prbs_a

Arguments

n

positive integer: length of the sequence.

nc

integer in [0, n-1]: number of commutations required.

positions

vector of integers in [0, n-1]: indices of required commutations in u.

u

Row vector of n values in {-1, 1}.

Description

prbs_a() will be useful to simulate the behavior of a 2-state random system.

u = prbs_a(n, nc) builds and returns a row vector u made of n values -1 or +1, in which nc commutations from -1 to 1 or from 1 to -1 occur at random positions in the vector.

The initial state u(1) has an equiprobable value -1 or +1.

The distribution of commutation positions along u is statistically uniform.

The positions of commutations can be retrieved with find(u(2:$) <> u(1:$-1)).

prbs_a(n,,positions) does the same, but sets commutations at the given positions, instead of at random ones. nc is then ignored. Setting a commutation at a position = i ensures that u(i+1) will be -u(i).

The initial state can be imposed with a trivial post-processing of the result. For instance, imposing u(1)=-1 will be done with if u(1)==1, u = -u; end.

Examples

clf
u = prbs_a(20, 7)
subplot(1,2,1)
plot2d2(1:20, u, rect=[0,-1.2,20,1.2]);
find(u(2:$) <> u(1:$-1))

u = prbs_a(100, 20);
subplot(1,2,2)
plot2d2(1:100, u, rect=[0,-1.2,100,1.2]);

--> u = prbs_a(20, 7)
 u  =
   1. -1. -1. -1. -1.  1. -1.  1.  1.  1. -1. -1. -1. -1.  1.  1.  1.  1. -1. -1.

--> find(u(2:$) <> u(1:$-1))
 ans  =
   1.   5.   6.   7.   10.   14.   18.

Example at given positions:

clf
u = prbs_a(100, , [13 20 25 40 65 67 80 90 91]);
plot2d2(1:100, u, rect=[0,-1.2,100,1.2]);
length(u)
find(u(2:$)<>u(1:$-1))

--> length(u)
 ans =
  100

--> find(u(2:$)<>u(1:$-1))
 ans  =
   13.   20.   25.   40.   65.   67.   80.   90.   91.

See Also

• grand — Generate random numbers
• grand — Generate random numbers
• sprand — sparse random matrix
• randpencil — random pencil

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