Effective Noise Bandwidth

[twomilimeter]

Hi,

I am a little confuse here.
What is effective noise bandwidth? I saw some definitions stated that:
"Effective Noise Bandwidth of a filter is defined as the width of an ideal filter which, with an identical reference amplitude gain, would transmit the same power from a white noise source."

In most cases, the formula is given as

where G is the power Gain and Go is the peak amplitude.

If G is the power Gain in (Watt/Watt), how does the integral of G with respect to frequency with give the total power in Watt?

Kindly advise.

Regards,
Twomilimeter

 

[FvM]

how does the integral of G with respect to frequency with give the total power in Watt?

ENBW dimension is bandwidth, not power. G is a dimensionless factor, so everything is correct. What's the problem?