Imagine you design a lowpass filter where the cutoff frequency is pi/4 radians/sample. That filter will pass [-pi/4 pi/4] radians/sample. Now what is that bandwidth in radians/second?
[-pi/4 pi/4] multiplied by the sampling frequency.
(radians/sample)(samples/second)
The larger the sampling frequency, the larger the bandwidth.
As a simple example, just take a 20-point (order 20) FIR moving average filter.
Assume a sampling rate of 1000 Hz.
b = 1/20*ones(20,1);
fvtool(b,1,'Fs',1000)
Now increase the sampling rate by a factor of 10 and you'll see the bandwidth increases by the same factor
fvtool(b,1,'Fs',1e4)
