# onepole~

## Description

The onepole~ object implements the simplest of IIR filters, providing a 6dB per octave attenuation. This filter is very efficient and useful for gently rolling off harsh high end and for smoothing out control signals.

## Discussion

The standard difference equation for this filter is

y(n) = a_{0} x(n) + b_{1} y(n-1)
Where

b_{1} = 1 - a_{0}

which can be factored down to

y(n) = y(n-1) + a_{0}[ x(n) - y(n-1) ]

As the value of the a_{0} coefficient is lowered (b_{1} increases) the input will be increasingly smoothed and the effective cutoff frequency (f_c) lowered. Calculating the a_0 coefficient from the f_c cutoff frequency is performed with the equation

a_{0} = sin(f_c * (pi/nyquist))

where f_s is the sampling frequency and f_c the cutoff frequency expressed in Hertz. onepole~ is a more efficient implementation of a biquad~ object with the following coefficients:

a_{0} &= a_{0}
a_{1} &= 0
a_{2} &= 0
b_{1} &= -b_{1}
b_{2} &= 0
Note the sign flip for b_{1} as biquad uses flipped signs for the feedback coefficients.

## Arguments

### center-frequency [float]

Optional
Unitshz

Sets the center frequency for the filter, as described above.

Optional

Using the symbols Hz, linear, or radians for an optional second argument sets the frequency input mode. The default mode is Hz (which is the same as providing no mode argument). Using the linear argument sets the frequency input mode to linear (0 - 1). Using the radians argument sets the frequency input mode to radians (0 - 1).

## Attributes

### annotation [symbol]

Sets the text that will be displayed in the Clue window when the user moves the mouse over the object.

### background [int] (default: 0)

Adds or removes the object from the patcher's background layer. background 1 adds the object to the background layer, background 0 removes it. Objects in the background layer are shown behind all objects in the default foreground layer.

### color [4 floats]

Sets the color for the object box outline.

### fontface [int]

Sets the type style used by the object. The options are:

plain
bold
italic
bold italic Possible values:

0 = 'regular'
1 = 'bold'
2 = 'italic'
3 = 'bold italic'

### fontname [symbol]

Sets the object's font.

### fontsize [float]

Sets the object's font size (in points). Possible values:

'8'
'9'
'10'
'11'
'12'
'13'
'14'
'16'
'18'
'20'
'24'
'30'
'36'
'48'
'64'
'72'

### hidden [int] (default: 0)

Toggles whether an object is hidden when the patcher is locked.

### hint [symbol]

Sets the text that will be displayed in as a pop-up hint when the user moves the mouse over the object in a locked patcher.

### ignoreclick [int] (default: 0)

Toggles whether an object ignores mouse clicks in a locked patcher.

JS Painter File

### patching_rect [4 floats] (default: 0. 0. 100. 0.)

Sets the position and size of the object in the patcher window.

### position [2 floats]

g/s(set)

Sets the object's x and y position in both patching and presentation modes (if the object belongs to its patcher's presentation), leaving its size unchanged.

### presentation [int] (default: 0)

Sets whether an object belongs to the patcher's presentation.

### presentation_rect [4 floats] (default: 0. 0. 0. 0.)

Sets the x and y position and width and height of the object in the patcher's presentation, leaving its patching position unchanged.

### rect [4 floats]

g/s(set)

Sets the x and y position and width and height of the object in both patching and presentation modes (if the object belongs to its patcher's presentation).

### size [2 floats]

g/s(set)

Sets the object's width and height in both patching and presentation modes (if the object belongs to its patcher's presentation), leaving its position unchanged.

### textcolor [4 floats]

Sets the color for the object's text in RGBA format.

### textjustification [int]

Sets the justification for the object's text. Possible values:

0 = 'left'
1 = 'center'
2 = 'right'

### varname [symbol]

Sets the patcher's scripting name, which can be used to address the object by name in pattr, scripting messages to thispatcher, and the js object.

## Messages

### int

#### Arguments

center-frequency (Hz) [int]
In right inlet: Sets the frequency for the filter (if no signal is connected). By default, frequency is expressed in Hz, where the allowable range is from 0 to one fourth of the current sampling rate. For convenience, onepole~ has two additional input modes that use the more conventional input range, 0 - 1 (see the linear and radians messages).

### float

#### Arguments

center-frequency (Hz or 0 through 1 specified by object-argument) [float]
In right inlet: Sets the frequency for the filter (if no signal is connected). By default, frequency is expressed in Hz, where the allowable range is from 0 to one fourth of the current sampling rate. For convenience, onepole~ has two additional input modes that use the more conventional input range, 0 - 1 (see the linear and radians messages).

### Hz

In either inlet: Sets the frequency input mode to Hz (the default).
In either inlet: Clears the internal state of onepole~. Since onepole~ does not have the inherent instability of other filter types, this should never be necessary.

### linear

In either inlet: Sets the frequency input mode to linear (0 - 1). Linear mode is simply a scaled version of the standard Hz mode, except that values in the 0-1 range traverses the full frequency range.

In either inlet: Sets the frequency input mode to radians (0 - 1). Radians mode lets you set the center frequency (f_c) of the equation directly, while the input has the same range (0-1), the output has a curved frequency response that is closer to the exponential pitch scale of the human ear.

### signal

In left inlet: Signal to be filtered.

In right inlet: A signal can be used to set the frequency for the filter, with the same effect as a float. If a signal is connected to this inlet, its value is sampled once every signal vector.

## Output

### signal

The filtered signal.