biquad — A sweepable general purpose biquadratic digital filter.
iskip (optional, default=0) -- if non-zero, intialization will be skipped. Default value 0. (New in Csound version 3.50)
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.
Here is an example of the biquad opcode. It uses the file biquad.csd.
Example 102. 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 103. 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>