biquad

biquad — A sweepable general purpose biquadratic digital filter.

Description

A sweepable general purpose biquadratic digital filter.

Syntax

ares 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 file biquad.csd.

Example 84. Example of the biquad opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

<CsoundSynthesizer>
<CsOptions>
; Select audio/midi flags here according to platform
; Audio out   Audio in    No messages
-odac           -iadc     -d     ;;;RT audio I/O
; For Non-realtime ouput leave only the line below:
; -o biquad.wav -W ;;; for file output any platform
</CsOptions>
<CsInstruments>

; 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


</CsInstruments>
<CsScore>

; 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


</CsScore>
</CsoundSynthesizer>


Here is another example of the biquad opcode used for modal synthesis. It uses the file biquad-2.csd. See the Modal Frequency Ratios appendix for other frequency ratios.

Example 85. Example of the biquad opcode for modal synthesis.

<CsoundSynthesizer>
<CsOptions>
; Select audio/midi flags here according to platform
; Audio out   Audio in
-odac           -iadc    ;;;RT audio I/O
; For Non-realtime ouput leave only the line below:
; -o biquad-2.wav -W ;;; for file output any platform
</CsOptions>
<CsInstruments>
sr = 44100
kr = 4410
ksmps = 10
nchnls = 2

/*  modal synthesis using biquad filters as oscillators
    Example by Scott Lindroth 2007 */


instr 1

    ipi = 3.1415926
    idenom = sr*0.5

    ipulseSpd = p4
    icps     = p5
    ipan = p6
    iamp    = p7
    iModes = p8

    apulse    mpulse iamp, 0

    icps    = cpspch( icps )

    ; filter gain

    iamp1 = 600
    iamp2 = 1000
    iamp3 = 1000
    iamp4 = 1000
    iamp5 = 1000
    iamp6 = 1000

    ; resonance

    irpole1 = 0.99999
    irpole2 = irpole1
    irpole3 = irpole1
    irpole4 = irpole1
    irpole5 = irpole1
    irpole6 = irpole1

    ; modal frequencies

    if (iModes == 1) goto modes1
    if (iModes == 2) goto modes2
    
    modes1:
    if1    = icps * 1            ;pot lid
    if2    = icps * 6.27
    if3    = icps * 3.2
    if4    = icps * 9.92
    if5    = icps * 14.15
    if6    = icps * 6.23
    goto nextPart

    modes2:
    if1     = icps * 1            ;uniform wood bar
    if2     = icps * 2.572
    if3     = icps * 4.644
    if4     = icps * 6.984
    if5     = icps * 9.723
    if6     = icps * 12.0
    goto nextPart

    nextPart:

    ; convert frequency to radian frequency

    itheta1 = (if1/idenom) * ipi
    itheta2 = (if2/idenom) * ipi
    itheta3 = (if3/idenom) * ipi
    itheta4 = (if4/idenom) * ipi
    itheta5 = (if5/idenom) * ipi
    itheta6 = (if6/idenom) * ipi

    ; calculate coefficients

    ib11 = -2 * irpole1 * cos(itheta1)
    ib21 = irpole1 * irpole1
    ib12 = -2 * irpole2 * cos(itheta2)
    ib22 = irpole2 * irpole2
    ib13 = -2 * irpole3 * cos(itheta3)
    ib23 = irpole3 * irpole3
    ib14 = -2 * irpole4 * cos(itheta4)
    ib24 = irpole4 * irpole4
    ib15 = -2 * irpole5 * cos(itheta5)
    ib25 = irpole5 * irpole5
    ib16 = -2 * irpole6 * cos(itheta6)
    ib26 = irpole6 * irpole6

    ;printk 1, ib 11
    ;printk 1, ib 21

    ;  also try setting the -1 coeff. to 0, but be sure to scale down the amplitude!

    asin1     biquad  apulse * iamp1, 1, 0, -1, 1, ib11, ib21
         asin2       biquad  apulse * iamp2, 1, 0, -1, 1, ib12, ib22
         asin3       biquad  apulse * iamp3, 1, 0, -1, 1, ib13, ib23
         asin4       biquad  apulse * iamp4, 1, 0, -1, 1, ib14, ib24
         asin5       biquad  apulse * iamp5, 1, 0, -1, 1, ib15, ib25
         asin6       biquad  apulse * iamp6, 1, 0, -1, 1, ib16, ib26


    afin    =    (asin1 + asin2 + asin3 + asin4 + asin5 + asin6)

    outs        afin * sqrt(p6), afin*sqrt(1-p6)

endin
</CsInstruments>
<CsScore>
;ins     st    dur  pulseSpd   pch    pan    amp     Modes
i1        0    12    0       7.089    0      0.7    2
i1        .    .    .        7.09     1      .      .
i1        .    .    .        7.091    0.5    .      .

i1        0    12    0       8.039    0      0.7    2
i1        0    12    0       8.04     1      0.7    2
i1        0    12    0       8.041    0.5    0.7    2

i1        9    .    .        7.089    0      .      2
i1        .    .    .        7.09     1      .      .
i1        .    .    .        7.091    0.5    .      .

i1        9    12    0       8.019    0      0.7    2
i1        9    12    0       8.02     1      0.7    2
i1        9    12    0       8.021    0.5    0.7    2
e
</CsScore>
</CsoundSynthesizer>


See Also

biquada, moogvcf, rezzy

Credits

Author: Hans Mikelson
October 1998

New in Csound version 3.49