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

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

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)

Bode plot of the filter:

A bandpass filter using the full specification:

Bode plot of the filter:

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

## Scope(8)

A symbolic lowpass filter with cutoff frequency ω and quality factor :

Use the full specification:

Specify cutoff frequency :

Bode plot of the filter:

A symbolic highpass filter with cutoff frequency and quality factor :

Use cutoff frequency :

A symbolic bandpass filter with center frequency and quality factor :

Use quality factor :

A symbolic bandstop filter with center frequency and quality factor :

Use quality factor :

A symbolic allpass filter with center frequency and quality factor :

Use quality :

A symbolic "Peaking" allpass filter with center frequency , quality factor , and gain value :

Use peak gain value of decibels:

A symbolic "LowShelf" filter with center frequency , quality factor , and gain value :

Use low-shelf gain value of decibels:

A symbolic "HighShelf" filter with center frequency , quality factor , and gain value :

Use low-shelf gain value of decibels:

## Generalizations & Extensions(1)

Improve stopband attenuation by connecting two or more filters in series:

## Applications(1)

Filter out the high-frequency tone in a pair of sinusoidal tones:

Create a higher-order filter by combining three filters to improve the filtering quality:

## Properties & Relations(7)

Phase responses of the four basic filter types:

Extract the order of a BiquadraticFilterModel:

Stopband attenuation increases by a factor of 40 decibels per decade:

Gain at cutoff frequency increases with increasing values of quality factor :

Width of bandpass filter decreases with increasing quality factor :

Gain values "boost" magnitude response of peaking equalizer:

Gain values "cut" magnitude response of peaking equalizer:

Gain values "boost" magnitude response of the low-shelf filter:

Gain values "cut" magnitude response of the low-shelf filter:

#### CMS

Wolfram Language. 2016. "BiquadraticFilterModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BiquadraticFilterModel.html.