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From: Ondrej Hlinka on 5 Mar 2007 17:24
Hi there,

I'm facing one interesting problem that I couldn't so far solve. I don't even know if there are any known methods available that could be used to solve it.

The problem is finding the global maximum value of the following function:

f(a_0,a_1,a_2,...,a_(N-1),t) = | a_0 * exp(j*2pi*0*t) + a_1 * exp(j*2pi*1*t) + a_2 * exp(j*2pi*2*t) + ... + a_(N-1) * exp(j*2pi*(N-1)*t) |

where:

|.| -> denotes absolute value of a complex number
j -> is imaginary unit
t -> is a variable taking values from set {0; 1/N; 2/N; 3/N; ... ; (N-1)/N} where N = 2^k (k is integer > 0)
a_0 ... a_(N-1) -> are variables taking values from set {-1; +1}

there however exist certain relationships between a_n values:

a_0 = -a_1*a_N/2*a_(N/2+1)
a_2 = -a_3*a_(N/2+2)*a_(N/2+3)
...
...
a_(N/2-2) = -a_(N/2-1)*a_(N/2+N/2-2)*a_(N/2+N/2-1)

the are no constraints regarding the remaining a_n values (they can obtain either +1 or -1 value)


Any ideas would be very helpful and appreciated. Thanks in advance.

Ondrej
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