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### Oonepole

INSTRUMENT design -- simple one-pole filter object

The Oonepole object instantiates a simple one-pole IIR filter, based on designs found in Computer Music: Synthesis, Composition, and Performance by Charles Dodge and Thomas Jerse and the Synthesis ToolKit (STK) authored by Perry Cook and Gary Scavone. The general recursive filter equation used for this object is:
```y[n] = a*x[n] + b*y[n-1]
```
where y[n] and y[n-1] are the current and previous outputs of the equation, respectively, and x[n] is the current input. a and b are the coefficients to the equation that determine what kind of filter is constructed. Simple low-pass and high-pass filters are possible with characteristics depending upon the values of the a and b coefficients.

The OonepoleTrack object does the same thing as Oonepole except that it 'tracks' changes to the state of the filter and only performs computations if the cutoff frequency or lag time of the filter has changed. More generally, the older functions reson and resonz do similar kinds of filtering operations. See also the Oequalizer object for filtering capabilities.

### Constructors

Oonepole(float SR)

SR is the current sampling rate (an Instrument class variable).

The coefficient a in the filter equation will be set to the value 0.1, and the coefficient b in the filter equation will be 0.9 (a smooth low-pass filter).

Oonepole(float SR, float freq)

SR is the current sampling rate (an Instrument class variable).
freq sets the cutoff point for the filter. If freq is positive it will be set up as a low-pass filter, if freq is negative it will be a high-pass filter. The values for the coefficients a and b in the filter equation will be set accordingly.

### Access Methods

void Oonepole::setfreq(float freq)

sets the cutoff point of the constructed filter to freq.

void Oonepole::setlag(float lag)

is an alternative to the setfreq method for use in control-rate signals. The lag determines how long the filter will take to travel to the next data point. lag is in the range [0, 1] and is inversely proportional to the way the cutoff frequency operates. Values closer to 1 will result in lower cutoff frequencies. The conversion to filter cutoff frequency is:
``` #define LAGFACTOR 12.0
#define MAXCF     500.0

cutoff = MAXCF * pow(2, -lag * LAGFACTOR);
```
John Gibson determined the parameters in order to achieve a linear "feel" to the lag range.

void Oonepole::clear()

will reinitialize the filter by setting the 'past history' of this recursive filter to 0.0.

void Oonepole::setpole(float coefficient)

sets the "b" term of the filter equation:
```y[n] = a*x[n] + b*y[n-1]
```
to coefficient. The "a" term is set to 1.0 - coefficient if "b" is greater than 0.0, otherwise it is set to 1.0 + coefficient.

float Oonepole::next(float input)

returns the next floating-point sample value from the filter and places an incoming sample into the filter (input).

### Examples

```#include <Ougens.h>

Oonepole *thefilt;

// this instrument has a delay line
int MYINSTRUMENT::init(float p[], int n_args)
{

...

thefilt = new Oonepole(SR, -100.0); // high-pass filter, cutoff at 100.0 Hz

...

}

int MYINSTRUMENT::run()
{
float out[2];
float sample;

...

for (int i = 0; i < framesToRun(); i++)
{
sample = someSampleGeneratingProcess();
out[0] = thefilt->next(sample);
}

...

}
```