I'm taking a communication systems course and we use GNURadio in the lab. In an exam, we had a simple question where we were asked to demodulate a Dual Side Band (with carrier) AM signal in GNURadio. Carrier frequency was known to be precisely 500KHz and message was audio (known to be < 15KHz). The incoming signal has sampling rate of 1.92MHz.
EDIT: i.e incoming signal is given to be of the form $(1 + k_am(t))cos(2{\pi}{f_c}t)$ with $|k_am(t)| < 1$
To do that, I took the absolute value of the incoming signal, and used a Low pass Filter with cutoff frequency 17KHz and transition width 100Hz to obtain the audio clip. I was listening to the audio sampled at 48KHz (with proper decimation of 40 set in the Low Pass filter block). However the received audio clip was very jittery. I could listen and identify the song, but there were periodic higher frequency spiky noises.
The TA observed this, changed the transition width of the LPF from 100Hz to 1KHz and it was completely fine now - I could hear it neat and clear! I argued that I only tried to make the filter better by making it more ideal - brick-wall type, and also, this transition is happening where I don't have my message (transition occurs at 17KHz and my message < 15KHz). He replies that I pay a price when I make a filter transit faster, and added I would understand that when I do the digital communications course.
Could someone kindly explain to me, what price I pay (in digital domain) when I decrease the transition width of the Low Pass filter? Thanks in advance.