Gtaylor@rtqe.net at 15:31, 28 June 2012

2012-06-28T15:31:22Z

Admin at 21:15, 25 June 2012

2012-06-25T21:15:06Z

Admin: Created page with "Click here to open the tutorial patch: 02fVariableTypeFilters.maxpat In the last tutorial we introduced some basic filters in MSP. This tutorial looks at two new filter o..."

2012-06-22T21:20:38Z

Created page with "Click here to open the tutorial patch: 02fVariableTypeFilters.maxpat In the last tutorial we introduced some basic filters in MSP. This tutorial looks at two new filter o..."

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Click here to open the tutorial patch: [[02fVariableTypeFilters.maxpat]]

In the last tutorial we introduced some basic filters in MSP. This tutorial
looks at two new filter objects: {{maxword|name=biquad~}}, which can create any kind of
simple filter, and {{maxword|name=cascade~}}, which can create and manage multiple
independent filters in a single object. We'll also look at a user interface
object that helps us edit these filters in an intuitive way.

===Biquadratic filters===

* Look at the tutorial patcher. Just as in the last tutorial, area <code>1</code> consists
of a looping playback system that plays a {{maxword|name=buffer~}} using the {{maxword|name=groove~}} object. Turn on the audio, turn up the {{maxword|name=number}} box labeled 'Dry Volume', click on a
note in the {{maxword|name=kslider}}, and make sure you can hear some sound.

* Take a look at area <code>2</code> of the tutorial. The sound from the {{maxword|name=groove~}}
object feeds into an object called {{maxword|name=biquad~}}. Turn down the 'Dry Volume'
and turn up the {{maxword|name=number}} box labeled 'Biquad Volume'. Click on the different
circles in the {{maxword|name=preset}} object at the top of patcher aread <code>2</code>.
Listen to the changes in the sound.

In the last tutorial, we discussed how filters could be expressed as equations, e.g.

yn = 0.5xn + 0.5yn-1

The <code>0.5</code> values in the equation above set the respective gains of the
different samples used in the filter. If we wanted a more flexible filter,
we could generalize this filter so that those numbers are variable, e.g.:

yn = Axn + Byn-1

By modifying the values of <code>A</code> and <code>B</code>, we could control the frequency
response of this filter. While the math behind this operation is beyond the scope
of this tutorial, it's generally true that the more energy given to the delayed
output sample (the yn-1 term), the smoother the output and the more
the high frequencies are supressed.

A fairly standard tactic in digital filter design is to create a filter equation
that can perform any kind of standard filtering operation (lowpass, bandpass,
etc.) on an input signal. The most common implementation of this is called
the ''biquadratic filter equation'' (or ''biquad''). It consists of
the following equation:

yn = Axn + Bxn-1 + Cxn-2 - Dyn-1 - Eyn-2

This equation uses the incoming sample, the ''last two'' incoming samples,
and the last two ''outgoing'' samples to generate its filter (another term
for a biquadratic filter is a ''two-pole'', ''two-zero'' filter, because
it has four delay coefficients to affect its behavior). By adjusting the
five ''coefficients'' (A, B, C, D, E), you can generate all manner of filters.
The MSP {{maxword|name=biquad~}} object implements a biquadratic filter. Unfortunately,
it takes as its input the input signal and the five coefficients that define
the filter. What we really want to do, though, is specify our filter not by
the equation, but by how we want it to sound.

===The {{maxword|name=filtergraph~}} object===

The user-interface object connected to the {{maxword|name=biquad~}} object in the tutorial
patcher is called a {{maxword|name=filtergraph~}}. It allows us to physically drag around
within a box to set parameters of a filter. In addition, you can send messages
to a {{maxword|name=filtergraph~}} object to set its parameters, as well as change what
kind of filter it shows. Whenever you make a change to the {{maxword|name=filtergraph~}}
object, it outputs a set of coefficients as a Max list which the {{maxword|name=biquad~}}
object interprets to perform the equivalent filter equation. The {{maxword|name=message}} box
below the {{maxword|name=filtergraph~}} in the patcher shows us these coefficients.

* Using the {{maxword|name=umenu}} object, select a <code>lowpass</code> filter from the
{{maxword|name=filtergraph~}}. Using the mouse, click and drag in the pink region
in the middle of the filter response. You can adjust the cutoff frequency
of the filter as well as its overall gain. Click on the edges of the pink
region and drag inward and outward. This allows you to set the resonance of
the filter. The values you are creating (in terms of cutoff frequency, gain,
and slope) can be seen in the <link type="refpage" name="number">number box</link> objects to the right of the object.

The {{maxword|name=filtergraph~}} object is capable of graphing and generating
coefficients for a wide variety of filter curves, including lowpass,
highpass, bandpass, bandstop (or notch), ''peaknotch'' (a band filter
that can either boost or cut a frequency band), ''lowshelf / highshelf''
(filters that can boost or cut frequencies lower or higher than a cutoff),
''resonant'' (a bandpass filter where its gain increasing with the Q),
and ''allpass'' (a filter that changes the phase relationships of frequencies
without altering their gains). All of these filters can be modeled by
a {{maxword|name=biquad~}} object.

