# Wolfram Mathematica

## Equalization Using Biquadratic Filters

Filter an audio object using an analog transfer function.

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`a = AudioNormalize[Import["ExampleData/rule30.wav"]]`
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`filterModel = BiquadraticFilterModel[{\[Omega], q}]`
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```RecurrenceFilter[ ToDiscreteTimeModel[filterModel, 1/44100, z] /. {\[Omega] -> 1000 2 Pi, q -> 10}, a]```
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Build an equalizer using analog transfer functions.

show complete Wolfram Language input
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```eq[g1_, g2_, g3_] := SystemsModelSeriesConnect[ SystemsModelSeriesConnect[ ToDiscreteTimeModel[ BiquadraticFilterModel[{"LowShelf", {{Quantity[5000, "Hz"], 2}}, Quantity[g1, "decibel"]}], 1/44100, z, Method -> {"BilinearTransform", "CriticalFrequency" -> 5000 2 Pi}], ToDiscreteTimeModel[ BiquadraticFilterModel[{"Peaking", {{Quantity[10000, "Hz"], 2}}, Quantity[g2, "decibel"]}], 1/44100, z, Method -> {"BilinearTransform", "CriticalFrequency" -> 10000 2 Pi}]], ToDiscreteTimeModel[ BiquadraticFilterModel[{"HighShelf", {{Quantity[15000, "Hz"], 2}}, Quantity[g3, "decibel"]}], 1/44100, z, Method -> {"BilinearTransform", "CriticalFrequency" -> 15000 2 Pi}]]; white = RandomReal[{-1, 1}, 44100]; Manipulate[ Periodogram[ RecurrenceFilter[eq[gainLow, gainPeak, gainHigh], Audio@white], 4000, PlotRange -> {-35, 20}, ImageSize -> 300], {{gainLow, 0}, -20, 20}, {{gainPeak, 0}, -20, 20}, {{gainHigh, 0}, -20, 20}, SaveDefinitions -> True]```
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