First cleaning step in "dsp_files" directory.

[Faustine.git] / dsp_files / mrfaustlib / fft.lib

diff --git a/dsp_files/mrfaustlib/fft.lib b/dsp_files/mrfaustlib/fft.lib
new file mode 100644 (file)
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+++ b/dsp_files/mrfaustlib/fft.lib
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+/******************************************************************
+ *  FFT
+ *  Implementation contributed by Remy Muller
+ *****************************************************************/
+
+// bus(n) : n parallel cables
+bus(2) = _,_; // avoids a lot of "bus(1)" labels in block diagrams
+bus(n) = par(i, n, _);
+
+// twiddle_mult(n) : n parallel cables
+
+W(k, n) = 1, (0, ( k, ((2 * PI) / n) : *) : -) : polar_cplx;
+
+twiddle_mult(k, n) = _, W(k, n) : pcplx_mul;
+
+// selector(i,n) : select ith cable among n
+selector(i,n) = par(j, n, S(i, j))    with { S(i,i) = _; S(i,j) = !; };
+
+// interleave(m,n) : interleave m*n cables : x(0), x(m), x(2m), ..., x(1),x(1+m), x(1+2m)...
+//interleave(m,n) = bus(m*n) <: par(i, m, par(j, n, selector(i+j*m,m*n))); 
+
+// interleave(row,col) : interleave row*col cables from column order to row order.
+// input : x(0), x(1), x(2) ..., x(row*col-1)
+// output: x(0+0*row), x(0+1*row), x(0+2*row), ..., x(1+0*row), x(1+1*row), x(1+2*row), ...
+interleave(row,col) = bus(row*col) <: par(r, row, par(c, col, selector(r+c*row,row*col))); 
+
+// butterfly(n) : addition then substraction of interleaved signals : 
+xbutterfly(n) = (bus(n/2), par(k, n/2, twiddle_mult(k, n))) <: interleave(n/2,2), interleave(n/2,2) : par(i, n/2, pcplx_add), par(i, n/2, pcplx_sub);
+
+//btf_downside(n) = bus(n) : interleave(n/2,2);
+
+// fft(n) : fft matrix function of size n = 2^k
+//fft(2) = butterfly(2);
+//fft(n) = butterfly(n) : (fft(n/2) , fft(n/2));
+
+xbutterflies(2) = xbutterfly(2);
+xbutterflies(n) = (xbutterflies(n/2) , xbutterflies(n/2)) : xbutterfly(n);
+
+
+evens = case {
+       (2) => _ , ! ;
+       (n) => _ , ! , evens(n - 2);
+};
+odds = case {
+       (2) => ! , _ ;
+       (n) => ! , _ , odds(n - 2);
+};
+
+eo(n) = evens(n), odds(n);
+
+shuffling = case {
+       (2) => eo(2);
+       (n) => (evens(n) <: shuffling(n/2)), (odds(n) <: shuffling(n/2));
+};
+
+shuffle(n) = bus(n) <: shuffling(n);
+
+real2pcplx(n) = par(i, n, (sca2pcplx));
+
+//fft(n) =  shuffle(n) : xbutterflies(n);
+fft(n) = _ <: picks(n) : real2pcplx(n) : shuffle(n) : xbutterflies(n);
+fftc(n) = _ <: picks(n) : shuffle(n) : xbutterflies(n) : pcplx_moduls(n); // already complex input
+
+
+picks(n) = par(i, n, [i]);
+
+concats = case {
+       (1) => vectorize(1);
+       (n) => concats(n-1) # vectorize(1);
+};
+
+nconcat(n) = concats(n); //fake name for svg block encapsulation
+
+pack = case {
+       (1) => _;
+       (n) => pack(n-1), _ : #;
+};
+
+delays(m) = _ <: par(i, m, @(i)); 
+
+overlap(n,m) = vectorize(n/m) : delays(m) : pack(m);
+
+stops(n) = par(i, n, !);