# Correct way to compute the power of a pulsed signal

I'm developing an application with my SDR Board and I've managed to produce a calibration table to verify the output power of the transmitter for every TX configuration of antenna gain and IQ digital word, for a given center frequency.

I.e., by setting the transmitter to that fixed center frequency, I've changed the TX gain and then transmitted a sinusoidal signal at different IQ amplitudes, using a spectrum analyzer to obtain the power of the transmitted signal.

So far so good, but I've now reached some problems and I can't seem to find a clear a solution for them online. I'm just an hobbyist, I have no previously experience with RF whatsoever.

The first problem is how should I properly use the RBW (resolution bandwidth) of the spectrum analyzer within my measurements.

For instance, if I measured an output power of 10dbm with a RBW of 100Hz, does that mean that within those 100Hz, there is a total of 10dbm power? Because if that is correct, then how can I correctly measured the power at the frequency of interest (which is inside that bin)? Surely those 10dbm will also account with the power from the frequencies close to the frequency of interest and inside my bin. What is the formula that I can use to correctly measure the output power at the given frequency with some error associated?

The second problem is related to what happens to the power when I change the window applied to the signal. In particular, I have my measurements performed for a CW setup, but I intend to transmit pulses and, at every time, I must know an estimative of the power at the carrier frequency, as well as some estimative of the total power of the signal.

These pulses are just simple amplitude modulation pulses, e.g: gaussian pulses, sinc pulses, hermite pulses, hard pulses, etc...

The way I thought about this problem is that it is just the application of another window to the already rectangular window that I use when I'm obtaining the initial power results. So, my idea was that since I know the shape of the pulses that I'm transmitting, i.e., I know the windowing functions, I should somehow be able to convert the measured power into the new power that is actually sent with the pulse transmitted.

However I can't find any formulas or any theory that would enlight me and I've been stuck in this problem for a few days now. I could just perform the power calibration for different pulse shapes but that would take me ages.

Can someone enlight me with some papers/theory? Is my approach incorrect? What should be my approach then?