The above mentioned inverse proportionality between pulse width and its spectrum width (also called bandwidth) is fundamental indeed. It can be proved (with a little college-grade mathematics) that for any function, width of the pulse multiplied by the width of the spectrum is bounded below by a constant (detail depending on the way we define "width"). Therefore, whatever is the way we transform (we say modulate) the transmitted signal, the range resolution attainable is inversely proportional to the radar bandwidth (this also means that an high resolution radar requires a large stretch in the radio-wave frequency spectrum, which may pose problem with other user of radio-wave such as broadcast, telecommunications or radio-astronomy). For the little story it is even more fundamental than that ! Our very existence is due to the fact that electrons of our atoms do not collapse on the atom kernels (hence can play subtle interactions with electrons of neighbouring atoms called chemistry), and this fact is a direct consequence of this fact! Indeed, electron is a wave, the kinetic energy of which is proportional to the frequency, would it collapse to the kernel (this would minimise the potential energy because the electron is attracted by the electrical charge of the kernel) it position (pulse width) will be concentrated on a very small area, but then its spectrum would be very wide, hence its kinetic energy would be very high as its wave would contain high frequencies. In fact the so called fundamental (lowest energy) "orbit" of the electron is a trade off between potential (pulse width proportional) and kinetic (inverse proportional to pulse width) of the electronic wave. (It is one of the well know Heisenberg's inequalities)
In our application, if the radar bandwidth is B (that is the measured).... TO BE CONTNUED