Brennon Bortz

I'm working through the second volume of Musimathics, by Gareth Loy, and learning quite a lot. I'd like to actually start realizing some of the topics he covers on my own in Max/MSP to help make them more concrete, and I'm having some troubles.

For instance, I'm now reading about filters, and their supporting mathematics. As a rather simple example, I'd like to build my own lowpass filter in Max/MSP. I know how to implement one through the built in filtering objects in Max/MSP, but building one on my own will give me the opportunity to better understand what's really occuring.

He gives the equation for a lowpass filter thus:

where y(nT) is the input signal, n is an instantaneous sample, and T is time.

His explanation of the operation of this filter makes perfect sense, but realizing it in Max/MSP is giving me problems. I'm sure there's a simple answer, but I'm just not getting it.

How would one realize such an equation? I appreciate your help!

I'm working through the second volume of Musimathics, by Gareth Loy, and learning quite a lot.  I'd like to actually start realizing some of the topics he covers on my own in Max/MSP to help make them more concrete, and I'm having some troubles.

For instance, I'm now reading about filters, and their supporting mathematics.  As a rather simple example, I'd like to build my own lowpass filter in Max/MSP.  I know how to implement one through the built in filtering objects in Max/MSP, but building one on my own will give me the opportunity to better understand what's really occuring.

His explanation of the operation of this filter makes perfect sense, but realizing it in Max/MSP is giving me problems.  I'm sure there's a simple answer, but I'm just not getting it.

How would one realize such an equation?  I appreciate your help!

building-a-filter

Have a look at the bufir~ object. You can build finite response filters with up to 256 points.There is a patch in the examples folder called buffir-eq-help.pat using bufir~

Here is a patch on convolution I made years ago when I was studying this. You need the lobjects for that.

On Jan 4, 2008, at 11:32 AM, Brennon wrote

> He gives the equation for a lowpass filter thus:

> where y(nT) is the input signal, n is an instantaneous sample, and 

> His explanation of the operation of this filter makes perfect 

> sense, but realizing it in Max/MSP is giving me problems. I'm sure 

> there's a simple answer, but I'm just not getting it.

Well, you'd want to rearrange this to be in terms of the output signal:

So you subtract a 1 sample delay of the output from the input. 

Unfortunately, you can't get a 1 sample delay in a feedback path in a 

Max patch. You can use comb~ or biquad~ for example, but I don't 

think that's the autodidactic answer you were looking for...

On Jan 4, 2008, at 11:32 AM, Brennon wrote
>
> He gives the equation for a lowpass filter thus:
>
> y(nT) = x(nT) + x[(n-1)T]
>
> where y(nT) is the input signal, n is an instantaneous sample, and  
> T is time.
>
> His explanation of the operation of this filter makes perfect  
> sense, but realizing it in Max/MSP is giving me problems.  I'm sure  
> there's a simple answer, but I'm just not getting it.

So you subtract a 1 sample delay of the output from the input.   
Unfortunately, you can't get a 1 sample delay in a feedback path in a  
Max patch.  You can use comb~ or biquad~ for example, but I don't  
think that's the autodidactic answer you were looking for...


1) FYI - I recently got an email from Gareth re: the Musimat 

programming language he created to demo the ideas in the books. He 

gave me some detailed info on getting it to run on Intel Macs. I'll 

check with him to make sure it's OK to post the info here, and follow 

2) I believe you have the interpretation of the equation slightly 

wrong: y is the output, x is the input. In a nutshell, a given output 

sample y(nT) is produced by averaging the current x(nT) and most 

previous x((n-1)T) inputs. There should, however, be some 

coefficients in there, in this case to multiply each of the two 

inputs by .5 before adding them, in order to average them. That's 

what simple low-pass filtering is, averaging inputs to generate 

outputs. You could achieve this in MSP by using [delay~] set to one 

sample delay, and adding that to the direct signal after multiply the 

delayed and direct signals by .5. This will then give you the 

filtered (averaged) output. It achieves this by simply 'slowing down' 

fast-changing signals (i.e. signals with high-frequency components).

