Useful Information: Mathematics
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TRIGONOMETRIC FORMULAE

sin(A)*sin(B) =  cos(A-B)/2 - cos(A+B)/2
cos(A)*cos(B) =  cos(A-B)/2 + cos(A+B)/2
sin(A)*cos(B) =  sin(A-B)/2 + sin(A+B)/2
cos(A)*sin(B) = -sin(A-B)/2 + sin(A+B)/2

sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)
sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B)
cos(A+B) = cos(A)*cos(B) - sin(A)*sin(B)
cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B)

sin(2*A) = 2*sin(A)*cos(A)
cos(2*A) = cos^2(A)-sin^2(A)
         = 1-2*sin^2(A)

sinc(x) = sin(PI*x)/(PI*x)


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NORMAL DISTRIBUTION

p(x) = 1/(SQR(2*PI)*sigma) * exp(-(x-u)^2/(2*sigma^2))

  where  sigma = standard deviation
         u     = mean


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RAYLEIGH DISTRIBUTION

p(x) = (x/sigma^2)*e^(-1/2*(v/sigma)^2)


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PROBABILITY

Probability of exactly n events in N tries (e.g. n errors in N bits)

prob = N!/(n!*(N-n)!)*(1-P)^(N-n)*P^n

  where P = probability of an event


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BARKER SEQUENCES

A sequence of values 1 or -1
aperiodic autocorrelation coefficients are <= 1 for lag other than 0
known sequences exist for length 2, 3, 4, 5, 7, 11, 13

length            sequence
2                 +-  (and ++)
3                 ++-
4                 ++-+  (and +++-)
5                 +++-+
7                 +++--+-
11                +++---+--+-
13                +++++--++-+-+


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RECTIFIED SINEWAVE

Average value = 2/PI * peak           approx.  0.637
                2*SQR(2)/PI * rms     approx.  0.900