator formula bandwidth - quality factor Q to bandwidth per octave width convert filter BW octave mastering slope dB/oct steepness - sengpielaudio Sengpiel Berlin

Is this what you're looking for? Sorry for the hit and run reply if it's not......
Click to expand...

Thanks Dick,
I saw that but I'm not even sure if that's what I'm looking for.
Here is an example of a yorkville spec. 2140hz(freq), -4dB(amount), 1248hz(width)

Thanks,
BJ
 
Re: help with hz to octave conversion for dsp

BJ James said:
Thanks Dick,
I saw that but I'm not even sure if that's what I'm looking for.
Here is an example of a yorkville spec. 2140hz(freq), -4dB(amount), 1248hz(width)

Thanks,
BJ
Click to expand...

Cobbling some numbers together I get a Q of 1.845 for the specified width @ the center frequency. I'll throw it out to get corrected.
 
Re: help with hz to octave conversion for dsp

Just putting the same numbers in between different brands of DSP is no guarantee of same filter behavior. Much better to confirm by measuring with SMAART or similar.

What's the processor, anyway? Most of them can be switched to read either Q or bandwidth as a user option.
 
Re: help with hz to octave conversion for dsp

Scott Helmke said:
Just putting the same numbers in between different brands of DSP is no guarantee of same filter behavior. Much better to confirm by measuring with SMAART or similar.

What's the processor, anyway? Most of them can be switched to read either Q or bandwidth as a user option.
Click to expand...

True, but all i need is to get in the ballpark for now. Still looking.
 
Re: help with hz to octave conversion for dsp

Hi BJ,

BJ James said:
I saw that but I'm not even sure if that's what I'm looking for.
Here is an example of a yorkville spec. 2140hz(freq), -4dB(amount), 1248hz(width)
Click to expand...

If I follow correctly, it'll do almost what you need. You know the centre frequency, fc, and bandwidth, w, so the filter Q is just fc/w. Converting Q to octave bandwidth, n, you get:

n = 2 * log((sqrt(4Q^2+1)+1)/2Q) / log(2)

So, for fc=2140, w=1248, the Q is 1.715 and the octave bandwidth is 0.830.

FWIW, though, I agree with Scott's advice to measure and compare the results.

Nick
 
Re: help with hz to octave conversion for dsp

Nick Hickman said:
Hi BJ,



If I follow correctly, it'll do almost what you need. You know the centre frequency, fc, and bandwidth, w, so the filter Q is just fc/w. Converting Q to octave bandwidth, n, you get:

n = 2 * log((sqrt(4Q^2+1)+1)/2Q) / log(2)

So, for fc=2140, w=1248, the Q is 1.715 and the octave bandwidth is 0.830.

FWIW, though, I agree with Scott's advice to measure and compare the results.

Nick
Click to expand...
ok, Math is not my strong suit so I used the calculator to get the same results. So Q is fc divided by w. I punch Q in the conversion to find octave bw and I get a reasonable looking number. Here's what's messing with me.
The first filter Yorkville lists for my boxes is 205f, -6 dB, 5hz w. I punch the numbers into the magic box and i get a q of 41 = octave bw of .0352. That just doesn't seem right and my dsp certainly doesn't provide that tight a filter.

I'll probably give Yorkville another call, but I'd still like to understand this a bit more.
Also, i did try to do a TF in smaart but i am really new to it and don't trust what I'm seeing. But that is for another forum to help me with.

Thanks,
BJ
 
Re: help with hz to octave conversion for dsp

Calculating Q factor depends to some extent on the filter that is being implemented, but in an analogue musical setting, we can assume that the shape of the filter "bell" is symmetric on a logarithmic scale. If we have Q=0.5, then the -3dB points at maximum cut or boost should be one octave each side of the center frequency. Therefore, Q=fc/w will be flawed in most instances relating to real world filters.
 
Re: help with hz to octave conversion for dsp

Wow, a new group that hasn't heard my whine about Q/Octaves...

OK where are the -3dB points for an EQ with only 2 dB of boost?

To the best of my knowledge there is not a single widely accepted definition for Q for boost/cut EQ sections, but a few different definitions based on topology or algorithm. So it is not a matter of execution of math, but what math to use.

I asked the AES standards committee to address this years ago. AFAIK no results after the initial discussion that agreed there was an issue... I got tired and stopped bugging them.

For individual users, ask whoever gave you the number, what platform they got it from. I don't know if we are there yet with technology, but it would be nice to publish the complete desired frequency response plot in some useful digital media that could be compared. Maybe we could agree on that?

JR
 
Re: help with hz to octave conversion for dsp

John Roberts said:
I don't know if we are there yet with technology, but it would be nice to publish the complete desired frequency response plot in some useful digital media that could be compared. Maybe we could agree on that?

JR
Click to expand...

sure. as long as i can open and edit it on my iPad/iPhone/iPod/Android Tablet/Linux PC/Macbook/Nintendo DS/Kindle/Fire/Windows PC/Canon Copier/8.5"x14" Legal Pad....
 
Re: help with hz to octave conversion for dsp

brian maddox said:
sure. as long as i can open and edit it on my iPad/iPhone/iPod/Android Tablet/Linux PC/Macbook/Nintendo DS/Kindle/Fire/Windows PC/Canon Copier/8.5"x14" Legal Pad....
Click to expand...

Right now it looks like we have a better chance of that, than getting a single definition for Q in bell sections.

I don't see it as a computing platform issue, but communicating with the sundry (and less of them) measurement platforms.

