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# biquad

biquad -- A sweepable general purpose biquadratic digital filter.

## Description

A sweepable general purpose biquadratic digital filter.

## Syntax

ar biquad asig, kb0, kb1, kb2, ka0, ka1, ka2 [, iskip]

## Initialization

iskip (optional, default=0) -- if non-zero, intialization will be skipped. Default value 0. (New in Csound version 3.50)

## Performance

asig -- input signal

biquad is a general purpose biquadratic digital filter of the form:

a0*y(n) + a1*y[n-1] + a2*y[n-2] = b0*x[n] + b1*x[n-1] + b2*x[n-2]

This filter has the following frequency response:

B(Z) b0 + b1*Z-1 + b2*Z-2
H(Z) = ---- = ------------------
A(Z) a0 + a1*Z-1 + a2*Z-2

This type of filter is often encountered in digital signal processing literature. It allows six user-defined k-rate coefficients.

## Examples

Here is an example of the biquad opcode. It uses the files biquad.orc and biquad.sco.

Example 1. Example of the biquad opcode.

    /* biquad.orc */
    ; Initialize the global variables.
    sr = 44100
    kr = 4410
    ksmps = 10
    nchnls = 2

    ; Instrument #1.
    instr 1
      ; Get the values from the score.
      idur = p3
      iamp = p4
      icps = cpspch(p5)
      kfco = p6
      krez = p7

      ; Calculate the biquadratic filter's coefficients
      kfcon = 2*3.14159265*kfco/sr
      kalpha = 1-2*krez*cos(kfcon)*cos(kfcon)+krez*krez*cos(2*kfcon)
      kbeta = krez*krez*sin(2*kfcon)-2*krez*cos(kfcon)*sin(kfcon)
      kgama = 1+cos(kfcon)
      km1 = kalpha*kgama+kbeta*sin(kfcon)
      km2 = kalpha*kgama-kbeta*sin(kfcon)
      kden = sqrt(km1*km1+km2*km2)
      kb0 = 1.5*(kalpha*kalpha+kbeta*kbeta)/kden
      kb1 = kb0
      kb2 = 0
      ka0 = 1
      ka1 = -2*krez*cos(kfcon)
      ka2 = krez*krez

      ; Generate an input signal.
      axn vco 1, icps, 1

      ; Filter the input signal.
      ayn biquad axn, kb0, kb1, kb2, ka0, ka1, ka2
      outs ayn*iamp/2, ayn*iamp/2
    endin
    /* biquad.orc */

    /* biquad.sco */
    ; Table #1, a sine wave.
    f 1 0 16384 10 1

    ;    Sta  Dur  Amp    Pitch Fco   Rez
    i 1  0.0  1.0  20000  6.00  1000  .8
    i 1  1.0  1.0  20000  6.03  2000  .95
    e
    /* biquad.sco */

## See Also

biquada, moogvcf, rezzy

## Credits

Author: Hans Mikelson
October 1998

New in Csound version 3.49

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