The title is somewhat unclear because I do not know the words to describe this. Given $n \in \mathbb{N}^*$ , I want to find the real valued coefficients $(a_i, b_i), i \in [|1, n|]$ that minimize $max_{x_1, x_2 \in [0,1]} ||f(x_1) - f(x_2)||$ , where $f(x) = (sin(a_i x + b_i))_{i \in [|1, n |]}$ .
I really do not know where to start, could anyone point me towards a theory that solves this kind of problems ? For context, the point of this is to make values in a large interval with high resolution easier to process for a neural network. For instance, an input variable might take values in [0, 100], and the network must distinguish between 1.0 and 1.1, but also between 99.0 and 99.1.