langs a-z
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Ingy döt Net
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11389 changed files with 98361 additions and 1020 deletions
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open Complex
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let fac k n =
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let m2pi = -4.0 *. acos 0.0 in
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polar 1.0 (m2pi*.(float k)/.(float n))
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let merge l r n =
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let f (k,t) x = (succ k, (mul (fac k n) x) :: t) in
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let z = List.rev (snd (List.fold_left f (0,[]) r)) in
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(List.map2 add l z) @ (List.map2 sub l z)
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let fft lst =
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let rec ditfft2 a n s =
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if n = 1 then [List.nth lst a] else
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let odd = ditfft2 a (n/2) (2*s) in
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let even = ditfft2 (a+s) (n/2) (2*s) in
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merge odd even n in
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ditfft2 0 (List.length lst) 1;;
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let show l =
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let pr x = Printf.printf "(%f %f) " x.re x.im in
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(List.iter pr l; print_newline ()) in
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let indata = [one;one;one;one;zero;zero;zero;zero] in
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show indata;
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show (fft indata)
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@ -0,0 +1,2 @@
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FFT(v)=my(t=-2*Pi*I/#v,tt);vector(#v,k,tt=t*(k-1);sum(n=0,#v-1,v[n+1]*exp(tt*n)));
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FFT([1,1,1,1,0,0,0,0])
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49
Task/Fast-Fourier-transform/PL-I/fast-fourier-transform.pli
Normal file
49
Task/Fast-Fourier-transform/PL-I/fast-fourier-transform.pli
Normal file
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test: PROCEDURE OPTIONS (MAIN, REORDER); /* Derived from Fortran Rosetta Code */
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/* In-place Cooley-Tukey FFT */
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FFT: PROCEDURE (x) RECURSIVE;
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DECLARE x(*) COMPLEX FLOAT (18);
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DECLARE t COMPLEX FLOAT (18);
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DECLARE ( N, Half_N ) FIXED BINARY (31);
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DECLARE ( i, j ) FIXED BINARY (31);
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DECLARE (even(*), odd(*)) CONTROLLED COMPLEX FLOAT (18);
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DECLARE pi FLOAT (18) STATIC INITIAL ( 3.14159265358979323E0);
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N = HBOUND(x);
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if N <= 1 THEN return;
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allocate odd((N+1)/2), even(N/2);
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/* divide */
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do j = 1 to N by 2; odd((j+1)/2) = x(j); end;
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do j = 2 to N by 2; even(j/2) = x(j); end;
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/* conquer */
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call fft(odd);
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call fft(even);
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/* combine */
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half_N = N/2;
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do i=1 TO half_N;
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t = exp(COMPLEX(0, -2*pi*(i-1)/N))*even(i);
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x(i) = odd(i) + t;
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x(i+half_N) = odd(i) - t;
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end;
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FREE odd, even;
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END fft;
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DECLARE data(8) COMPLEX FLOAT (18) STATIC INITIAL (
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1, 1, 1, 1, 0, 0, 0, 0);
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DECLARE ( i ) FIXED BINARY (31);
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call fft(data);
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do i=1 TO 8;
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PUT SKIP LIST ( fixed(data(i), 25, 12) );
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end;
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END test;
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sub fft {
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return @_ if @_ == 1;
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my @evn = fft( @_[0,2...^* >= @_] );
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my @odd = fft( @_[1,3...^* >= @_] );
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my $twd = 2i * pi / @_; # twiddle factor
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@odd »*=« (^@odd).map(* * $twd)».exp;
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return @evn »+« @odd, @evn »-« @odd;
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}
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my @seq = ^16;
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my $cycles = 3;
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my @wave = (@seq »*» (2*pi / @seq * $cycles))».sin;
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say "wave: ", @wave.fmt("%7.3f");
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say "fft: ", fft(@wave)».abs.fmt("%7.3f");
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100
Task/Fast-Fourier-transform/Run-BASIC/fast-fourier-transform.run
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100
Task/Fast-Fourier-transform/Run-BASIC/fast-fourier-transform.run
Normal file
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@ -0,0 +1,100 @@
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cnt = 8
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sig = int(log(cnt) /log(2) +0.9999)
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pi = 3.14159265
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real1 = 2^sig
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real = real1 -1
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real2 = int(real1 / 2)
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real4 = int(real1 / 4)
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real3 = real4 +real2
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dim rel(real1)
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dim img(real1)
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dim cmp(real3)
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for i = 0 to cnt -1
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read rel(i)
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read img(i)
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next i
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data 1,0, 1,0, 1,0, 1,0, 0,0, 0,0, 0,0, 0,0
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sig2 = int(sig / 2)
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sig1 = sig -sig2
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cnt1 = 2^sig1
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cnt2 = 2^sig2
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dim v(cnt1 -1)
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v(0) = 0
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dv = 1
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ptr = cnt1
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for j = 1 to sig1
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hlfPtr = int(ptr / 2)
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pt = cnt1 - hlfPtr
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for i = hlfPtr to pt step ptr
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v(i) = v(i -hlfPtr) + dv
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next i
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dv = dv + dv
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ptr = hlfPtr
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next j
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k = 2 *pi /real1
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for x = 0 to real4
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cmp(x) = cos(k *x)
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cmp(real2 - x) = 0 - cmp(x)
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cmp(real2 + x) = 0 - cmp(x)
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next x
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print "fft: bit reversal"
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for i = 0 to cnt1 -1
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ip = i *cnt2
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for j = 0 to cnt2 -1
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h = ip +j
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g = v(j) *cnt2 +v(i)
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if g >h then
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temp = rel(g)
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rel(g) = rel(h)
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rel(h) = temp
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temp = img(g)
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img(g) = img(h)
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img(h) = temp
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end if
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next j
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next i
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t = 1
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for stage = 1 to sig
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print " stage:- "; stage
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d = int(real2 / t)
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for ii = 0 to t -1
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l = d *ii
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ls = l +real4
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for i = 0 to d -1
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a = 2 *i *t +ii
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b = a +t
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f1 = rel(a)
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f2 = img(a)
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cnt1 = cmp(l) *rel(b)
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cnt2 = cmp(ls) *img(b)
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cnt3 = cmp(ls) *rel(b)
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cnt4 = cmp(l) *img(b)
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rel(a) = f1 + cnt1 - cnt2
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img(a) = f2 + cnt3 + cnt4
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rel(b) = f1 - cnt1 + cnt2
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img(b) = f2 - cnt3 - cnt4
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next i
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next ii
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t = t +t
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next stage
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print " Num real imag"
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for i = 0 to real
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if abs(rel(i)) <10^-5 then rel(i) = 0
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if abs(img(i)) <10^-5 then img(i) = 0
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print " "; i;" ";using("##.#",rel(i));" ";img(i)
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next i
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end
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@ -0,0 +1,10 @@
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#import nat
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#import flo
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f = <1+0j,1+0j,1+0j,1+0j,0+0j,0+0j,0+0j,0+0j> # complex sequence of 4 1's and 4 0's
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g = c..mul^*D(sqrt+ float+ length,..u_fw_dft) f # its fft
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#cast %jLW
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t = (f,g)
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