Building a Filter

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~

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

have fun

falk

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.

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...

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.

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.

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

>
> 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
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Atrium Sound Space
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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?

Thanks again,
Brennon

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).

Thank you again,
Brennon

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
> 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).

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

Home
SFIFEM
Atrium Sound Space
OVOS
CMP

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,
as well.

>

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

Home
SFIFEM
Atrium Sound Space
OVOS
CMP

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?

Thanks,
Brennon