Mathematica Error with Finding Maximum in Mathematica

[madness]

I want to find the maximum of the total of a list of numbers, of which each depends on some variable x. I'm taking the discrete Fourier transform of a set of points of a function, and trying to maximise the sum of the resulting list. Although I can plot the sum of the list as a function of x, when I try to maximise it Mathematica tells me Fourier::fftl:Argument{my list} is not a non-empty list or rectangular array of numeric quantities. The error seems to be associated with taking the discrete Fourier transform of a non-numerical quantity. It should be taking this Fourier transform with a range of possible numbers and finding the maximum, but seems to be getting it wrong. Can anyone help?

 

[FunkyDwarf]

I'm not sure i understand the problem but you can perhaps convert the set to an interpolating funciton which is essentially a list of numbers to MM.

 

[madness]

That's not quite it. I have a list L={a(x), b(x),...,n(x)}, the discrete Fourier transform gives Fourier[L]={A(x), B(x),..., N(x)} and my function is f(x)=A(x)+B(x)+...+N(x). This function plots perfectly and I can clearly see the maximum, but I want Mathematica to find it for me. So I say FindMaximum[F[x],{x,0}] and get the error mentioned above. It can't evaluate Fourier of x, when x isn't a number.