TV output on low-cost portable computers

[Dave Long]

> The minimal LFSR also has period 1, so it's always within half-a-bit
> of synchronized, so it's not a counterexample :)

OK, here's a better counterexample:

max [15 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 15]
sub [15 -1 -1 -1 -5 -1 -1  7  7 -1 -1 -5 -1 -1 -1 15]

It's fixed point; divide by 15 to get the -1..1 range we've been 
discussing.

Note the application of MXOR to form a shift register with taps.

-Dave

:: :: ::

from Numeric import *

iota = arange
rho  = reshape
def l(*es): return array(es)

maximal = rho(l(0,0,0,1,
                 1,0,0,1,
                 0,1,0,0,
                 0,0,1,0), (4,4))

submax =  rho(l(0,0,0,1,
                 1,0,0,1,
                 0,1,0,1,
                 0,0,1,0), (4,4))

def cycle(m):
         def mxor(m,v):  return matrixmultiply(m,v) % 2
         n  = m.shape[0]
         v  = zeros(n) + 1
         rs = []
         for i in iota(2**n-1):
                 rs.append(v[0])
                 v = mxor(m,v)
         return rs

def autocorr(seq):
         def phi(v,n):   return concatenate((v[n:],v[:n]))
         def corr(a,b):  return sum((a==b)-(a!=b))
         return array([corr(seq,phi(seq,i))
                          for i in iota(len(seq)+1)])

print "max", autocorr(cycle(maximal))
print "sub", autocorr(cycle(submax))