Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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The Faust programming language for signal processing [455,453] includes support for Lagrange fractional-delay filtering, up to order five, in the library file filter.lib. For example, the fourth-order case is listed below:
// fourth-order (quartic) case, delay d in [1.5,2.5]
fdelay4(n,d,x) = delay(n,id,x) * fdm1*fdm2*fdm3*fdm4/24
+ delay(n,id+1,x) * (0-fd*fdm2*fdm3*fdm4)/6
+ delay(n,id+2,x) * fd*fdm1*fdm3*fdm4/4
+ delay(n,id+3,x) * (0-fd*fdm1*fdm2*fdm4)/6
+ delay(n,id+4,x) * fd*fdm1*fdm2*fdm3/24
with {
o = 1.49999;
dmo = d - o; // assumed nonnegative
id = int(dmo);
fd = o + frac(dmo);
fdm1 = fd-1;
fdm2 = fd-2;
fdm3 = fd-3;
fdm4 = fd-4;
};
An example calling program is shown in Fig.4.12.
// tlagrange.dsp - test Lagrange interpolation in Faust import("filter.lib"); N = 16; % Allocated delay-line length % Compare various orders: D = 5.4; process = 1-1' <: fdelay1(N,D), fdelay2(N,D), fdelay3(N,D), fdelay4(N,D), fdelay5(N,D); // To see results: // [in a shell]: // faust2octave tlagrange.dsp // [at the Octave command prompt]: // plot(db(fft(faustout,1024)(1:512,:))); // Alternate example for testing a range of 4th-order cases // (change name to "process" and rename "process" above): process2 = 1-1' <: fdelay4(N, 1.5), fdelay4(N, 1.6), fdelay4(N, 1.7), fdelay4(N, 1.8), fdelay4(N, 1.9), fdelay4(N, 2.0), fdelay4(N, 2.1), fdelay4(N, 2.2), fdelay4(N, 2.3), fdelay4(N, 2.4), fdelay4(N, 2.499), fdelay4(N, 2.5); |