On Jan 4, 2008, at 12:32 PM, Brennon wrote:

> I'm working through the second volume of Musimathics, by Gareth 

> Loy, and learning quite a lot. I'd like to actually start 

> realizing some of the topics he covers on my own in Max/MSP to help 

> make them more concrete, and I'm having some troubles.

> For instance, I'm now reading about filters, and their supporting 

> mathematics. As a rather simple example, I'd like to build my own 

> lowpass filter in Max/MSP. I know how to implement one through the 

> built in filtering objects in Max/MSP, but building one on my own 

> will give me the opportunity to better understand what's really 

> How would one realize such an equation? I appreciate your help!

1) FYI - I recently got an email from Gareth re: the Musimat  
programming language he created to demo the ideas in the books. He  
gave me some detailed info on getting it to run on Intel Macs. I'll  
check with him to make sure it's OK to post the info here, and follow  
up accordingly.

2) I believe you have the interpretation of the equation slightly  
wrong: y is the output, x is the input. In a nutshell, a given output  
sample y(nT) is produced by averaging the current x(nT) and most  
previous x((n-1)T) inputs. There should, however, be some  
coefficients in there, in this case to multiply each of the two  
inputs by .5 before adding them, in order to average them. That's  
what simple low-pass filtering is, averaging inputs to generate  
outputs. You could achieve this in MSP by using [delay~] set to one  
sample delay, and adding that to the direct signal after multiply the  
delayed and direct signals by .5. This will then give you the  
filtered (averaged) output. It achieves this by simply 'slowing down'  
fast-changing signals (i.e. signals with high-frequency components).

>
> Hello all,
>
> I'm working through the second volume of Musimathics, by Gareth  
> Loy, and learning quite a lot.  I'd like to actually start  
> realizing some of the topics he covers on my own in Max/MSP to help  
> make them more concrete, and I'm having some troubles.
>
> For instance, I'm now reading about filters, and their supporting  
> mathematics.  As a rather simple example, I'd like to build my own  
> lowpass filter in Max/MSP.  I know how to implement one through the  
> built in filtering objects in Max/MSP, but building one on my own  
> will give me the opportunity to better understand what's really  
> occuring.
>
> He gives the equation for a lowpass filter thus:
>
> y(nT) = x(nT) + x[(n-1)T]
>
> where y(nT) is the input signal, n is an instantaneous sample, and  
> T is time.
>
> His explanation of the operation of this filter makes perfect  
> sense, but realizing it in Max/MSP is giving me problems.  I'm sure  
> there's a simple answer, but I'm just not getting it.
>
> How would one realize such an equation?  I appreciate your help!
>

----
Steven M. Miller
Professor, Contemporary Music Program
College of Santa Fe

Home 
SFIFEM 
Atrium Sound Space 
OVOS 
CMP 

Quote: Falk wrote on Fri, 04 January 2008 12:52

----------------------------------------------------

> Have a look at the bufir~ object. You can build finite response filters with up to 256 points.There is a patch in the examples folder called buffir-eq-help.pat using bufir~

I'm starting to see how buffir~ might help, but it's abstracted the problem in such a way that I don't really see how such an equation is really operating in the filter. Is there no way to build such a filter out of "rudimentary" objects?

Quote: Falk wrote on Fri, 04 January 2008 12:52
----------------------------------------------------
> Hi Brennon, 
>
> Have a look at the bufir~ object. You can build finite response filters with up to 256 points.There is a patch in the examples folder called buffir-eq-help.pat using bufir~
>

I'm starting to see how buffir~ might help, but it's abstracted the problem in such a way that I don't really see how such an equation is really operating in the filter.  Is there no way to build such a filter out of "rudimentary" objects?


