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

- 0 = Peaking
- 1 = Low Shelving
- 2 = High Shelving

### 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)

Signal Modifiers: Specialized Filters