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// How to emulate Faust's seq, par, sum.
// x(k) is assumed to yield the kth signal.
xseq(1,x) = x(0);
xseq(n,x) = xseq(n-1,x) : x(n-1);
xpar(1,x) = x(0);
xpar(n,x) = xpar(n-1,x) , x(n-1);
xsum(1,x) = x(0);
xsum(n,x) = xsum(n-1,x) + x(n-1);
// These are all very similar. Abstracting
// on the binary "accumulator" function, we
// get the familiar fold(-left) function:
fold(1,f,x) = x(0);
fold(n,f,x) = f(fold(n-1,f,x),x(n-1));
// Now seq, par, sum can be defined as:
fseq(n) = fold(n,\(x,y).(x:y));
fpar(n) = fold(n,\(x,y).(x,y));
fsum(n) = fold(n,+);
fprod(n) = fold(n,*);
// Often it is more convenient to specify
// parameters as a Faust tuple. We can match
// against the (xs,x) pattern to decompose
// these.
vfold(f,(xs,x)) = f(vfold(f,xs),x);
vfold(f,x) = x;
// Tuple version of seq, par, sum:
vseq = vfold(\(x,y).(x:y));
vpar = vfold(\(x,y).(x,y));
vsum = vfold(+);
vprod = vfold(*);
// Examples:
import("music.lib");
f0 = 440;
a(0) = 1;
a(1) = 0.5;
a(2) = 0.3;
h(i) = a(i)*osc((i+1)*f0);
// sums
//process = xsum(3,h);
//process = fsum(3,h);
//process = vsum((h(0),h(1),h(2)));
reverse (x:y) = reverse(y):reverse(x);
reverse(x) = x;
// sequences from tuples (parallel -> serial)
process = reverse(vseq((sin,cos,tan)));
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