dsp::FilterDesign< FloatType > Struct Template Reference
juce_dsp » filter_design

This class provides a set of functions which generates FIR::Coefficients and IIR::Coefficients, of high-order low-pass filters. More...

## Classes

struct | IIRPolyphaseAllpassStructure
| The structure returned by the function designIIRLowpassHalfBandPolyphaseAllpassMethod. More...

## Public Types

using | FIRCoefficientsPtr = typename FIR::Coefficients< FloatType >::Ptr
using | IIRCoefficients = typename IIR::Coefficients< FloatType >
using | WindowingMethod = typename WindowingFunction< FloatType >::WindowingMethod

## Static Public Member Functions

static FIRCoefficientsPtr | designFIRLowpassWindowMethod (FloatType frequency, double sampleRate, size_t order, WindowingMethod type, FloatType beta=static_cast< FloatType >(2))
| This method generates a FIR::Coefficients for a low-pass filter, using the windowing design method, applied to a sinc impulse response. More...
static FIRCoefficientsPtr | designFIRLowpassKaiserMethod (FloatType frequency, double sampleRate, FloatType normalisedTransitionWidth, FloatType amplitudedB)
| This a variant of the function designFIRLowpassWindowMethod, which allows the user to specify a transition width and a negative gain in dB, to get a low-pass filter using the Kaiser windowing function, with calculated values of the filter order and of the beta parameter, to satisfy the constraints. More...
static FIRCoefficientsPtr | designFIRLowpassTransitionMethod (FloatType frequency, double sampleRate, size_t order, FloatType normalisedTransitionWidth, FloatType spline)
| This method is also a variant of the function designFIRLowpassWindowMethod, using a rectangular window as a basis, and a spline transition between the pass band and the stop band, to reduce the Gibbs phenomenon. More...
static FIRCoefficientsPtr | designFIRLowpassLeastSquaresMethod (FloatType frequency, double sampleRate, size_t order, FloatType normalisedTransitionWidth, FloatType stopBandWeight)
| This method generates a FIR::Coefficients for a low-pass filter, by minimizing the average error between the generated filter and an ideal one using the least squares error criterion and matrices operations. More...
static FIRCoefficientsPtr | designFIRLowpassHalfBandEquirippleMethod (FloatType normalisedTransitionWidth, FloatType amplitudedB)
| This method generates a FIR::Coefficients for a low-pass filter, with a cutoff frequency at half band, using an algorithm described in the article "Design of Half-Band FIR Filters for Signal Compression" from Pavel Zahradnik, to get an equiripple like high order FIR filter, without the need of an iterative method and convergence failure risks. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRLowpassHighOrderButterworthMethod (FloatType frequency, double sampleRate, FloatType normalisedTransitionWidth, FloatType passbandAmplitudedB, FloatType stopbandAmplitudedB)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band and in the stop band. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRLowpassHighOrderButterworthMethod (FloatType frequency, double sampleRate, int order)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band and in the stop band. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRHighpassHighOrderButterworthMethod (FloatType frequency, double sampleRate, int order)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase high-pass filter without any ripple in the pass band and in the stop band. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRLowpassHighOrderChebyshev1Method (FloatType frequency, double sampleRate, FloatType normalisedTransitionWidth, FloatType passbandAmplitudedB, FloatType stopbandAmplitudedB)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the stop band only. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRLowpassHighOrderChebyshev2Method (FloatType frequency, double sampleRate, FloatType normalisedTransitionWidth, FloatType passbandAmplitudedB, FloatType stopbandAmplitudedB)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band only. More...
static ReferenceCountedArray< IIRCoefficients > | designIIRLowpassHighOrderEllipticMethod (FloatType frequency, double sampleRate, FloatType normalisedTransitionWidth, FloatType passbandAmplitudedB, FloatType stopbandAmplitudedB)
| This method returns an array of IIR::Coefficients, made to be used in cascaded IIR::Filters, providing a minimum phase low-pass filter with ripples in both the pass band and in the stop band. More...
static IIRPolyphaseAllpassStructure | designIIRLowpassHalfBandPolyphaseAllpassMethod (FloatType normalisedTransitionWidth, FloatType stopbandAmplitudedB)
| This method generates arrays of IIR::Coefficients for a low-pass filter, with a cutoff frequency at half band, using an algorithm described in the article "Digital Signal Processing Schemes for efficient interpolation and decimation" from Pavel Valenzuela and Constantinides. More...

