I am solving a question, where a signal g(t) is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0.
I understand that since for this filter the bandwidth, $ \Delta f \to 0$ , the transfer function is practically an impulse. I also understand that the width of the impulse should be $ 2 * 2 \pi \Delta f = 4 \pi \Delta f $. But I don't understand why the transfer function is expressed as $ 4 \pi \Delta f \delta(f) $, that is, why is it expressed as an impulse function of area $4 \pi \Delta f $
Here is the question and the official solution to the question: