You can demonstrate the exact effect you have been suffering to any
official who comes to visit you, but a meter reading in dBC, coupled
with a log of the times it occurs, is often sufficient to convince them.
You wouldn't normally be expected to demonstrate it in a court.

Unless the noise is of some particularly irritating character or
requires specialist identification, you may not need to record it at
all. The action you take will depend on three properties of the noise:

1) Its loudness
2) What time of day or night it occurs - and for how long
3) Its annoyance factor (is it a hum, intermittent banging noises,
thudding bass, sounds of a murder, bagpipe practice?)

...only the third property might need a recording to demonstrate the
point you want to make.

Excellent advice. Listen to the man...