## Detailed Description

### template<typename FloatType>
struct dsp::FilterDesign< FloatType >

This class provides a set of functions which generates FIR::Coefficients and IIR::Coefficients, of high-order low-pass filters.

They can be used for processing directly audio as an equalizer, in resampling algorithms etc.

see FIRFilter::Coefficients, FIRFilter, WindowingFunction, IIRFilter::Coefficients, IIRFilter

## Member Typedef Documentation

## FIRCoefficientsPtr

template<typename FloatType >

using dsp::FilterDesign< FloatType >::FIRCoefficientsPtr = typename FIR::Coefficients<FloatType>::Ptr

## IIRCoefficients

template<typename FloatType >

using dsp::FilterDesign< FloatType >::IIRCoefficients = typename IIR::Coefficients<FloatType>

## WindowingMethod

template<typename FloatType >

using dsp::FilterDesign< FloatType >::WindowingMethod = typename WindowingFunction<FloatType>::WindowingMethod

## Member Function Documentation

## designFIRLowpassWindowMethod()

template<typename FloatType >

static FIRCoefficientsPtr dsp::FilterDesign< FloatType >::designFIRLowpassWindowMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | size_t | order,
|  | WindowingMethod | type,
|  | FloatType | beta = `static_cast< FloatType >(2)`
| ) |  |

static

This method generates a FIR::Coefficients for a low-pass filter, using the windowing design method, applied to a sinc impulse response.

It is one of the simplest method used to generate a high order low-pass filter, which has the downside of needing more coefficients than more complex method to perform a given attenuation in the stop band.

It generates linear phase filters coefficients.

Note: The flatTop WindowingMethod generates an impulse response with a maximum amplitude higher than one, and might be normalised if necessary depending on the applications.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  order | the order of the filter
  type | the type, must be a WindowingFunction::WindowingType
  beta | an optional additional parameter useful for the Kaiser windowing function

## designFIRLowpassKaiserMethod()

template<typename FloatType >

static FIRCoefficientsPtr dsp::FilterDesign< FloatType >::designFIRLowpassKaiserMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | amplitudedB
| ) |  |

static

This a variant of the function designFIRLowpassWindowMethod, which allows the user to specify a transition width and a negative gain in dB, to get a low-pass filter using the Kaiser windowing function, with calculated values of the filter order and of the beta parameter, to satisfy the constraints.

It generates linear phase filters coefficients.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  amplitudedB | the maximum amplitude in dB expected in the stop band (must be negative)

## designFIRLowpassTransitionMethod()

template<typename FloatType >

static FIRCoefficientsPtr dsp::FilterDesign< FloatType >::designFIRLowpassTransitionMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | size_t | order,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | spline
| ) |  |

static

This method is also a variant of the function designFIRLowpassWindowMethod, using a rectangular window as a basis, and a spline transition between the pass band and the stop band, to reduce the Gibbs phenomenon.

It generates linear phase filters coefficients.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  order | the order of the filter
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  spline | between 1.0 and 4.0, indicates how much the transition is curved, with 1.0 meaning a straight line

## designFIRLowpassLeastSquaresMethod()

template<typename FloatType >

static FIRCoefficientsPtr dsp::FilterDesign< FloatType >::designFIRLowpassLeastSquaresMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | size_t | order,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | stopBandWeight
| ) |  |

static

This method generates a FIR::Coefficients for a low-pass filter, by minimizing the average error between the generated filter and an ideal one using the least squares error criterion and matrices operations.

It generates linear phase filters coefficients.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  order | the order of the filter
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  stopBandWeight | between 1.0 and 100.0, indicates how much we want attenuation in the stop band, against some oscillation in the pass band

## designFIRLowpassHalfBandEquirippleMethod()

template<typename FloatType >

static FIRCoefficientsPtr dsp::FilterDesign< FloatType >::designFIRLowpassHalfBandEquirippleMethod | ( | FloatType | normalisedTransitionWidth,
|  | FloatType | amplitudedB
| ) |  |

static

This method generates a FIR::Coefficients for a low-pass filter, with a cutoff frequency at half band, using an algorithm described in the article "Design of Half-Band FIR Filters for Signal Compression" from Pavel Zahradnik, to get an equiripple like high order FIR filter, without the need of an iterative method and convergence failure risks.

It generates linear phase filters coefficients.

Parameters

  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  amplitudedB | the maximum amplitude in dB expected in the stop band (must be negative)

## designIIRLowpassHighOrderButterworthMethod() [1/2]

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRLowpassHighOrderButterworthMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | passbandAmplitudedB,
|  | FloatType | stopbandAmplitudedB
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band and in the stop band.

