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