/*! \page filtering Using Filters

In this section, we demonstrate the use of a few of the STK filter classes.  The Filter class provides functionality to implement a generalized digital filter of any type, similar to the \c filter function in Matlab.  In this example, we create a Filter instance and initialize it with specific numerator and denominator coefficients.  We then compute its impulse response for 20 samples.

\code
#include "Filter.h"

int main()
{
  StkFrames output( 20, 1 );   // initialize StkFrames to 20 frames and 1 channel (default: interleaved)
  output[0] = 1.0;

  std::vector<StkFloat> numerator( 5, 0.1 ); // create and initialize numerator coefficients
  std::vector<StkFloat> denominator;         // create empty denominator coefficients
  denominator.push_back( 1.0 );              // populate our denomintor values
  denominator.push_back( 0.3 );
  denominator.push_back( -0.5 );

  Filter filter( numerator, denominator );

  filter.tick( output );
  for ( unsigned int i=0; i<output.size(); i++ ) {
    std::cout << "i = " << i << " : output = " << output[i] << std::endl;
  }

  return 0;
}
\endcode

The Filter class implements the standard difference equation
\code
 a[0]*y[n] = b[0]*x[n] + ... + b[nb]*x[n-nb] - a[1]*y[n-1] - ... - a[na]*y[n-na],
\endcode

where "b" values are numerator coefficients and "a" values are denominator coefficients.  Note that if the first denominator coefficient is not 1.0, the Filter class automatically normalizes all filter coefficients by that value.  The coefficient values are passed to the Filter class via a C++ <a href="http://www.roguewave.com/support/docs/sourcepro/stdlibref/vector.html">vector</a>, a container object provided by the C++ Standard Library.

Most STK classes use more specific types of digital filters, such as the OneZero, OnePole, TwoPole, or BiQuad varieties.  These classes inherit from the Filter class and provide specific functionality particular to their use, as well as functions to independently control individual coefficient values.

\section reson Resonances:

The STK BiQuad and TwoPole classes provide functionality for creating resonance filters.  The following example demonstrates how to create a resonance centered at 440 Hz that is used to filter the output of a Noise generator.

\code
#include "BiQuad.h"
#include "Noise.h"

int main()
{
  StkFrames output( 20, 1 );   // initialize StkFrames to 20 frames and 1 channel (default: interleaved)
  Noise noise;

  BiQuad biquad;
  biquad.setResonance( 440.0, 0.98, true ); // automatically normalize for unity peak gain

  for ( unsigned int i=0; i<output.size(); i++ ) {
    output[i] = biquad.tick( noise.tick() );  // single-sample computations
    std::cout << "i = " << i << " : output = " << output[i] << std::endl;
  }

  return 0;
}
\endcode

By passing a boolian value of \c true as the third argument to the BiQuad::setResonance() function, the filter coefficients are automatically scaled to achieve unity gain at the resonance peak frequency.  The previous code could be easily modified for "vector-based" calculations:

\code
#include "BiQuad.h"
#include "Noise.h"

int main()
{
  StkFrames output( 20, 1 );   // initialize StkFrames to 20 frames and 1 channel (default: interleaved)
  Noise noise;

  BiQuad biquad;
  biquad.setResonance( 440.0, 0.98, true ); // automatically normalize for unity peak gain

  biquad.tick( noise.tick( output ) );      // vector-based computations
  for ( unsigned int i=0; i<output.size(); i++ ) {
    std::cout << "i = " << i << " : output = " << output[i] << std::endl;
  }

  return 0;
}
\endcode

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*/