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pp::Filters::ButterworthFilter Class Template Reference

Here's a bit from an article by Arun Chandra at: http://ems.music.uiuc.edu/news/fall94/news.html. More...

#include <Filters.h>

Inheritance diagram for pp::Filters::ButterworthFilter

[legend]Collaboration diagram for pp::Filters::ButterworthFilter:

[legend]List of all members.

Public Methods
	ButterworthFilter (float a1=0.5f, float a2=0.5f, float a3=0.5f, float b1=0.5f, float b2=0.5f)
void	SetNotchCoefficients (int fc, int sr, float r)
void	SetLowPassCoefficients (int fc, int sr)
void	SetBandPassCoefficients (int fc, int sr, int bw)
	But for a band-pass filter, the coefficients are: . More...
void	SetFastBandpassCoefficients (int fc, int sr, float r)
virtual const char*	GetName () const
void	SetCoefficients (float a1, float a2, float a3, float b1, float b2)
void	GetCoefficients (float& a1, float& a2, float& a3, float& b1, float& b2) const
float	GetA1 () const
float	GetA2 () const
float	GetA3 () const
float	GetB1 () const
float	GetB2 () const
void	SetA1 (float a1)
void	SetA2 (float a2)
void	SetA3 (float a3)
void	SetB1 (float b1)
void	SetB2 (float b2)
T	operator() (const T& x)
double	FrequencyResponse (float f)

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Detailed Description

template<typename T = short> template class pp::Filters::ButterworthFilter

Here's a bit from an article by Arun Chandra at: http://ems.music.uiuc.edu/news/fall94/news.html.

         An intriguing aspect of Butterworth filters is that merely by 
         changing the coefficients, you can change the behavior of the 
         filter from low-pass to high-pass to band-pass to band-reject. 
         All Butterworth filters use the following algorithm: 

         y(n) = a1*x(n) + a2*x(n-1) + a3*x(n-2) - b1*y(n-1) - b2*y(n-2) 

         As you can see, this filter has two input taps x(n-1) and x(n-2), 
         and two output taps y(n-1) and y(n-2). To get a low-pass filter, 
         the coefficients a1, a2, a3, b1, b2 are calculated thusly: 

         fc = cutoff frequency 
         sr = sample rate
         C  = tan(pi*fc/sr) 
         a1 = 1 / (1 + sqrt(2)*C + C*C) 
         a2 = 2*a1 
         a3 = a1 
         b1 = 2 * (1 - C*C) * a1 
         b2 = (1 - sqrt(2)*C + C*C) * a1 


         But for a band-pass filter, the coefficients are: 

         fc = center frequency 
         sr = sample rate
         bw = band width 
         
         C = 1 / tan(pi*bw/sr)
         D = 2 * cos(2*pi*fc/sr)
         a1 = pow((1+C), -1);
         a2 = 0 
         a3 = -a1 
         b1 = -C * D * a1 
         b2 = (C - 1) * a1 
         

The frequency response is given by (a1*cos(2*pi*df)+a2*cos(2*2*df)+a3*cos(2*3*df))/(1-b1*cos(2*pi*f)-b2*cos(2*2*pi*f))

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Member Function Documentation

template<typenameT = short> void pp::Filters::ButterworthFilter<T>::SetBandPassCoefficients ( int fc, int sr, int bw ) [inline]

But for a band-pass filter, the coefficients are: . fc = center frequency sr = sample rate bw = band width C = 1 / tan(pi*bw/sr) D = 2 * cos(2*pi*fc/sr) a1 = pow((1+C), -1); a2 = 0 a3 = -a1 b1 = -C * D * a1 b2 = (C - 1) * a1 \endverbatim

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The documentation for this class was generated from the following file:

• /home/pcburns/c/penguinsound/include/PenguinSound/Filters.h

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