Search: a280816 -id:a280816
|
| |
|
|
A282339
|
|
A pseudorandom binary sequence with minimum variance of the absolute values of its discrete Fourier transform.
|
|
+10
1
|
|
|
|
1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
a(1) = 1. Each subsequent term is chosen so as to minimize the variance of the absolute values of the discrete Fourier transform of the partial sequence. If the variance doesn't change with different choices for the next term, then the complement of the previous term is used. The algorithm works on a sequence of 1's and -1's then, as a last step, all -1's are replaced by 0's.
This sequence is similar to A282343 where the peak-to-peak distance is considered instead of the variance.
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
varfourier[x_]:=Variance[Abs[Fourier[x]]];
a={1}; (*First element*)
nmax=120; (*number of appended elements*)
Do[If[varfourier[Append[a, 1]]<varfourier[Append[a, -1]], AppendTo[a, 1], If[varfourier[Append[a, 1]]>varfourier[Append[a, -1]], AppendTo[a, -1], AppendTo[a, -a[[-1]]]]], {j, nmax}];
a=a/.{-1->0};
Print[a]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A282343
|
|
A pseudorandom binary sequence with minimum peak to peak distance of the absolute values of its discrete Fourier transform.
|
|
+10
1
|
|
|
|
1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
a(1) = 1. Each subsequent term is chosen so as to minimize the peak to peak distance of the absolute values of the discrete Fourier transform of the partial sequence. If the peak to peak distance doesn't change with different choices for the next term, then the complement of the previous term is used. The algorithm works on a sequence of 1's and -1's then, as a last step, all -1's are replaced by 0's.
This sequence is similar to A282339 where it is considered the variance instead of the peak to peak distance.
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
peaktopeakfourier[x_] := Max[Abs[Fourier[x]]] - Min[Abs[Fourier[x]]];
a = {1}; (*First element*)
nmax = 120; (*number of appended elements*)
Do[If[peaktopeakfourier[Append[a, 1]] <
peaktopeakfourier[Append[a, -1]], AppendTo[a, 1],
If[peaktopeakfourier[Append[a, 1]] >
peaktopeakfourier[Append[a, -1]], AppendTo[a, -1],
AppendTo[a, -a[[-1]]]]], {j, nmax}];
a = a /. {-1 -> 0};
print[a]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.009 seconds
|
