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Signal Modifiers: Specialized Filters

pareq


  ar      pareq      asig, kc, iv, iq, imode


Description

Implementation of Zoelzer's parametric equalizer filters, with some modifications by the author.

The formula for the low shelf filter is:


	omega = 2*pi*f/sr

	K     = tan(omega/2)

	

	b0    = 1 + sqrt(2*V)*K + V*K^2

	b1    = 2*(V*K^2 - 1)

	b2    = 1 - sqrt(2*V)*K + V*K^2

	

	a0    = 1 + K/Q + K^2

	a1    = 2*(K^2 - 1)

	a2    = 1 - K/Q + K^2

The formula for the high shelf filter is:


	omega = 2*pi*f/sr

	K     = tan((pi-omega)/2)

	

	b0    = 1 + sqrt(2*V)*K + V*K^2

	b1    = -2*(V*K^2 - 1)

	b1    = 1 - sqrt(2*V)*K + V*K^2

	

	a0    = 1 + K/Q + K^2

	a1    = -2*(K^2 - 1)

	a2    = 1 - K/Q + K^2

The formula for the peaking filter is:


	omega = 2*pi*f/sr

	K     = tan(omega/2)

	

	b0 =  1 + V*K/2 + K^2

	b1 =  2*(K^2 - 1)

	b2 =  1 - V*K/2 + K^2

	

	a0 =  1 + K/Q + K^2

	a1 =  2*(K^2 - 1)

	a2 =  1 - K/Q + K^2

Initialization

iv – amount of boost or cut. If iv > 1, gain of kc is increased. If iv <1, gain of kc is decreased. If iv = 1, there is no gain change at kc.

iq – Q of the filter (sqrt(.5) is no resonance)

imode – operating mode

Performance

kc - center frequency in peaking mode, corner frequency in shelving mode.

asig – the incoming signal

Example


instr 15

  ifc     =       p4                       ; Center / Shelf

  iq      =       p5                       ; Quality factor sqrt(.5) is no resonance

  iv      =       ampdb(p6)                ; Volume Boost/Cut

  imode   =       p7                       ; Mode 0=Peaking EQ, 1=Low Shelf, 2=High Shelf

  kfc     linseg  ifc*2, p3, ifc/2

  asig    rand    5000                     ; Random number source for testing

  aout    pareq   asig, kfc, iv, iq, imode ; Parmetric equalization

          outs    aout, aout               ; Output the results

endin



; SCORE:

  ;   Sta  Dur  Fcenter  Q        Boost/Cut(dB)  Mode

  i15 0    1    10000   .2          12             1

  i15 +    .    5000    .2          12             1

  i15 .    .    1000    .707       -12             2

  i15 .    .    5000    .1         -12             0

  e

Author

Hans Mikelson
December, 1998 (New in Csound version 3.50)


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Signal Modifiers: Specialized Filters