Capacity of AWGN channel with infinite bandwidth

Question

I am supposed to find the capacity of an AWGN communication channel with infinite bandwidth $B$, signal power $S$ and spectral density of noise $n/2$.

Now, I know that the formula for calculating capacity is

$C = B * log2(1 + S/N)$,

where

$N = n/2 * 2B $,

but the infinite bandwidth is confusing me.

Answer 1

The capacity of a continuous-time AWGN channel with bandwith $B$ is (ref),

$$ C=B \log\left(1+\frac{S}{N_0 B}\right)$$

You just need to let $B\to \infty$ and compute the limit (note that there is an indeterminancy here to resolve, as the first factor tends to $\infty$ and the second to $0$).