* Acclimatize yourself to the user interface of the {{maxword|name=filtergraph~}}
object by selecting different filter types from the {{maxword|name=umenu}} and
dragging around to create different filters. Note that some filters
have inherently more potential gain than others.

===Filters in series: {{maxword|name=cascade~}}===

Filtering plays a huge role in audio-related creative work, whether we're
discussing contemporary music production techniques or avant-garde sound art.
It's often the case that a simple filter that only affects one range of frequencies
isn't enough to perform the task we want. You can easily chain {{maxword|name=biquad~}} objects
(or other filters) by hand in an MSP patcher to create filters operating in series.
If you have an idea of how many filters you want to operate in this manner, you
can instead use a single object that creates and manages up to 24 different filters
arranged in series: {{maxword|name=cascade~}}.

* Turn down the 'Biquad Volume' and turn your attention to area <code>3</code> of the
tutorial patcher. Turn up the 'Cascade Volume' {{maxword|name=number}} box and click on the
different selections in the {{maxword|name=preset}} object. Notice how the sound changes.
Using the {{maxword|name=number}} box labeled 'Select a filter', send the message
<code>selectfilt 0</code> to the {{maxword|name=filtergraph~}} in this part of the patcher.
Change the {{maxword|name=number}} box to <code>1</code>, <code>2</code>, <code>3</code>, and <code>4</code>,
and see how different component filters within the {{maxword|name=filtergraph~}} highlight
themselves. The settings for each of these filters also comes out of the object,
setting the <link type="refpage" name="number">number box</link> objects to the right.

As we can see, the {{maxword|name=filtergraph~}} object is capable of maintaining the
state of more than one filter and showing us what the frequency response of
these filters would be if they were connected in series. The {{maxword|name=cascade~}} object
takes a signal in its left inlet and a set of coefficients in its right,
interpreting each incoming list as sets of 5 values, one set for each filter.

* Pick a {{maxword|name=preset}} setting you like for the {{maxword|name=cascade~}} object.
Select a filter to edit with the <code>selectfilt</code> message, and drag your
mouse in the {{maxword|name=filtergraph~}} to edit the filter. Notice how the filters
interact with one another. For example, a lowpass filter set at the same
frequency as a highpass filter will cancel one another out. Similarly,
a bandpass filter can sit at the 'slope' of a lowpass filter to simulate
a resonation point.

If we unlock the patcher and open the
<link type="vignette" module="core" name="inspector">Inspector</link>
for the {{maxword|name=filtergraph~}} object, we can edit the specific types of
filters that it generates coefficients for; in addition, we could change
how many filters are maintained and some features of the user interface.
By the opposite token, if you'd rather work with filters without a user
interface, the MSP object {{maxword|name=filtercoeff~}} takes the same settings
as the {{maxword|name=filtergraph~}} object without a graphical component, allowing
you to feed coefficients to a {{maxword|name=biquad~}} or {{maxword|name=cascade~}} object
without having to graph the filter yourself.

===Summary===

The {{maxword|name=biquad~}} object implements a generic filter equation that can
model most types of simple filters. Because it expects coefficients for
the filter equation, its often useful to use it in conjunction with
another object that will compute these numbers. The {{maxword|name=filtergraph~}}
object is a user-interface object that lets you visually construct simple
and complex filters of many types; the {{maxword|name=filtercoeff~}} object will
accomplish the same thing, without the user interface. The {{maxword|name=cascade~}}
object acts as a group of {{maxword|name=biquad~}} objects arranged in ''series'',
and allows you to easily construct compound filter curves in your patcher.

===See Also===

{{maxword|name=biquad~}} - Two-pole, two-zero filter

{{maxword|name=filtergraph~}} - Graphical filter editor

{{maxword|name=cascade~}} - Cascaded series of biquad filters

{{maxword|name=filtercoeff~}} - Signal-rate filter coefficient generator

[[Category:Teaching Material]]

← Older revision		Revision as of 15:31, 28 June 2012
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−	Click here to open the tutorial patch: [[02fVariableTypeFilters.maxpat]]	+	Click here to open the tutorial patch: [[Media:02fVariableTypeFilters.maxpat]]

	In the first filter tutorial, we introduced some basic filters in MSP. This tutorial looks at two new filter objects: {{maxword\|name=biquad~}}, which can create any kind of simple filter, and {{maxword\|name=cascade~}}, which can create and manage multiple independent filters in a single object. We'll also look at a user interface object that helps us edit these filters in an intuitive way.		In the first filter tutorial, we introduced some basic filters in MSP. This tutorial looks at two new filter objects: {{maxword\|name=biquad~}}, which can create any kind of simple filter, and {{maxword\|name=cascade~}}, which can create and manage multiple independent filters in a single object. We'll also look at a user interface object that helps us edit these filters in an intuitive way.

MSP Filter Tutorial 2: Variable Type Filters - Revision history

Gtaylor@rtqe.net at 15:31, 28 June 2012

Admin at 21:15, 25 June 2012

Admin: Created page with "Click here to open the tutorial patch: 02fVariableTypeFilters.maxpat In the last tutorial we introduced some basic filters in MSP. This tutorial looks at two new filter o..."