Quote: lists@grahamwakefield wrote on Fri, 04 January 2008 12:56

---------------------------------------------------- 

> Unfortunately, you can't get a 1 sample delay in a feedback path in a 

> Max patch. You can use comb~ or biquad~ for example, but I don't 

> think that's the autodidactic answer you were looking for...

So, how are such filters built? In a separate language? If so, what language is common?

Quote: lists@grahamwakefield wrote on Fri, 04 January 2008 12:56
----------------------------------------------------   
> Unfortunately, you can't get a 1 sample delay in a feedback path in a  
> Max patch.  You can use comb~ or biquad~ for example, but I don't  
> think that's the autodidactic answer you were looking for...
>

So, how are such filters built?  In a separate language?  If so, what language is common?

Quote: smill wrote on Fri, 04 January 2008 13:13

> 1) FYI - I recently got an email from Gareth re: the Musimat 

> programming language he created to demo the ideas in the books. He 

> gave me some detailed info on getting it to run on Intel Macs. I'll 

> check with him to make sure it's OK to post the info here, and follow 

That would be wonderful! I've fought with MUSIMAT quite a bit on Mac OS X to no avail. Although it seems that most of the music/DSP-related functions he has created seem relatively easy to implement in another language (classes in Java, etc.), I'd like to be able to play with MUSIMAT, as well. Please send my congratulations to him on these two excellent volumes. I've also struggled my way through the Digital Audio Signal Processing anthology edited by Strawn, and Musimathics has done wonders to fill in the holes for me.

> 2) I believe you have the interpretation of the equation slightly 

> wrong: y is the output, x is the input. In a nutshell, a given output 

> sample y(nT) is produced by averaging the current x(nT) and most 

> previous x((n-1)T) inputs. There should, however, be some 

> coefficients in there, in this case to multiply each of the two 

> inputs by .5 before adding them, in order to average them. That's 

> what simple low-pass filtering is, averaging inputs to generate 

> outputs. You could achieve this in MSP by using [delay~] set to one 

> sample delay, and adding that to the direct signal after multiply the 

> delayed and direct signals by .5. This will then give you the 

> filtered (averaged) output. It achieves this by simply 'slowing down' 

> fast-changing signals (i.e. signals with high-frequency components).

Thank you for the patch (I was mistaken in believing that delay~ took as it's argument a number of milliseconds--not samples.) And yes, I did transpose x(n) and y(n)--thank you for drawing my attention to this. Either way, I do understand what the filter is doing, and it's nice to see it in action--even if it is merely a simple example. Just a note, Loy does specify this primitive lowpass filter without averaging (at least at this point in the text).

Quote: smill wrote on Fri, 04 January 2008 13:13
----------------------------------------------------
> A couple things:
>
> 1) FYI - I recently got an email from Gareth re: the Musimat  
> programming language he created to demo the ideas in the books. He  
> gave me some detailed info on getting it to run on Intel Macs. I'll  
> check with him to make sure it's OK to post the info here, and follow  
> up accordingly.
>

That would be wonderful!  I've fought with MUSIMAT quite a bit on Mac OS X to no avail.  Although it seems that most of the music/DSP-related functions he has created seem relatively easy to implement in another language (classes in Java, etc.), I'd like to be able to play with MUSIMAT, as well.  Please send my congratulations to him on these two excellent volumes.  I've also struggled my way through the Digital Audio Signal Processing anthology edited by Strawn, and Musimathics has done wonders to fill in the holes for me.

