BiquadraticFilterModel

BiquadraticFilterModel[{ω,q}]

creates a lowpass biquadratic filter using the characteristic frequency ω and the quality factor q.

BiquadraticFilterModel[{"type",spec}]

creates a filter of a given {"type",spec}.

BiquadraticFilterModel[{"type",spec},var]

expresses the model in terms of the variable var.

Details

  • BiquadraticFilterModel returns the filter as a TransferFunctionModel.
  • Biquadratic filters are second-order filters defined by a ratio of two quadratic polynomials. They are among the most commonly used circuits in analog and digital signal processing.
  • Filter specifications {"type",spec} can be any of the following:
  • {"Lowpass",{{ω,q}}}uses cutoff frequency ω and quality factor q
    {"Highpass",{{ω,q}}}uses cutoff frequency ω and quality factor q
    {"Allpass",{{ω,q}}}uses frequency ω and quality factor q
    {"Bandpass",{ω1,ω2}}uses corner frequencies ω1 and ω2
    {"Bandpass",{{ω,q}}}uses center frequency ω and quality factor q
    {"Bandstop",{ω1,ω2}}uses corner frequencies ω1 and ω2
    {"Bandstop",{{ω,q}}}uses center frequency ω and quality factor q
  • The following filter specifications can be given to create equalizers:
  • {"Peaking",{{ω,q}},g}peaking equalizer using gain value g
    {"LowShelf",{{ω,q}},g}lowpass shelving equalizer using gain value g
    {"HighShelf",{{ω,q}},g}highpass shelving equalizer using gain value g
  • Given the gain value , the attenuation is .

Examples

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Basic Examples  (3)

A lowpass biquadratic filter:

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Bode plot of the filter:

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A bandpass filter using the full specification:

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Bode plot of the filter:

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Create a lowpass filter and apply it to a dual-tone signal:

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Scope  (8)

Generalizations & Extensions  (1)

Applications  (1)

Properties & Relations  (7)

See Also

ButterworthFilterModel  EllipticFilterModel  Chebyshev1FilterModel  Chebyshev2FilterModel  TransferFunctionModel  TransferFunctionTransform

Introduced in 2016
(10.4)