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biquad typo? was: Re: [Csnd] mode and amplitude

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Justin Glenn Smith

biquad typo? was: Re: [Csnd] mode and amplitude

also, I think that in the following equation in the csound manual for biquad, the '=' may be a typo
a0*y(n) + a1*y[n-1] + a2*y[n-2] = b0*x[n] + b1*x[n-1] + b2*x[n-2]

My grasp on DSP is a little shaky, but as I understand it the bN terms describe direct signal paths, while the aN terms are feedback paths. In this context I don't understand why there would be an equality here. Also I don't understand why there is an a0 term - how can one have an undelayed feedback term?

Apologies in advance if the manual is correct and I am simply misunderstanding it. Accuracy of the manual is of course the most important where our own knowledge is most likely to be found wanting :)

Moved over to devel, these questions seem more appropriate for that list.

Justin Glenn Smith wrote:

> For starters, a digital filter is usually a set of delay lines with different amplitudes applied to them. A biquad filter is one of the basic digital filters. In practice an engineer will usually use an application or formula where they describe properties they want in the filter (bandwidth, center frequency, highpass vs. lowpass vs. bandpass etc.) and it will spit out coefficients for a biquad filter.
>
> You can think of an opcode like mode or butterbp etc. as user friendly frontends where csound takes care of the filter design - under the hood it sets up one or more biquad filters in various configurations. Some of the csound filters use other, non biquad filters, for example lowres and lowpass2 don't specify their filter types, but they are probably digital low pass filters (an easier diagram to read, but less linear than biquad in frequency response).
>
> for starters here is the page for the biquad filter on Wikipedia:
> http://en.wikipedia.org/wiki/Digital_biquad_filter
>
> The arguments to the biquad opcode are exactly the variables in the equation described on that page.
> the kbx arguments are the zeros which happen to be amplitudes of non feedback delays (well b0 is a delay of zero which is the same as no delay really...) and the kax arguments are the poles, which happen to be the amplitues of the feedback delays. There is no a0, because in order to feed back you need at least a delay of one sample.
>
>
> The basic gist of it without the numbers is that by combining short (one or two sample) delays at various amplitudes (with feedback back into the filter from the filter's output), you cancel out some frequencies while amplifying others. If you consider the fact that sound is modified by a space like a room or a body of an instrument, where echoes interfere or reinforce depending on wavelength, it is a digital translation of that physical phenomenon. The arguments to the biquad opcode represent the relative levels of the various delays / feedbacks.
>
> tl;dr: if you don't understand biquad, you could take a class on Digital Signal Processing or teach yourself some DSP or just use one of the more user friendly filters (which are less flexible but more usable for non-engineers).
>
> Stefan Thomas wrote:
>> Dear Justin,
>> thanks for Your answer.
>> As far as I understood, reading some mails from this list, the mode-opcode
>> is related to the biquad-filter, isn't it?
>> I've read in the csound-manual:
>>
>> ares *biquad* asig, kb0, kb1, kb2, ka0, ka1, ka2 [, iskip]
>>
>>
>> But unfortunately I didn't find an explanation for kb0, kb1 (bandwith?) and
>> ka0, ka1
>> I would like to understand what this filter does.
>>
>> Am 12. Februar 2012 22:07 schrieb Justin Glenn Smith <[hidden email]>:
>>
>>> Because mode is a filter, the output amplitude will vary based on the
>>> settings of the filter and the frequency components of the input sound. To
>>> control amplitude you could use the balance opcode to peg the sum of the
>>> filtered sounds to the original input sound. Or you could balance each of
>>> the filtered sounds, but to some degree I think this would be undermining
>>> the purpose of the opcode.
>>>
>>> Stefan Thomas wrote:
>>>> Dear community,
>>>> I would once more like to ask a question about the mode opcode.
>>>> If I define different modes with different frequencies, how are there
>>>> relative amplitudes are balanced?
>>>> Are they of equal loudness?
>>>>
>>>> Send bugs reports to the Sourceforge bug tracker
>>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>>> Discussions of bugs and features can be posted here
>>>> To unsubscribe, send email [hidden email] with body
>>> "unsubscribe csound"
>>>
>>> Send bugs reports to the Sourceforge bug tracker
>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>> Discussions of bugs and features can be posted here
>>> To unsubscribe, send email [hidden email] with body "unsubscribe
>>> csound"
>>>
>>>
>> Send bugs reports to the Sourceforge bug tracker
>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email [hidden email] with body "unsubscribe csound"
>>
>>
>
>