> 2) I believe you have the interpretation of the equation slightly  
> wrong: y is the output, x is the input. In a nutshell, a given output  
> sample y(nT) is produced by averaging the current x(nT) and most  
> previous x((n-1)T) inputs. There should, however, be some  
> coefficients in there, in this case to multiply each of the two  
> inputs by .5 before adding them, in order to average them. That's  
> what simple low-pass filtering is, averaging inputs to generate  
> outputs. You could achieve this in MSP by using [delay~] set to one  
> sample delay, and adding that to the direct signal after multiply the  
> delayed and direct signals by .5. This will then give you the  
> filtered (averaged) output. It achieves this by simply 'slowing down'  
> fast-changing signals (i.e. signals with high-frequency components).
>
> Hope this helps.
>

Thank you for the patch (I was mistaken in believing that delay~ took as it's argument a number of milliseconds--not samples.)  And yes, I did transpose x(n) and y(n)--thank you for drawing my attention to this.  Either way, I do understand what the filter is doing, and it's nice to see it in action--even if it is merely a simple example.  Just a note, Loy does specify this primitive lowpass filter without averaging (at least at this point in the text).

On Jan 4, 2008, at 12:56 PM, Graham Wakefield wrote:

> Well, you'd want to rearrange this to be in terms of the output 

> So you subtract a 1 sample delay of the output from the input. 

> Unfortunately, you can't get a 1 sample delay in a feedback path in 

> a Max patch. You can use comb~ or biquad~ for example, but I don't 

Again, to be correct, x is an input, y is the output, so the 

explanation here is a little off. There are, however, filters of this 

sort (output = average of input & output), but this isn't the same 

topology as the original question, which was an example of a simple 

averaging FIR filter. For FIR (finite impulse response) filters, no 

feedback is need. IIR filters need feedback.

A good reference for these types of filter equations is Dodge & Jerse 

'Computer Music, 2nd Ed.' (pp. 201-219), and/or Roads 'Computer Music 

>
> Well, you'd want to rearrange this to be in terms of the output  
> signal:
>
> x(nT) = y(nT) - x[(n-1)T]
>
> So you subtract a 1 sample delay of the output from the input.   
> Unfortunately, you can't get a 1 sample delay in a feedback path in  
> a Max patch.  You can use comb~ or biquad~ for example, but I don't  
> think that's the autodidactic answer you were looking for...

Again, to be correct, x is an input, y is the output, so the  
explanation here is a little off. There are, however, filters of this  
sort (output = average of input & output), but this isn't the same  
topology as the original question, which was an example of a simple  
averaging FIR filter. For FIR (finite impulse response) filters, no  
feedback is need. IIR filters need feedback.

A good reference for these types of filter equations is Dodge & Jerse  
'Computer Music, 2nd Ed.' (pp. 201-219), and/or Roads 'Computer Music  
Tutorial' (pp. 397-419).

On Jan 4, 2008, at 2:42 PM, Brennon wrote:

> That would be wonderful! I've fought with MUSIMAT quite a bit on 

> Mac OS X to no avail. Although it seems that most of the music/DSP- 

> related functions he has created seem relatively easy to implement 

> in another language (classes in Java, etc.), I'd like to be able to 

> play with MUSIMAT, as well. Please send my congratulations to him 

> on these two excellent volumes. I've also struggled my way through 

> the Digital Audio Signal Processing anthology edited by Strawn, and 

> Musimathics has done wonders to fill in the holes for me.

Agreed! I'll post the info here if/when he gives me the OK.

> Thank you for the patch (I was mistaken in believing that delay~ 

> took as it's argument a number of milliseconds--not samples.) And 

> yes, I did transpose x(n) and y(n)--thank you for drawing my 

> attention to this. Either way, I do understand what the filter is 

> doing, and it's nice to see it in action--even if it is merely a 

> simple example. Just a note, Loy does specify this primitive 

> lowpass filter without averaging (at least at this point in the text).

You're welcome. See another post I just sent on this thread for other 

references to filter equations & examples. Yes, Loy's example does 

omit the coefficients, but the classic examples I've seen all use 

them in order to do actual averaging rather than simple addition of 

successive samples. You can also manipulate the coefficients (as long 

as they all add up to 1) to change the characteristics of the filter, 

On Jan 4, 2008, at 2:42 PM, Brennon wrote:
>
> That would be wonderful!  I've fought with MUSIMAT quite a bit on  
> Mac OS X to no avail.  Although it seems that most of the music/DSP- 
> related functions he has created seem relatively easy to implement  
> in another language (classes in Java, etc.), I'd like to be able to  
> play with MUSIMAT, as well.  Please send my congratulations to him  
> on these two excellent volumes.  I've also struggled my way through  
> the Digital Audio Signal Processing anthology edited by Strawn, and  
> Musimathics has done wonders to fill in the holes for me.

