Turns out, adding in the frequency domain looks like multiplication in the time domain, so we actually want to multiply the two signals together. In general, a good math model for a sine wave is: ...

I remember coming to the understanding that a square wave, which is a collection of fundamental and (odd) harmonics frequencies, could then be used to give an indication of frequency response.

However, onset TRANSIENTs being APERIODIC are difficult to reproduce accurately. The more general form of transferring the frequency domain to the time domain is termed the inverse Fourier transform.

According to the FOURIER THEOREM, periodic sound may be shown to consist of SINE WAVEs in the HARMONIC SERIES ... A more general form of analysis for transferring a time-domain signal to the frequency ...