Add 5 example Makefiles: primitives, dilation, erosion, open, close.
[Faustine.git] / architecture / fft.lib
1 /******************************************************************
2 * FFT
3 * Implementation contributed by Remy Muller
4 *****************************************************************/
5
6
7 // twiddle_mult(n) : n parallel cables
8
9 W(k, n) = 1, (0, ( k, ((2 * PI) / n) : *) : -) : polar_cplx;
10
11 twiddle_mult(k, n) = _, W(k, n) : pcplx_mul;
12
13 // butterfly(n) : addition then substraction of interleaved signals :
14 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);
15
16 //btf_downside(n) = bus(n) : interleave(n/2,2);
17
18 // fft(n) : fft matrix function of size n = 2^k
19 //fft(2) = butterfly(2);
20 //fft(n) = butterfly(n) : (fft(n/2) , fft(n/2));
21
22 xbutterflies(2) = xbutterfly(2);
23 xbutterflies(n) = (xbutterflies(n/2) , xbutterflies(n/2)) : xbutterfly(n);
24
25
26 evens = case {
27 (2) => _ , ! ;
28 (n) => _ , ! , evens(n - 2);
29 };
30 odds = case {
31 (2) => ! , _ ;
32 (n) => ! , _ , odds(n - 2);
33 };
34
35 eo(n) = evens(n), odds(n);
36
37 shuffling = case {
38 (2) => eo(2);
39 (n) => (evens(n) <: shuffling(n/2)), (odds(n) <: shuffling(n/2));
40 };
41
42 shuffle(n) = bus(n) <: shuffling(n);
43
44 real2pcplx(n) = par(i, n, (sca2pcplx));
45
46 //fft(n) = shuffle(n) : xbutterflies(n);
47 fft(n) = _ <: picks(n) : real2pcplx(n) : shuffle(n) : xbutterflies(n);
48 fftc(n) = _ <: picks(n) : shuffle(n) : xbutterflies(n) : pcplx_moduls(n); // already complex input
49
50
51 picks(n) = par(i, n, [i]);
52
53 concats = case {
54 (1) => vectorize(1);
55 (n) => concats(n-1) # vectorize(1);
56 };
57
58 nconcat(n) = concats(n); //fake name for svg block encapsulation
59
60 pack = case {
61 (1) => _;
62 (n) => pack(n-1), _ : #;
63 };
64
65 delays(m) = _ <: par(i, m, @(i));
66
67 overlap(n,m) = vectorize(n/m) : delays(m) : pack(m);
68
69 stops(n) = par(i, n, !);