The algorithms are based on "Lecture Notes on Elliptic Filter Design" by Sophocles J. Orfanidis.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  passbandAmplitudedB | the highest gain in dB expected in the pass band (must be negative)
  stopbandAmplitudedB | the gain in dB expected in the stop band (must be negative)

## designIIRLowpassHighOrderButterworthMethod() [2/2]

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRLowpassHighOrderButterworthMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | int | order
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band and in the stop band.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  order | the order of the resulting IIR filter, providing an attenuation of -6 dB times order / octave

## designIIRHighpassHighOrderButterworthMethod()

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRHighpassHighOrderButterworthMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | int | order
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase high-pass filter without any ripple in the pass band and in the stop band.

Parameters

  frequency | the cutoff frequency of the high-pass filter
  sampleRate | the sample rate being used in the filter design
  order | the order of the resulting IIR filter, providing an attenuation of -6 dB times order / octave

## designIIRLowpassHighOrderChebyshev1Method()

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRLowpassHighOrderChebyshev1Method | ( | FloatType | frequency,
|  | double | sampleRate,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | passbandAmplitudedB,
|  | FloatType | stopbandAmplitudedB
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the stop band only.

The algorithms are based on "Lecture Notes on Elliptic Filter Design" by Sophocles J. Orfanidis.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  passbandAmplitudedB | the highest amplitude in dB expected in the pass band (must be negative)
  stopbandAmplitudedB | the lowest amplitude in dB expected in the stop band (must be negative)

## designIIRLowpassHighOrderChebyshev2Method()

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRLowpassHighOrderChebyshev2Method | ( | FloatType | frequency,
|  | double | sampleRate,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | passbandAmplitudedB,
|  | FloatType | stopbandAmplitudedB
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIRFilters, providing a minimum phase low-pass filter without any ripple in the pass band only.

The algorithms are based on "Lecture Notes on Elliptic Filter Design" by Sophocles J. Orfanidis.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  passbandAmplitudedB | the highest amplitude in dB expected in the pass band (must be negative)
  stopbandAmplitudedB | the lowest amplitude in dB expected in the stop band (must be negative)

## designIIRLowpassHighOrderEllipticMethod()

template<typename FloatType >

static ReferenceCountedArray<IIRCoefficients> dsp::FilterDesign< FloatType >::designIIRLowpassHighOrderEllipticMethod | ( | FloatType | frequency,
|  | double | sampleRate,
|  | FloatType | normalisedTransitionWidth,
|  | FloatType | passbandAmplitudedB,
|  | FloatType | stopbandAmplitudedB
| ) |  |

static

This method returns an array of IIR::Coefficients, made to be used in cascaded IIR::Filters, providing a minimum phase low-pass filter with ripples in both the pass band and in the stop band.

The algorithms are based on "Lecture Notes on Elliptic Filter Design" by Sophocles J. Orfanidis.

Parameters

  frequency | the cutoff frequency of the low-pass filter
  sampleRate | the sample rate being used in the filter design
  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  passbandAmplitudedB | the highest amplitude in dB expected in the pass band (must be negative)
  stopbandAmplitudedB | the lowest amplitude in dB expected in the stop band (must be negative)

## designIIRLowpassHalfBandPolyphaseAllpassMethod()

template<typename FloatType >

static IIRPolyphaseAllpassStructure dsp::FilterDesign< FloatType >::designIIRLowpassHalfBandPolyphaseAllpassMethod | ( | FloatType | normalisedTransitionWidth,
|  | FloatType | stopbandAmplitudedB
| ) |  |

static

This method generates arrays of IIR::Coefficients for a low-pass filter, with a cutoff frequency at half band, using an algorithm described in the article "Digital Signal Processing Schemes for efficient interpolation and decimation" from Pavel Valenzuela and Constantinides.

The result is a IIRPolyphaseAllpassStructure object.

The two members of this structure directPath and delayedPath are arrays of IIR::Coefficients, made of polyphase second order allpass filters and an additional delay in the second array, that can be used in cascaded filters processed in two parallel paths, which must be summed at the end to get the high order efficient low-pass filtering.

The gain of the resulting pass-band is 6 dB, so don't forget to compensate it if you want to use that method for something else than two times oversampling.

Parameters

  normalisedTransitionWidth | the normalised size between 0 and 0.5 of the transition between the pass band and the stop band
  stopbandAmplitudedB | the maximum amplitude in dB expected in the stop band (must be negative)

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

- juce_FilterDesign.h