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jpff

Re: biquad typo? was: Re: [Csnd] mode and amplitude

rearrange the equation to

a0*y(n) = b0*x[n] + b1*x[n-1] + b2*x[n-2] - a1*y[n-1] - a2*y[n-2]

and you have the computation -- usually a0 is zero
yes y in outputs and x inputs

> also, I think that in the following equation in the csound manual for
> biquad, the '=' may be a typo
> a0*y(n) + a1*y[n-1] + a2*y[n-2] = b0*x[n] + b1*x[n-1] + b2*x[n-2]
>
> My grasp on DSP is a little shaky, but as I understand it the bN terms
> describe direct signal paths, while the aN terms are feedback paths. In
> this context I don't understand why there would be an equality here. Also
> I don't understand why there is an a0 term - how can one have an undelayed
> feedback term?
>
> Apologies in advance if the manual is correct and I am simply
> misunderstanding it. Accuracy of the manual is of course the most
> important where our own knowledge is most likely to be found wanting :)
>
> Moved over to devel, these questions seem more appropriate for that list.
>
> Justin Glenn Smith wrote:
>> For starters, a digital filter is usually a set of delay lines with
>> different amplitudes applied to them. A biquad filter is one of the
>> basic digital filters. In practice an engineer will usually use an
>> application or formula where they describe properties they want in the
>> filter (bandwidth, center frequency, highpass vs. lowpass vs. bandpass
>> etc.) and it will spit out coefficients for a biquad filter.
>>
>> You can think of an opcode like mode or butterbp etc. as user friendly
>> frontends where csound takes care of the filter design - under the hood
>> it sets up one or more biquad filters in various configurations. Some of
>> the csound filters use other, non biquad filters, for example lowres and
>> lowpass2 don't specify their filter types, but they are probably digital
>> low pass filters (an easier diagram to read, but less linear than biquad
>> in frequency response).
>>
>> for starters here is the page for the biquad filter on Wikipedia:
>> http://en.wikipedia.org/wiki/Digital_biquad_filter
>>
>> The arguments to the biquad opcode are exactly the variables in the
>> equation described on that page.
>> the kbx arguments are the zeros which happen to be amplitudes of non
>> feedback delays (well b0 is a delay of zero which is the same as no
>> delay really...) and the kax arguments are the poles, which happen to be
>> the amplitues of the feedback delays. There is no a0, because in order
>> to feed back you need at least a delay of one sample.
>>
>>
>> The basic gist of it without the numbers is that by combining short (one
>> or two sample) delays at various amplitudes (with feedback back into the
>> filter from the filter's output), you cancel out some frequencies while
>> amplifying others. If you consider the fact that sound is modified by a
>> space like a room or a body of an instrument, where echoes interfere or
>> reinforce depending on wavelength, it is a digital translation of that
>> physical phenomenon. The arguments to the biquad opcode represent the
>> relative levels of the various delays / feedbacks.
>>
>> tl;dr: if you don't understand biquad, you could take a class on Digital
>> Signal Processing or teach yourself some DSP or just use one of the more
>> user friendly filters (which are less flexible but more usable for
>> non-engineers).
>>
>> Stefan Thomas wrote:
>>> Dear Justin,
>>> thanks for Your answer.
>>> As far as I understood, reading some mails from this list, the
>>> mode-opcode
>>> is related to the biquad-filter, isn't it?
>>> I've read in the csound-manual:
>>>
>>> ares *biquad* asig, kb0, kb1, kb2, ka0, ka1, ka2 [, iskip]
>>>
>>>
>>> But unfortunately I didn't find an explanation for kb0, kb1 (bandwith?)
>>> and
>>> ka0, ka1
>>> I would like to understand what this filter does.
>>>
>>> Am 12. Februar 2012 22:07 schrieb Justin Glenn Smith
>>> <[hidden email]>:
>>>
>>>> Because mode is a filter, the output amplitude will vary based on the
>>>> settings of the filter and the frequency components of the input
>>>> sound. To
>>>> control amplitude you could use the balance opcode to peg the sum of
>>>> the
>>>> filtered sounds to the original input sound. Or you could balance each
>>>> of
>>>> the filtered sounds, but to some degree I think this would be
>>>> undermining
>>>> the purpose of the opcode.
>>>>
>>>> Stefan Thomas wrote:
>>>>> Dear community,
>>>>> I would once more like to ask a question about the mode opcode.
>>>>> If I define different modes with different frequencies, how are there
>>>>> relative amplitudes are balanced?
>>>>> Are they of equal loudness?
>>>>>
>>>>> Send bugs reports to the Sourceforge bug tracker
>>>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>>>> Discussions of bugs and features can be posted here
>>>>> To unsubscribe, send email [hidden email] with body
>>>> "unsubscribe csound"
>>>>
>>>> Send bugs reports to the Sourceforge bug tracker
>>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>>> Discussions of bugs and features can be posted here
>>>> To unsubscribe, send email [hidden email] with body
>>>> "unsubscribe
>>>> csound"
>>>>
>>>>
>>> Send bugs reports to the Sourceforge bug tracker
>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>> Discussions of bugs and features can be posted here
>>> To unsubscribe, send email [hidden email] with body
>>> "unsubscribe csound"
>>>
>>>
>>
>>
>
>
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> The most comprehensive online learning library for Microsoft developers
> is just $99.99! Visual Studio, SharePoint, SQL - plus HTML5, CSS3, MVC3,
> Metro Style Apps, more. Free future releases when you subscribe now!
> http://p.sf.net/sfu/learndevnow-dev2
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