>
> Thank you for the patch (I was mistaken in believing that delay~  
> took as it's argument a number of milliseconds--not samples.)  And  
> yes, I did transpose x(n) and y(n)--thank you for drawing my  
> attention to this.  Either way, I do understand what the filter is  
> doing, and it's nice to see it in action--even if it is merely a  
> simple example.  Just a note, Loy does specify this primitive  
> lowpass filter without averaging (at least at this point in the text).

You're welcome. See another post I just sent on this thread for other  
references to filter equations & examples. Yes, Loy's example does  
omit the coefficients, but the classic examples I've seen all use  
them in order to do actual averaging rather than simple addition of  
successive samples. You can also manipulate the coefficients (as long  
as they all add up to 1) to change the characteristics of the filter,  
as well.

Quote: smill wrote on Fri, 04 January 2008 14:51

> A good reference for these types of filter equations is Dodge & Jerse 

> 'Computer Music, 2nd Ed.' (pp. 201-219), and/or Roads 'Computer Music 

I do have the Dodge & Jerse. Thank you for drawing my attention to it again. I had pushed it to to the side when I started into Musimathics. I checked the Roads out of the library several times when I was a student, but never purchased it (quite pricey!) With what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and Allen Strange's "Electronic Music..."), do you think the Roads will give me much more (at this point?) In which areas might it be stronger?

Quote: smill wrote on Fri, 04 January 2008 14:51
----------------------------------------------------
>
> A good reference for these types of filter equations is Dodge & Jerse  
> 'Computer Music, 2nd Ed.' (pp. 201-219), and/or Roads 'Computer Music  
> Tutorial' (pp. 397-419).
>

I do have the Dodge & Jerse.  Thank you for drawing my attention to it again.  I had pushed it to to the side when I started into Musimathics.  I checked the Roads out of the library several times when I was a student, but never purchased it (quite pricey!)  With what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and Allen Strange's "Electronic Music..."), do you think the Roads will give me much more (at this point?)  In which areas might it be stronger?

> So, how are such filters built? In a separate language? If so, 

They are written in C. You can also write them in Java. You'll find an 

example of biquad in java in the "mxj~ examples" folder.

> So, how are such filters built?  In a separate language?  If so,  
> what language is common?

They are written in C. You can also write them in Java. You'll find an  
example of biquad in java in the "mxj~ examples" folder.

In terms of the specific filtering info, I don't think there's much 

'value added' in the Roads over the Dodge & Jerse. It is, however, in 

general more comprehensive and wide-ranging. I recently heard from 

Curtis that MIT Press gave the go-ahead on a new edition of it, 

though, so you might want to wait until it's out (he didn't give me a 

time frame...). I actually find that both books have strengths and 

have slightly different takes on similar material, which is a help in 

On Jan 4, 2008, at 3:11 PM, Brennon wrote:

> I do have the Dodge & Jerse. Thank you for drawing my attention to 

> it again. I had pushed it to to the side when I started into 

> Musimathics. I checked the Roads out of the library several times 

> when I was a student, but never purchased it (quite pricey!) With 

> what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and 

> Allen Strange's "Electronic Music..."), do you think the Roads will 

> give me much more (at this point?) In which areas might it be 

In terms of the specific filtering info, I don't think there's much  
'value added' in the Roads over the Dodge & Jerse. It is, however, in  
general more comprehensive and wide-ranging. I recently heard from  
Curtis that MIT Press gave the go-ahead on a new edition of it,  
though, so you might want to wait until it's out (he didn't give me a  
time frame...). I actually find that both books have strengths and  
have slightly different takes on similar material, which is a help in  
teaching.

