For more information including compatibility, examples and test cases, see https://github.com/petercrlane/r7rs-libs

Documentation: http://people.csail.mit.edu/jaffer/slib/Discrete-Fourier-Transform.html

There are three pairs of functions. The "-1" version is the inverse:

  • dft the general discrete fourier transform: operates on vectors/arrays of complex numbers

  • fft the fast fourier transform. Like dft but requires all dimensions to be powers of two.

  • sft works similarly to dft but with a different algorithm

Example:

sash[r7rs]> (dft #(1.0 2.0 1.0 -1.0 1.5))
#(4.5+0.0i 2.081559480312316-1.6510987627325229i
-1.8315594803123165+1.60822040644407i -1.8315594803123152-1.6082204064440717i
2.0815594803123165+1.6510987627325235i)

sash[r7rs]> (dft-1 (dft #(1.0 2.0 1.0 -1.0 1.5)))
#(1.0000000000000002-2.7755575615628914e-16i 2.0-5.551115123125783e-17i
1.0+0.0i -1.0000000000000004+2.463307335887066e-16i
1.5000000000000004+2.7755575615628914e-16i)

sash[r7rs]> (sft #(1.0 2.0 1.0 -1.0 1.5))
#(4.5+0.0i 2.081559480312316-1.6510987627325229i
-1.8315594803123165+1.60822040644407i -1.8315594803123152-1.6082204064440717i
2.0815594803123165+1.6510987627325235i)

sash[r7rs]> (sft-1 (sft #(1.0 2.0 1.0 -1.0 1.5)))
#(1.0000000000000002-2.7755575615628914e-16i 2.0-5.551115123125783e-17i
1.0+0.0i -1.0000000000000004+2.463307335887066e-16i
1.5000000000000004+2.7755575615628914e-16i)

sash[r7rs]> (fft '#(1 0+i -1 0-i 1 0+i -1 0-i))
#(0 0.0-0.0i 8.0+8.881784197001252e-16i 0.0+0.0i 0 0.0+0.0i
0.0-8.881784197001252e-16i -0.0+0.0i)

sash[r7rs]> (fft-1 '#(0 0 0 0 0 0 8 0))
#(1.0 -6.123233995736766e-17-1.0i -1.0+0.0i 6.123233995736766e-17+1.0i 1.0
-6.123233995736766e-17-1.0i -1.0-0.0i 6.123233995736766e-17+1.0i)

sash[r7rs]> (fft-1 (fft '#(1 0+i -1 0-i 1 0+i -1 0-i)))
#(1.0+0.0i -1.6081226496766364e-16+1.0i -1.0+0.0i 1.6081226496766364e-16-1.0i
1.0+0.0i -1.6081226496766364e-16+1.0i -1.0-0.0i 1.6081226496766364e-16-1.0i)