Of course what would I know... ?

JR
 
Re: help with hz to octave conversion for dsp

Aside of how upper and lower frequency point is defined, -3dB or a fraction of cut/boost (nearest to everyday reality) or whatever, calculating the missing parameters given a subset of the parameters Q, BW, f1, f0, f2 one has to realize that we are not dealing with a linear scale, that was my only point. Many internet-published formulaes and calculators are wrong, and misleads the user.
One good expanation of some of the maths Bandwidth in Octaves Versus Q in Bandpass Filters

Some manufacturers might use definitions of Q and BW that doesn't correspond too well with my mental model of a fully parametric filter, but i prefer to think they all at least work with a logarithmic scale.

Edit: My use of Q as 1/N is probably wrong in most settings
 
Last edited:
Re: help with hz to octave conversion for dsp

Per Søvik said:
Aside of how upper and lower frequency point is defined, -3dB or a fraction of cut/boost (nearest to everyday reality) or whatever, calculating the missing parameters given a subset of the parameters Q, BW, f1, f0, f2 one has to realize that we are not dealing with a linear scale, that was my only point. Many internet-published formulaes and calculators are wrong, and misleads the user.
One good expanation of some of the maths Bandwidth in Octaves Versus Q in Bandpass Filters

Some manufacturers might use definitions of Q and BW that doesn't correspond too well with my mental model of a fully parametric filter, but i prefer to think they all at least work with a logarithmic scale.
Click to expand...

The Q or octaves of a simple bandpass section can be established with good agreement, but how this bandpass is then applied to make the variable boost/cut response gives us different response shapes for different amounts of boost/cut even when using the identical base BP filter shape, thus the discrepancy.

This is an old problem and very noticeable with analog 1/3rd octave GEQ that are not all the same, despite all being 1/3 octave. There is only a small handful of different approaches and RANE has named theirs and done some Rosseta stone work on conversion between several.

I just don't want the OP to think it's his math skills that are to blame... the manufacturers have not yet been suitably motivated to solve this.

JR
 
Re: help with hz to octave conversion for dsp

Hi Per,

Per Søvik said:
Calculating Q factor depends to some extent on the filter that is being implemented, but in an analogue musical setting, we can assume that the shape of the filter "bell" is symmetric on a logarithmic scale. If we have Q=0.5, then the -3dB points at maximum cut or boost should be one octave each side of the center frequency. Therefore, Q=fc/w will be flawed in most instances relating to real world filters.
Click to expand...

How are you defining Q? The usage with which I'm familiar (and the one used in the Rane document you cite and in the converter referenced earlier) is the centre frequency divided by the bandwidth between -3dB points. By this definition, a two octave bandwidth filter has a Q of 0.666 not 0.5.

Nick
 
Re: help with hz to octave conversion for dsp

Nick Hickman said:
Hi Per,
How are you defining Q? The usage with which I'm familiar (and the one used in the Rane document you cite and in the converter referenced earlier) is the centre frequency divided by the bandwidth between -3dB points. By this definition, a two octave bandwidth filter has a Q of 0.666 not 0.5.

Nick
Click to expand...

Yeah, as I stated in the Edit, my definition of Q=1/N is probably wrong, and has allways been. Made an ASSumption once when using an old parametric and has never questioned it.
I mistook this discussion to be similar to a discussion years ago where it was claimed that centre frequency f0=(f1+f2)/2 and thus calculating the different frequencies would be easy. Sorry :blush:
 
Re: help with hz to octave conversion for dsp

Agreement should be 100% for Q/octaves in crossover HP and LP filter sections. Only Q in corrective EQ is undefined or lacking a single clear definition. Center frequency and amount of boost/cut should also be well defined.

If they can't get the corner frequency right they have no excuse from me. I am not aware of any disputed definition there. Cascaded mutli-pole sections will not be trivial to confirm empirically, especially if overlaid with all pass sections and EQ.

I repeat my call for a simple comprehensive target frequency response plot saved in some digital media or computer file that could be easily compared to. Back in the very old days things like RIAA phono or IEC tape Equalization curves were often defined as simple poles and zeros time constants and by tables of amplitude values vs frequency. No questions there about what the response should be.

If current DSP are inaccurate in even more ways than I predict, that is even more reason to compare actual transfer function to some digital reference response target file.


JR
 
Re: help with hz to octave conversion for dsp

Yorkville was good enough to get back to me with q values, and they appear to make much more sense then the numbers i came up with when converting. Apparently you can't just divide freq by hz to get the q ......when i did that with a set of numbers i came up with a q of 41 where Yorkville provided a more reasonable q of .75 for the same numbers.
Now here's hoping the q to octave bw conversion is not too far off.
I wish i was a little more experienced with smaart. i have a ways to go before i can do anything useful with it.
Cheers,
BJ
 
Re: help with hz to octave conversion for dsp

BJ James said:
Yorkville was good enough to get back to me with q values, and they appear to make much more sense then the numbers i came up with when converting. Apparently you can't just divide freq by hz to get the q ......when i did that with a set of numbers i came up with a q of 41 where Yorkville provided a more reasonable q of .75 for the same numbers.
Now here's hoping the q to octave bw conversion is not too far off.
I wish i was a little more experienced with smaart. i have a ways to go before i can do anything useful with it.
Cheers,
BJ
Click to expand...

connecting a DSP to smaart to measure what it is doing is way easier than making acoustic measurements, and easier to get right.
I think you should give it a try. even if just to see what your processor spits out after you enter the settings

Jason
 
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