edit: to add to this, the capacity C ("throughput") of the communications channel is linear with bandwidth B (in Hertz) but only logarithmic (log_2) with noise power N. This was derived by Shannon (https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theore...) and in equation form:
C = B*log_2(1+S/N)
Example: signal to noise ratio is 1 (S/N = 1). Result:
C = B
Now we increase the bandwidth of our channel by a factor of 10, keeping the signal power equal. This will lead to a factor 10 more noise power (S/N = 1/10). Result:
C = 10*B*log_2(1 + 1/10) = 1.38*B
So we can improve the channel capacity by increasing the bandwidth even in a noisy channel.
edit: to add to this, the capacity C ("throughput") of the communications channel is linear with bandwidth B (in Hertz) but only logarithmic (log_2) with noise power N. This was derived by Shannon (https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theore...) and in equation form:
Example: signal to noise ratio is 1 (S/N = 1). Result: Now we increase the bandwidth of our channel by a factor of 10, keeping the signal power equal. This will lead to a factor 10 more noise power (S/N = 1/10). Result: So we can improve the channel capacity by increasing the bandwidth even in a noisy channel.