The noise bandwidth “BN” is defined as the bandwidth of an ideal (rectangular) filter which passes the same noise power as does the real filter.
Assume that a white noise is present at the input of a receiver (filter).
Let the filter have a transfer function H (f) as shown in fig.
This filter is being used to reduce the noise power actually passed on to the receiver.
Now consider the dotted plot (ideal filter)
The centre frequency of this ideal filter is f0
Let the bandwidth “BN” of the ideal filter be adjusted in such a way that the noise output power of the ideal filter is exactly equal to the noise output power of a real R-C filter. Then “BN” is called as the noise bandwidth of the real filter.