> I do have the Dodge & Jerse.  Thank you for drawing my attention to  
> it again.  I had pushed it to to the side when I started into  
> Musimathics.  I checked the Roads out of the library several times  
> when I was a student, but never purchased it (quite pricey!)  With  
> what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and  
> Allen Strange's "Electronic Music..."), do you think the Roads will  
> give me much more (at this point?)  In which areas might it be  
> stronger?

A very nice book and a classic for intro to DSP with Java code in the back is:

Introductory Digital Signal Processing with Computer Applications, by

specially if using linear difference equations (as per the low pass

Their example of a low pass and derivatives are very clear and informative.

http://www.quantumbooks.com/p/03COMMS/0471976318

> In terms of the specific filtering info, I don't think there's much

> 'value added' in the Roads over the Dodge & Jerse. It is, however, in

> general more comprehensive and wide-ranging. I recently heard from

> Curtis that MIT Press gave the go-ahead on a new edition of it,

> though, so you might want to wait until it's out (he didn't give me a

> time frame...). I actually find that both books have strengths and

> have slightly different takes on similar material, which is a help in

> On Jan 4, 2008, at 3:11 PM, Brennon wrote:

> > I do have the Dodge & Jerse. Thank you for drawing my attention to

> > it again. I had pushed it to to the side when I started into

> > Musimathics. I checked the Roads out of the library several times

> > when I was a student, but never purchased it (quite pricey!) With

> > what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and

> > Allen Strange's "Electronic Music..."), do you think the Roads will

> > give me much more (at this point?) In which areas might it be

"You will never know what size worm is in your next byte"!

A very nice book and a classic for intro to DSP with Java code in the back is:
Introductory Digital Signal Processing with Computer Applications, by
Lynn and Fuerst

specially if using linear difference equations (as per the low pass
discussed here)

here:
http://www.quantumbooks.com/p/03COMMS/0471976318

On 04/01/2008, Steven Miller  wrote:
> In terms of the specific filtering info, I don't think there's much
> 'value added' in the Roads over the Dodge & Jerse. It is, however, in
> general more comprehensive and wide-ranging. I recently heard from
> Curtis that MIT Press gave the go-ahead on a new edition of it,
> though, so you might want to wait until it's out (he didn't give me a
> time frame...). I actually find that both books have strengths and
> have slightly different takes on similar material, which is a help in
> teaching.
>
>
> On Jan 4, 2008, at 3:11 PM, Brennon wrote:
>
> > I do have the Dodge & Jerse.  Thank you for drawing my attention to
> > it again.  I had pushed it to to the side when I started into
> > Musimathics.  I checked the Roads out of the library several times
> > when I was a student, but never purchased it (quite pricey!)  With
> > what I do have handy (Loy, Dodge & Jerse, the Strawn anthology, and
> > Allen Strange's "Electronic Music..."), do you think the Roads will
> > give me much more (at this point?)  In which areas might it be
> > stronger?
>
>
> ----
> Steven M. Miller
> Professor, Contemporary Music Program
> College of Santa Fe
>
> Home 
> SFIFEM 
> Atrium Sound Space 
> OVOS 
> CMP 
>
>
>

-- 
A Pereshaped definition of an Apple:
"You will never know what size worm is in your next byte"!


For 1st and 2nd order FIR and IIR filters biquad~ is your friend. For 

higher order filters there is the possibility of figuring out how to 

translate the coefficients so that you can use cascade~.

Or you can make your own filters in C or Java. ASAIR there is a filter 

example in the examples for mxj~. Java filters will be a bit less 

efficient than filters programmed in C, but it's way simpler to code 

audio objects in Java for mxj~, so it could be a good point of 

departure. There is also a filter example in the Max SDK.

Tim Place and myself are currently working on a new filter object that 

Building a Filter